In this NL cash game I made 3 straights in the first hour, and another straight for 4 straights within two hours. I swear this is true, on the second straight in the first 30 minutes I said to myself "I'm gonna get stomped by someone else who makes a straight against me when I also have a big hand later tonight." Here's my sad story and how I should have played differently.
I get to limp in the SB with 6-8 off with four players to the flop. Flop is 5-6-8 off and I come out betting. I get min raised by the BB, all others fold back to me and I call. An ace on the turn, board has four suits. I know the player in the BB pretty well, so I check, he bets the pot, and I think for 5 minutes. I go all-in (there is $120 in the pot, I have $180 behind and BB has another $61). He shows 4-7 for a flopped straight and the river doesn't get me a boat.
On the turn, I eliminate the nuts (7-9) and any over pairs, as I didn't think the BB would bet the nuts on this turn so aggressively, and would have raised any significant over-pairs pre-flop. BB could easily have just a 7, like A-7 (he has top pair on the turn with an open-ended) but I also eliminate that type of hand as I thought he would have bet something more like half to two-thirds of the pot. So I put him on the 4-7 or a 5-5 (for a set) - both hands which beat me - or something like a 5-7 (for a pair and an open-ender). I didn't eliminate the 5-5 completely, the betting pattern was certainly indicative of that type of hand as well, but the math says that the 4-7 is actually more likely (I think it's about 3x more likely to have the 4-7 than the 5-5, maybe 6.4% to 2.4%). But the thing is I also thought he could have been playing a smaller two-pair (like 5-6). I was a little stumped when the ace on the turn came out and he bet the pot ($60) - stumped in the sense that I didn't think that board would fear anything for someone with a 4-7 (the odds that I have a 7-9 for the nuts given that he knows he has the 4-7 is about 4.8%). Based on the pot size and his chip stack (lower than mine), I ignored my instincts about the 4-7 and went all-in. I thought it was a "fold or all-in" type of scenario and chose the latter sadly.
I hate when I don't follow my instincts and deductions (and the fact that I told myself I would lose a big pot in this exact way earlier in the night), but I think I could have played the hand differently (other than folding outright after the $60 bet on the turn). In one scenario, I could have re-raised my opponent's min-raise on the flop. One reason why I don't necessarily like that play is if I am re-raised, the same thinking applies - he could have a set or the 4-7 in that spot too, as easily as a lower two-pair or something like the 5-7. Instead, I like the play where on the turn, I come out betting. There was about $60 in the pot at that point, I could have bet anything, like maybe $25 or $30 to gauge where I am. At that point: a) My opponent raises me again, and he would likely raise to say $75 if he had the 4-7 or 5-5, or he may even go all-in at that point (since $75 would be more than half of his stack anyway). Then I have an easy fold. In this case I end up losing about $50. Or, b) He could simply smooth call, putting me on any other hand that is obviously weaker than his, hoping to get another bet out of me on the river assuming no scare cards (like the board pairing) come on the river. Let's say he smooth calls a $30 bet from me so now there is $120 in the pot (and I have $50 committed). On the river, my opponent has $91 left, so I could bet another $30 (I don't think checking is the right thing, even though you suspect you may be beat by a monster), and if he goes all-in, I have an easy fold. If he just calls (for some reason afraid that I have the stone cold nuts - a higher straight), I end up losing $80 total in this scenario - less than the $140 I really lost.
What do you think?
Showing posts with label Poker Theory / Scenarios. Show all posts
Showing posts with label Poker Theory / Scenarios. Show all posts
Wednesday, October 15, 2008
Tuesday, August 5, 2008
Geting It All-In
To me, this hand is not really very interesting, but I thought I would mention it for some food for thought.
1-3 NL cash game. Three players to the flop, I am in middle position with KJ off. Flop comes out J-10-4 with two clubs. Player1 bets, I call, Player3 raises big (all-in), Player1 thinks and calls, I fold. Player1 has KQ clubs and Player3 has AJ. Player1 ends up making the flush and wins.
There was a big debate about the odds in this hand. I would have thought (without knowing my cards) Player1 with his huge draw was a 21-out max potential (flush, open-ender, two over-cards), but from a tactical perspective, you can figure on the flush and the open-ender at least for say 15 outs, which in my head is roughly 55% to win with two cards to come. With 21 outs, I would have thought Player1 is a huge favorite for like 80% with two cards but as it turns out they are exactly 2/3 (67%). It's intriguing that this particular hand combination only gives Player1 67% rather than a much higher favorite. I'll leave it to the reader to think about that one on their own. You can use the poker odds calculator links at the bottom of the blog for some help.
I like Player1's play - with such a huge draw, you really are committed to seeing this through, especially when the re-raise all-in doesn't felt you. For Player3, with my call before him, and with so much potential action after him on this flop, I would have just called and taken a turn. If I have AJ, I am afraid of big draws and bigger hands on a flop with this texture.
1-3 NL cash game. Three players to the flop, I am in middle position with KJ off. Flop comes out J-10-4 with two clubs. Player1 bets, I call, Player3 raises big (all-in), Player1 thinks and calls, I fold. Player1 has KQ clubs and Player3 has AJ. Player1 ends up making the flush and wins.
There was a big debate about the odds in this hand. I would have thought (without knowing my cards) Player1 with his huge draw was a 21-out max potential (flush, open-ender, two over-cards), but from a tactical perspective, you can figure on the flush and the open-ender at least for say 15 outs, which in my head is roughly 55% to win with two cards to come. With 21 outs, I would have thought Player1 is a huge favorite for like 80% with two cards but as it turns out they are exactly 2/3 (67%). It's intriguing that this particular hand combination only gives Player1 67% rather than a much higher favorite. I'll leave it to the reader to think about that one on their own. You can use the poker odds calculator links at the bottom of the blog for some help.
I like Player1's play - with such a huge draw, you really are committed to seeing this through, especially when the re-raise all-in doesn't felt you. For Player3, with my call before him, and with so much potential action after him on this flop, I would have just called and taken a turn. If I have AJ, I am afraid of big draws and bigger hands on a flop with this texture.
Tuesday, June 3, 2008
Ivey v Cunningham
I watch poker hands play out on YouTube from time to time. This is one of the best hands I've seen. What I love about this is how both players play this hand on every street beginning with pre-flop action, and the ending is pure poker mastery - again, the way both players played it. Honorable mention goes to Matusow who also played his hand perfectly.
Ivey v Cunningham on YouTube
Ivey v Cunningham on YouTube
Sunday, May 25, 2008
Aggressive Playing Results in a Bust
I don't like to admit it, because quite frankly it doesn't happen often (hardly ever), but I think I was outplayed on this hand. The end result is that I was busted very early in a small buy-in tournament ($100). I went into this one thinking I was going for the gold and wanted to chip up early (blinds at 20 minutes); Well, that didn't work out as planned. Moral of the story: Always play great poker. Like I need to teach myself that lesson again (apparently I do). In this hand, I'm going to write it with you only knowing my cards, then I'll tell you the opponent's cards at the end.
The PLAY
Blinds at 50-100. Fold to me in middle position, I open raise with Q-9d for 300. Folds around to SB who thinks about it and calls, BB calls. 900 to flop. Flop is Q-x-x (rainbow), SB checks, BB bets 500, I raise to 1,500, SB folds, BB calls. 3,900 to turn. Turn is a K (still rainbow board, no straight draws). BB checks, I bet 2,100, BB thinks a bit and calls. 8,100 to river. River is a small blank, BB checks, I put the rest of it in (5,300), BB thinks a bit and calls. I'm out.
The ANALYSIS
When BB bets on the flop, he could be betting with anything there - you know the range of hands already: a medium pocket pair (he didn't re-raise pre-flop), a big ace (including A-K), maybe a queen (Q-J, Q-K, or perhaps A-Q). I raised to show continued strength and get some more information, as well as knock out SB just in case he was thinking about sticking around, so when BB calls I have a good chance I'm beat right there. I narrow the hands down to a bigger Q, and possibly a big pair like J-J just in case he doesn't believe me and is putting me on A-K. When the K comes on the turn and he check-calls my bet, it's pretty clear I am beat at that point - with a bigger Q or Q-K for top two (I eliminate A-K, K-K at this point, but it is also possible he has A-A). That would explain both actions so far from my opponent. When he checks on the river though, I'm pretty sure he doesn't have a monster (top two or even a set) so the only way I could win the hand is to go all-in and hope he only has a Q and will fold due to the K out there. Of course, I also thought he could be checking because I've been aggressive on every street - pre-flop, flop, and turn. I go all-in and he calls off the rest of his stack - very early in the tourney - with A-Q. What do you think of that call? Would you have made that call in that spot?
Alternate Play
The only other way I think I would have played this is simply to call the 500 on the flop and then check it down with the guy. Obviously that would have been the more conservative approach. With all my aggression on every street, I really felt like I needed to continue it to the river to take the large pot. With the pre-flop call and then bet on the flop, if my opponent is in fact playing a smaller pocket pair which is why he checks the turn and then the river, the most I would have won is the 1,900 (900 pre-flop + 1,000 on the flop with the 500 bet and my call theoretically), since he would have folded to any continued aggression with a smaller pocket pair. But I think as soon as I get caught in the aggression mode with the chips in the pot, I think I am committed to seeing it through.
Final Thoughts
The only thing I'm happy about in this hand is that I pretty much nailed his hand by the river on a bigger Q, so I was pretty sure he would fold to my all-in bet. Obviously he smelled a rat somehow and caught me. Whoever you are, kudos to you sir.
The PLAY
Blinds at 50-100. Fold to me in middle position, I open raise with Q-9d for 300. Folds around to SB who thinks about it and calls, BB calls. 900 to flop. Flop is Q-x-x (rainbow), SB checks, BB bets 500, I raise to 1,500, SB folds, BB calls. 3,900 to turn. Turn is a K (still rainbow board, no straight draws). BB checks, I bet 2,100, BB thinks a bit and calls. 8,100 to river. River is a small blank, BB checks, I put the rest of it in (5,300), BB thinks a bit and calls. I'm out.
The ANALYSIS
When BB bets on the flop, he could be betting with anything there - you know the range of hands already: a medium pocket pair (he didn't re-raise pre-flop), a big ace (including A-K), maybe a queen (Q-J, Q-K, or perhaps A-Q). I raised to show continued strength and get some more information, as well as knock out SB just in case he was thinking about sticking around, so when BB calls I have a good chance I'm beat right there. I narrow the hands down to a bigger Q, and possibly a big pair like J-J just in case he doesn't believe me and is putting me on A-K. When the K comes on the turn and he check-calls my bet, it's pretty clear I am beat at that point - with a bigger Q or Q-K for top two (I eliminate A-K, K-K at this point, but it is also possible he has A-A). That would explain both actions so far from my opponent. When he checks on the river though, I'm pretty sure he doesn't have a monster (top two or even a set) so the only way I could win the hand is to go all-in and hope he only has a Q and will fold due to the K out there. Of course, I also thought he could be checking because I've been aggressive on every street - pre-flop, flop, and turn. I go all-in and he calls off the rest of his stack - very early in the tourney - with A-Q. What do you think of that call? Would you have made that call in that spot?
Alternate Play
The only other way I think I would have played this is simply to call the 500 on the flop and then check it down with the guy. Obviously that would have been the more conservative approach. With all my aggression on every street, I really felt like I needed to continue it to the river to take the large pot. With the pre-flop call and then bet on the flop, if my opponent is in fact playing a smaller pocket pair which is why he checks the turn and then the river, the most I would have won is the 1,900 (900 pre-flop + 1,000 on the flop with the 500 bet and my call theoretically), since he would have folded to any continued aggression with a smaller pocket pair. But I think as soon as I get caught in the aggression mode with the chips in the pot, I think I am committed to seeing it through.
Final Thoughts
The only thing I'm happy about in this hand is that I pretty much nailed his hand by the river on a bigger Q, so I was pretty sure he would fold to my all-in bet. Obviously he smelled a rat somehow and caught me. Whoever you are, kudos to you sir.
Thursday, January 10, 2008
Pre-flop Action: Pot Odds Calls
When you have a mediocre hand but there are plenty of callers in front of you, most poker players end up calling too, setting the stage for late position players to call as well. In these situations, should you always call? Since that topic alone can be quite lengthy, let me just take one scenario.
Let's say you are in middle position with 7-8 suited and there are a bunch of limpers in front of you. Putting the possibility of a raise here aside, should you call? If there are already three callers, right there you are getting 3:1 on your money when you are likely only a 2:1 dog. So from a pot odds perspective you should call. And your implied odds are greater than that of course. Implied odds in this scenario means if you call, do you think other players will call as well? If another four players end up calling (for example, two other players and the blinds), now you're getting 7:1 on your money - pretty good pot odds! Poker players know this, and this is why limped pots can become an epidemic on some tables.
Are you really getting pot odds to call? First of all, what are the odds of getting a 7 or 8 high flop? We can re-phrase the question and ask, "What are the chances a card higher than an 8 will come out"? In my simple calculation, there are six types of cards higher than an 8, and three chances to hit one of those cards. That math works out to be (6 X 4)/49 + (6 X 4)/48 + (6 X 4)/47 or roughly 50%. And what are the odds of getting a flop with at best 8 high and no other higher cards? (7 X 4 - 2)/49 X 25/48 X 24/47 or roughly 14%, or 6:1. So you are in fact getting pot odds to call, you are 6:1 to get a favorable flop and you are getting 7:1 on your money.
Is hitting a 7 or 8 high flop good enough though? The implication in this question is if you may be up against a high pocket pair like 9-9 or 10-10 or perhaps even J-J (on a 7 or 8 high board). We assume that QQ or better would have raised pre-flop. The odds of getting one of those pocket pairs knowing your hole cards is 4/50 X 3/49 = 0.0049 or 0.49% or about 200:1. The chances your opponent has one of the three types of pocket pairs mentioned is 200:3 or 1.5%.
I hope the reader can use the information in this entry to make some better decisions on a limped pre-flop action.
Let's say you are in middle position with 7-8 suited and there are a bunch of limpers in front of you. Putting the possibility of a raise here aside, should you call? If there are already three callers, right there you are getting 3:1 on your money when you are likely only a 2:1 dog. So from a pot odds perspective you should call. And your implied odds are greater than that of course. Implied odds in this scenario means if you call, do you think other players will call as well? If another four players end up calling (for example, two other players and the blinds), now you're getting 7:1 on your money - pretty good pot odds! Poker players know this, and this is why limped pots can become an epidemic on some tables.
Are you really getting pot odds to call? First of all, what are the odds of getting a 7 or 8 high flop? We can re-phrase the question and ask, "What are the chances a card higher than an 8 will come out"? In my simple calculation, there are six types of cards higher than an 8, and three chances to hit one of those cards. That math works out to be (6 X 4)/49 + (6 X 4)/48 + (6 X 4)/47 or roughly 50%. And what are the odds of getting a flop with at best 8 high and no other higher cards? (7 X 4 - 2)/49 X 25/48 X 24/47 or roughly 14%, or 6:1. So you are in fact getting pot odds to call, you are 6:1 to get a favorable flop and you are getting 7:1 on your money.
Is hitting a 7 or 8 high flop good enough though? The implication in this question is if you may be up against a high pocket pair like 9-9 or 10-10 or perhaps even J-J (on a 7 or 8 high board). We assume that QQ or better would have raised pre-flop. The odds of getting one of those pocket pairs knowing your hole cards is 4/50 X 3/49 = 0.0049 or 0.49% or about 200:1. The chances your opponent has one of the three types of pocket pairs mentioned is 200:3 or 1.5%.
I hope the reader can use the information in this entry to make some better decisions on a limped pre-flop action.
Why I Just Called on the River
I was in a hand in a NL home cash game last night where one player chided me for not raising on the river.
The Hand
In early position I raise to $3 with 7-8, get re-raised to $8 and call along with one other player. Three players and $25 to the flop. Flop comes out Kd-Jc-7d. Check-check [me]-check. Turn is a 2c. Check-check [me]-check. River is a 7h. $25 bet from player in bb, I call, last player thinks and complains and calls too. My trip sevens are the best hand against the last player's J (bb was on a steal) and I take the $100 pot.
Why I Just Called
When the bb bets out on the river after two checks, I knew they were on a steal, so there was no point in raising them. I also know that the only way I'm getting re-raised (if I were to raise the $25 bet to $75 or so) is if the last player had some sort of monster like pocket J-J for a full house or something like that. It doesn't make sense in this scenario that the last player has any King or better hand based on two checks on an otherwise dangerous board. Since I can't get any more out of the bb, the only way I am getting anything out of the third opponent is to smooth call and hope they think I'm calling with Ace high or something (perhaps even two pair with a low pocket pair) and hope they do in fact have a Jack they think could be good, which is exactly what happened. If I raise, I am only getting re-raised by a better hand most likely (although it would be quite odd for a player to have slow played a set all the way to the river on this board, so I would have a decision to make there), and I also figured the $100 pot is enough for me getting lucky on the river.
The Hand
In early position I raise to $3 with 7-8, get re-raised to $8 and call along with one other player. Three players and $25 to the flop. Flop comes out Kd-Jc-7d. Check-check [me]-check. Turn is a 2c. Check-check [me]-check. River is a 7h. $25 bet from player in bb, I call, last player thinks and complains and calls too. My trip sevens are the best hand against the last player's J (bb was on a steal) and I take the $100 pot.
Why I Just Called
When the bb bets out on the river after two checks, I knew they were on a steal, so there was no point in raising them. I also know that the only way I'm getting re-raised (if I were to raise the $25 bet to $75 or so) is if the last player had some sort of monster like pocket J-J for a full house or something like that. It doesn't make sense in this scenario that the last player has any King or better hand based on two checks on an otherwise dangerous board. Since I can't get any more out of the bb, the only way I am getting anything out of the third opponent is to smooth call and hope they think I'm calling with Ace high or something (perhaps even two pair with a low pocket pair) and hope they do in fact have a Jack they think could be good, which is exactly what happened. If I raise, I am only getting re-raised by a better hand most likely (although it would be quite odd for a player to have slow played a set all the way to the river on this board, so I would have a decision to make there), and I also figured the $100 pot is enough for me getting lucky on the river.
Wednesday, December 19, 2007
Playing The Nuts and Ockham's Razor
You know I like to fantasize about poker hands. Actually, it helps me think about various situations that I have not specifically come across yet so when I do encounter them I can think lucidly about the situation when I am actually in it. In the following situation you are playing a $100-$200 NL cash game (I told you it was a fantasy). You can put yourself in the shoes of either player in this scenario and hopefully get something out of it.
You open raise from middle position to $700 after looking down at KK, folds around to bb who calls. $1,500 to the flop. Flop is AKK. Check-check to the turn, which brings a Q. Your opponent bets $1,000, you raise to $3,000, he calls. $7,500 to the river, which brings a blank, say a 5. Your opponent bets $8,000, you raise all-in (you have $16,300 total), your opponent calls. He flips over AA for AAAKK and of course you show the nuts and take the pot of $40,100.
Pre-flop action
Your opponent flat calls your raise with rockets. That works of course. He did this for a few reasons: i) He is disguising his hand, ii) He is already heads-up with you, so a re-raise here is not necessary, iii) A re-raise to say $2,500 and he risks you folding (sure, it's better to win a small pot than lose a big one of course) - he does not want you to fold, he wants to get maximum value out of his rockets, and iv) If he does raise to say $2,500, he "risks" you making a third raise, which at that point essentially commits his stack. Naturally he doesn't mind that at all, but seeing a flop allows him greater room to maneuver and may bring greater rewards than getting you off your hand pre-flop. If the small blind had called then it would make sense for the big blind to re-raise.
On the flop
It's difficult to argue against slow playing the stone cold nuts here. Certainly you're hoping for a juicy turn to stir your opponent to action.
On the turn
On the turn the board is now AKKQ. When your opponent comes out betting $1,000 into the $1,500 pot, he: i) Is trying to buy the pot right there [I would consider someone trying to buy the pot in this situation if they did not have at least an A or Q] since you checked behind him on the flop, ii) Has QQ, and would bet out since he wants to see if you have any of the hands that beat him such as KK, AA, AK or KQ, iii) Has a big ace, and thinks he could either win it there or may be in a chop situation [any two hands like AQ or worse (AJ, A-10, etc.) is a chop since the hand would be AAKKQ], or iv) Has AA. Why the bet then? Well, it's a value bet that may get your attention regardless of what you have. And if you do have a big hand, your opponent figures, like AK or QQ perhaps, then he may be able to induce a raise out of you figuring that he has disguised his hand pretty good up to this point. Also, if you don't at least call a bet on the turn with this board, your opponent thinks, then you may not call another bet on the river anyway.
So when you raise on the turn, your opponent ought to be putting you on AK, QQ or KK at that point. Why raise with the nuts when you know that only one card on the river is truly a scare card (the ace, which of course would be a sick quad over quad situation)? The same reason that your opponent bet out on the turn - you think to yourself if your opponent does have a big ace or AA then they would certainly at least call your raise, and if they didn't have much, they would fold and you wouldn't have got any more value out of them on the river anyway. From your opponent's perspective the chances you hold the following hands on the turn: a) AK -- (1/46 X 2/45) = 0.00097 or 0.097% or about 1 in 1,000; b) QQ -- (3/46 X 2/45) = 0.0029 or 0.29% or about 3 in 1,000; c) KK -- (2/46 X 1/45) = 0.00097 or about 1 in 1,000 [same as AK]. So it is three times more likely you have QQ than you do either AK or KK, and the only hand that your opponent cannot beat is KK.
As an aside, another option on the turn is to smooth call your opponent's bet. That would have made the pot $3,500 to the river. Say your opponent again bets out on the river to the tune of $4,000, you are raising big anyway. If you go all-in, at this point your opponent has some chance to get away from his aces full with $5,700 committed still sitting with $14,300 behind, "your money" left on the table (if your opponent is good enough to get away from aces full here). And if you raise to $12,000 for example, he can call and if he loses does have $6,300 left, which was again "your money" left on the table. Thus I believe the best thing to do on the turn is raise and you force an even bigger bet on the river which would commit your opponent, or you may induce a re-raise on the turn from your opponent right then and there.
On the river
Here is the thing about Ockham's razor, which paraphrased is generally accepted to translate to, "The simplest solution is the best, however implausible it may seem." On the river your opponent makes a slight overbet of the pot, perhaps trying to give the impression that he is buying the pot (assuming you don't have at least an ace), then you go all-in. At this level your opponent knows you don't have QQ (which would be afraid of KK, AA, AK or KQ), and thus you have either AK or KK. He is committed to calling another $8,300 (remember he has $12,000 in already) since he now is a 50% chance to win and as I demonstrated with the math, either hand is equally likely. Is that true? From the action and the math, either AK or KK are equally likely indeed. However, can the 14th century theorist help us out here? If you're your opponent, can you get away from AAAKK, knowing that the only hand that beats you is KKKK? It sure is possible if you think about it in this way: i) "The simplest solution is the best..." Would AK go all-in on the river knowing that AA beats them? (KK is not possible for your opponent to have if you do in fact have AK) Probably not in this spot. Would they (you) go all-in with AK for just a chop, if the opponent also has AK? Probably not. Thus they (you) must have KK. ii) "...however implausible it may seem." From a deduced math perspective (don't know the exact term, if there is one) the odds that you have either AK or KK are 1 in 1,000, your opponent thinks to himself, but the fact that you went over the top all-in on the river now makes that chance 100% (that you have either) and 0.5 not 0.001 for each hand - an increase of 500 times! It is 500 times more likely you do have KK now, consistent with point (i).
If you were your opponent, would you be able to fold AA in this spot?
This hand is an example of the nuts versus the second nuts. If you held KK would you play it this way for maximum value? If you held AA would you be able to get away from the hand on the river? If you were the player who held AA and you thought they were the nuts the whole time, should you have also checked on the turn? I hope this entry helps the reader to think about similar situations they may have been in and invite additional comments for this post.
You open raise from middle position to $700 after looking down at KK, folds around to bb who calls. $1,500 to the flop. Flop is AKK. Check-check to the turn, which brings a Q. Your opponent bets $1,000, you raise to $3,000, he calls. $7,500 to the river, which brings a blank, say a 5. Your opponent bets $8,000, you raise all-in (you have $16,300 total), your opponent calls. He flips over AA for AAAKK and of course you show the nuts and take the pot of $40,100.
Pre-flop action
Your opponent flat calls your raise with rockets. That works of course. He did this for a few reasons: i) He is disguising his hand, ii) He is already heads-up with you, so a re-raise here is not necessary, iii) A re-raise to say $2,500 and he risks you folding (sure, it's better to win a small pot than lose a big one of course) - he does not want you to fold, he wants to get maximum value out of his rockets, and iv) If he does raise to say $2,500, he "risks" you making a third raise, which at that point essentially commits his stack. Naturally he doesn't mind that at all, but seeing a flop allows him greater room to maneuver and may bring greater rewards than getting you off your hand pre-flop. If the small blind had called then it would make sense for the big blind to re-raise.
On the flop
It's difficult to argue against slow playing the stone cold nuts here. Certainly you're hoping for a juicy turn to stir your opponent to action.
On the turn
On the turn the board is now AKKQ. When your opponent comes out betting $1,000 into the $1,500 pot, he: i) Is trying to buy the pot right there [I would consider someone trying to buy the pot in this situation if they did not have at least an A or Q] since you checked behind him on the flop, ii) Has QQ, and would bet out since he wants to see if you have any of the hands that beat him such as KK, AA, AK or KQ, iii) Has a big ace, and thinks he could either win it there or may be in a chop situation [any two hands like AQ or worse (AJ, A-10, etc.) is a chop since the hand would be AAKKQ], or iv) Has AA. Why the bet then? Well, it's a value bet that may get your attention regardless of what you have. And if you do have a big hand, your opponent figures, like AK or QQ perhaps, then he may be able to induce a raise out of you figuring that he has disguised his hand pretty good up to this point. Also, if you don't at least call a bet on the turn with this board, your opponent thinks, then you may not call another bet on the river anyway.
So when you raise on the turn, your opponent ought to be putting you on AK, QQ or KK at that point. Why raise with the nuts when you know that only one card on the river is truly a scare card (the ace, which of course would be a sick quad over quad situation)? The same reason that your opponent bet out on the turn - you think to yourself if your opponent does have a big ace or AA then they would certainly at least call your raise, and if they didn't have much, they would fold and you wouldn't have got any more value out of them on the river anyway. From your opponent's perspective the chances you hold the following hands on the turn: a) AK -- (1/46 X 2/45) = 0.00097 or 0.097% or about 1 in 1,000; b) QQ -- (3/46 X 2/45) = 0.0029 or 0.29% or about 3 in 1,000; c) KK -- (2/46 X 1/45) = 0.00097 or about 1 in 1,000 [same as AK]. So it is three times more likely you have QQ than you do either AK or KK, and the only hand that your opponent cannot beat is KK.
As an aside, another option on the turn is to smooth call your opponent's bet. That would have made the pot $3,500 to the river. Say your opponent again bets out on the river to the tune of $4,000, you are raising big anyway. If you go all-in, at this point your opponent has some chance to get away from his aces full with $5,700 committed still sitting with $14,300 behind, "your money" left on the table (if your opponent is good enough to get away from aces full here). And if you raise to $12,000 for example, he can call and if he loses does have $6,300 left, which was again "your money" left on the table. Thus I believe the best thing to do on the turn is raise and you force an even bigger bet on the river which would commit your opponent, or you may induce a re-raise on the turn from your opponent right then and there.
On the river
Here is the thing about Ockham's razor, which paraphrased is generally accepted to translate to, "The simplest solution is the best, however implausible it may seem." On the river your opponent makes a slight overbet of the pot, perhaps trying to give the impression that he is buying the pot (assuming you don't have at least an ace), then you go all-in. At this level your opponent knows you don't have QQ (which would be afraid of KK, AA, AK or KQ), and thus you have either AK or KK. He is committed to calling another $8,300 (remember he has $12,000 in already) since he now is a 50% chance to win and as I demonstrated with the math, either hand is equally likely. Is that true? From the action and the math, either AK or KK are equally likely indeed. However, can the 14th century theorist help us out here? If you're your opponent, can you get away from AAAKK, knowing that the only hand that beats you is KKKK? It sure is possible if you think about it in this way: i) "The simplest solution is the best..." Would AK go all-in on the river knowing that AA beats them? (KK is not possible for your opponent to have if you do in fact have AK) Probably not in this spot. Would they (you) go all-in with AK for just a chop, if the opponent also has AK? Probably not. Thus they (you) must have KK. ii) "...however implausible it may seem." From a deduced math perspective (don't know the exact term, if there is one) the odds that you have either AK or KK are 1 in 1,000, your opponent thinks to himself, but the fact that you went over the top all-in on the river now makes that chance 100% (that you have either) and 0.5 not 0.001 for each hand - an increase of 500 times! It is 500 times more likely you do have KK now, consistent with point (i).
If you were your opponent, would you be able to fold AA in this spot?
This hand is an example of the nuts versus the second nuts. If you held KK would you play it this way for maximum value? If you held AA would you be able to get away from the hand on the river? If you were the player who held AA and you thought they were the nuts the whole time, should you have also checked on the turn? I hope this entry helps the reader to think about similar situations they may have been in and invite additional comments for this post.
Friday, December 14, 2007
Advanced Poker Theory: Monster Folds
This entry is designed as a brainstorming session to try and figure out what to do in a hypothetical situation. To set this up properly, let's say you're playing in a large NL tournament where the buy-in is at least $300. The assumption here is that in tournaments, players in general don't place chips into the pot on stone cold bluffs, they have a tendency to play a bit tighter than usual, and therefore typically have a made hand or monster draw or some juicy pot odds to keep them around. (The reader may immediately disagree with this statement, regardless, the scenario below stands.)
So here is the scenario: Blinds at 25-50 no antes, you have about 6000 chips and your opponent in question has about 4000 in chips. Folds around to a late position raiser (to 150), you look down at AK on the button and re-raise (to 500), player calls. 1075 in the pot. Flop comes out K-6-K with two diamonds. Player checks, you bet 600, player goes all-in, you call. Player flips over 6-6 which holds up (you need the case K or another A to win).
Was there anything else you could have done differently?
Your opponent check-raised you all-in. It is clear that your opponent is afraid of something, what is he afraid of? Why didn't he come out betting on the flop? Because he only became scared because of your bet. Your bet indicates to him that you have a K, likely with a big kicker like A or Q let's say, or you could even have a pocket pair like QQ for example. If your opponent correctly puts you on one of these types of hands (he could pretty much eliminate quad kings because who would come out betting with the stone cold nuts?, and he could probably eliminate K6 based on your pre-flop re-raise), his check-raise - and not just any check-raise, an all-in check-raise at that - is saying he wants to take down the pot right then and there and not get drawn out on. If you are holding a hand like AK or QQ, your opponent thinks to himself, then any A, K or Q on the turn or river beats him. He may not know exactly what you have, but he could certainly be afraid of any over-cards. Overcards to what? Overcards to pocket 6's! If another seven shows up on the turn or river, how does he know you don't have pocket 7's or K7 for example?
If your opponent is not afraid because he has a monster he would just slow-play and check-call (another way to play the 6-6 of course), or has a weak hand (he would fold to almost any reasonable bet) or maybe thinks you are just trying to buy the pot (and may call hoping to outplay you or check it down, etc.). Thus, does not the check-raise all-in play give you some pause?! Another piece of psychology is that your opponent may put you on a big ace, even AK, and confident you will call an all-in with that hand! So if you are thinking that the all-in play is unsophisticated, think again - it could that the player puts you on AK and knows you will call. However, if that's the case, why not milk you for all your chips slowly rather than risk you folding to the all-in check-raise? Because perhaps that's the only way your opponent believes they can get your chips, and they are comfortable taking the risk of you hitting what they know to be a four outter. If we look at the hands you can put your opponent on when he check-raises you all-in, they can be reasonably described as either: A flush draw (remember that?!), AA (an overpair), AK (same as you), KQ (any other weaker kicker than you), QQ (any underpair), AQ (representing any two non-paired cards), K6 (the nuts) or 66 (the second nuts). I mean, any poker player right off the bat without this minutiae level of detail knows there is pretty much only one hand that beats him and that is 66. So does your opponent have 66?
Let's break this down: We should reasonably eliminate the flush draw, AA, KQ, QQ and AQ types of hands (see statement in opening paragraph). (In addition, can we not eliminate these hands only unless you think your opponent is putting you on a steal, and thus he has essentially re-bluffed you in his mind. If in fact your opponent is putting you on a steal, then would they not just call to try and outplay you on a later street or hope to check it down? The all-in play here is just too reckless - especially for a flush draw early in the tournament when the player has enough chips - to believe your opponent is bluffing, unless they have something like KQ, and that is the only hand you can reasonably beat here is the point, since hands like AA or QQ should come out betting a value bet on the flop.) Thus your opponent either has AK (same as you), K6 (the nuts) or 66 (the second nuts). At this point can we not eliminate K6 as well? Would he likely call a big re-raise pre-flop with K6? Probably not. Anything is possible, but probably not in this case. And would he check-raise all-in with the nuts? So that's two strikes against that hand. (Although K6 can also get drawn out on by the same AK or KQ type of hands roughly 10% of the time with two cards to come.) So we're down to AK or 66. (At this point the astute reader will see that the best you can do is chop.) You're put to a decision early in a tournament for a good portion of your chips, but you also know that soon the blinds are going up to 50-100 and if you have 2000 chips you're still at 20 times the big blind and can still fight, so you're tempted to call since you could have the best hand and still won't be out of the tournament if you lose.
From a math perspective, which hand is more likely, AK or 66? Since you have AK and there are two kings on the flop, your opponent will be holding AK approximately (1/47 X 3/46 = 0.0014) or 0.14% of the time. Since there is one 6 on the flop, the chances your opponent is holding 66 is (3/47 X 2/46 = 0.0028) or 0.28%. So it is twice as likely (.28 > .14) your opponent has the 66! And you could understand why he would go-all-in too, he doesn't want to get drawn out on by a better boat, even if it is only 9:1. (And if he does have the K6, then you're dead to three outs instead of four anyway.) Since you've invested 1100 into the pot, you still have around 5000 chips, plenty for early play at 25-50 with the next level at 50-100. If your opponent has any of the other types of hands then what a hell of a play he made.
So lay it down when your opponent check-raises you all-in, assured you thought through the scenario, and live to fight another hand. Even though there pragmatically is only one hand that beats you, that one hand is vulnerable to any overcard that may come. It's a nice pot for early in the tournament for your opponent to take it with an all-in, let it go. Now that's one monster lay down.
So here is the scenario: Blinds at 25-50 no antes, you have about 6000 chips and your opponent in question has about 4000 in chips. Folds around to a late position raiser (to 150), you look down at AK on the button and re-raise (to 500), player calls. 1075 in the pot. Flop comes out K-6-K with two diamonds. Player checks, you bet 600, player goes all-in, you call. Player flips over 6-6 which holds up (you need the case K or another A to win).
Was there anything else you could have done differently?
Your opponent check-raised you all-in. It is clear that your opponent is afraid of something, what is he afraid of? Why didn't he come out betting on the flop? Because he only became scared because of your bet. Your bet indicates to him that you have a K, likely with a big kicker like A or Q let's say, or you could even have a pocket pair like QQ for example. If your opponent correctly puts you on one of these types of hands (he could pretty much eliminate quad kings because who would come out betting with the stone cold nuts?, and he could probably eliminate K6 based on your pre-flop re-raise), his check-raise - and not just any check-raise, an all-in check-raise at that - is saying he wants to take down the pot right then and there and not get drawn out on. If you are holding a hand like AK or QQ, your opponent thinks to himself, then any A, K or Q on the turn or river beats him. He may not know exactly what you have, but he could certainly be afraid of any over-cards. Overcards to what? Overcards to pocket 6's! If another seven shows up on the turn or river, how does he know you don't have pocket 7's or K7 for example?
If your opponent is not afraid because he has a monster he would just slow-play and check-call (another way to play the 6-6 of course), or has a weak hand (he would fold to almost any reasonable bet) or maybe thinks you are just trying to buy the pot (and may call hoping to outplay you or check it down, etc.). Thus, does not the check-raise all-in play give you some pause?! Another piece of psychology is that your opponent may put you on a big ace, even AK, and confident you will call an all-in with that hand! So if you are thinking that the all-in play is unsophisticated, think again - it could that the player puts you on AK and knows you will call. However, if that's the case, why not milk you for all your chips slowly rather than risk you folding to the all-in check-raise? Because perhaps that's the only way your opponent believes they can get your chips, and they are comfortable taking the risk of you hitting what they know to be a four outter. If we look at the hands you can put your opponent on when he check-raises you all-in, they can be reasonably described as either: A flush draw (remember that?!), AA (an overpair), AK (same as you), KQ (any other weaker kicker than you), QQ (any underpair), AQ (representing any two non-paired cards), K6 (the nuts) or 66 (the second nuts). I mean, any poker player right off the bat without this minutiae level of detail knows there is pretty much only one hand that beats him and that is 66. So does your opponent have 66?
Let's break this down: We should reasonably eliminate the flush draw, AA, KQ, QQ and AQ types of hands (see statement in opening paragraph). (In addition, can we not eliminate these hands only unless you think your opponent is putting you on a steal, and thus he has essentially re-bluffed you in his mind. If in fact your opponent is putting you on a steal, then would they not just call to try and outplay you on a later street or hope to check it down? The all-in play here is just too reckless - especially for a flush draw early in the tournament when the player has enough chips - to believe your opponent is bluffing, unless they have something like KQ, and that is the only hand you can reasonably beat here is the point, since hands like AA or QQ should come out betting a value bet on the flop.) Thus your opponent either has AK (same as you), K6 (the nuts) or 66 (the second nuts). At this point can we not eliminate K6 as well? Would he likely call a big re-raise pre-flop with K6? Probably not. Anything is possible, but probably not in this case. And would he check-raise all-in with the nuts? So that's two strikes against that hand. (Although K6 can also get drawn out on by the same AK or KQ type of hands roughly 10% of the time with two cards to come.) So we're down to AK or 66. (At this point the astute reader will see that the best you can do is chop.) You're put to a decision early in a tournament for a good portion of your chips, but you also know that soon the blinds are going up to 50-100 and if you have 2000 chips you're still at 20 times the big blind and can still fight, so you're tempted to call since you could have the best hand and still won't be out of the tournament if you lose.
From a math perspective, which hand is more likely, AK or 66? Since you have AK and there are two kings on the flop, your opponent will be holding AK approximately (1/47 X 3/46 = 0.0014) or 0.14% of the time. Since there is one 6 on the flop, the chances your opponent is holding 66 is (3/47 X 2/46 = 0.0028) or 0.28%. So it is twice as likely (.28 > .14) your opponent has the 66! And you could understand why he would go-all-in too, he doesn't want to get drawn out on by a better boat, even if it is only 9:1. (And if he does have the K6, then you're dead to three outs instead of four anyway.) Since you've invested 1100 into the pot, you still have around 5000 chips, plenty for early play at 25-50 with the next level at 50-100. If your opponent has any of the other types of hands then what a hell of a play he made.
So lay it down when your opponent check-raises you all-in, assured you thought through the scenario, and live to fight another hand. Even though there pragmatically is only one hand that beats you, that one hand is vulnerable to any overcard that may come. It's a nice pot for early in the tournament for your opponent to take it with an all-in, let it go. Now that's one monster lay down.
Wednesday, December 5, 2007
On The Flop: Set Over Set Over Top Two
Last month (November) I witnessed a flop that was wicked, which I don't think I've ever seen before. We all have seen set over set on the flop at least a few times, and know how unlikely that is. But how about set over set over two pair (and not just any two pair, top two)!! All three players in the hand were essentially allin on the flop, with the winner went to the player who held the best set (set of 10's).
Flop: A - 10 - 3
Player1 holds A - 10
Player2 holds 10-10
Player3 holds 3-3
Odds of that flop coming out given the three known hands:
a) Flop can come out in the following ways --> A-10-3, A-3-10, 10-A-3, 10-3-A, 3-A-10, 3-10-A
b) Each combination odds is --> (3/46 X 1/45 X 2/44) + (3/46 X 2/45 X 1/44) + (1/46 X 3/45 X 2/44) + (1/46 X 2/45 X 3/44) + (2/46 X 3/45 X 1/44) + (2/46 X 1/45 X 3/44) = 0.000066 X 6 (appx.) = 0.000395 or 0.0395% or about 4 in 10,000. Ouch!!
Odds that A - 10 will win: He needs an ace for a boat 2/43 + 2/42 = appx 9.4%
Odds that 3 - 3 will win: He needs the case 3, bummer. 1/43 + 1/42 = appx 4.7%
Odds that 10 - 10 will hold against the two other hands: 100 - (9.4 + 4.7) = 85.9%
Aside - Set over set over two pair in another type of combination -->
Say the flop is AKx and the players have AA KK and AK. What are the odds of that flop coming out given the three players' known hole cards?
We have: (1/46 X 1/45) X 6 = 0.000483 or 0.0483 or about 5 in 10,000.
As an aside, the odds of having set over set on the flop is:
Given that two players each have a pair already, the flop needs to come out with one of each of their hole cards. Say players hold JJ and 99. Thus the flop could be J-9-x or J-x-9 or 9-J-x or 9-x-J or x-J-9 or x-9-J (six combinations). Each combination is appx 2/48 X 2/47 = 0.00177 or 0.177%. Thus odds of set over set are appx 0.00177 X 6 = 1%.
As another aside, the odds of having set over set over set on the flop is:
Given that three players already have a pair, the flop needs to come out with one of each of their hole cards. 2/48 X 2/47 X 2/46 = 0.000077 X 6 = 0.00046. Thus the odds of set over set over set on the flop are appx 0.046% or almost 5 in 10,000.
Flop: A - 10 - 3
Player1 holds A - 10
Player2 holds 10-10
Player3 holds 3-3
Odds of that flop coming out given the three known hands:
a) Flop can come out in the following ways --> A-10-3, A-3-10, 10-A-3, 10-3-A, 3-A-10, 3-10-A
b) Each combination odds is --> (3/46 X 1/45 X 2/44) + (3/46 X 2/45 X 1/44) + (1/46 X 3/45 X 2/44) + (1/46 X 2/45 X 3/44) + (2/46 X 3/45 X 1/44) + (2/46 X 1/45 X 3/44) = 0.000066 X 6 (appx.) = 0.000395 or 0.0395% or about 4 in 10,000. Ouch!!
Odds that A - 10 will win: He needs an ace for a boat 2/43 + 2/42 = appx 9.4%
Odds that 3 - 3 will win: He needs the case 3, bummer. 1/43 + 1/42 = appx 4.7%
Odds that 10 - 10 will hold against the two other hands: 100 - (9.4 + 4.7) = 85.9%
Aside - Set over set over two pair in another type of combination -->
Say the flop is AKx and the players have AA KK and AK. What are the odds of that flop coming out given the three players' known hole cards?
We have: (1/46 X 1/45) X 6 = 0.000483 or 0.0483 or about 5 in 10,000.
As an aside, the odds of having set over set on the flop is:
Given that two players each have a pair already, the flop needs to come out with one of each of their hole cards. Say players hold JJ and 99. Thus the flop could be J-9-x or J-x-9 or 9-J-x or 9-x-J or x-J-9 or x-9-J (six combinations). Each combination is appx 2/48 X 2/47 = 0.00177 or 0.177%. Thus odds of set over set are appx 0.00177 X 6 = 1%.
As another aside, the odds of having set over set over set on the flop is:
Given that three players already have a pair, the flop needs to come out with one of each of their hole cards. 2/48 X 2/47 X 2/46 = 0.000077 X 6 = 0.00046. Thus the odds of set over set over set on the flop are appx 0.046% or almost 5 in 10,000.
Top Two On The Flop Continued...A Combinatorial Perspective
So to continue the discussion about the 5-10-J flop and me holding 10-J. Remember there are two other players in the hand. The question this discussion asks is this, "What are the odds I am beat, or if both players call, what are the odds I will get drawn out on?"
I think this topic is an advanced poker topic that warrants further discussion after this initial post.
Please read the previous post first to understand the hand in question in more detail.
What hands you can likely put your opponents on in this scenario:
1) A big overpair (QQ or KK or AA)
2) A flush draw
3) A straight draw (something like QK or 9Q or 89) [NOTE: The 89 is much less likely, as is the 9Q for the big re-raise.]
4) A set
5) Another two pair, like J-5 or 10-5 (most likely for UTG here)
As a side point, it is more likely for UTG check-raiser to have a made hand like (1) or (4).
First question -- What are the odds I am beat?
Answer: There is only one hand that beats my top two, and that's a set. As in the previous blog entry, the odds of someone having a set are about 0.37% here. As an aside, the odds of the other hands are:
Odds of (1) = 4/47 X 3/46 X 3 = 0.01665 = about 1.7% (of having any of the three overpairs)
Odds of (2) = 11/47 X 10/46 = about 5%
Odds of (3) = 4/47 X 4/46 X 3 = about 0.74% (of having any of the three draws)
Odds of (4) = See last post. About 0.37%
Odds of (5) = 2/47 X 3/46 X 2 = about 0.56% (of having any of the two choices)
And as it turned out, the most likely hands (1) and (2) were the hands that were being held by the other two players.
Second question -- What are the odds I could get drawn out on, if both players call?
Answer: We need to look at the winning percentages of each likely hand.
Re-draw winning percentages with two cards to come:
Odds of (1) = (1/45 + 1/44) = about 4.5% (any of the three overpairs, given a flush draw) to make a set + make a better two pair (can only make a 5) is 3/45 + 3/44 = 13.5% thus 18%
Odds of (2) = (8/45 + 8/44) = about 36% to make the flush (cannot make a 10 clubs) + make a better two-pair = (3/45 X 3/44 X 2) = 0.0091 or 0.91% + make a set of aces = (3/45 X 2/44) = 0.003 or 0.3%, thus total is 36 + .91 + .3 = about 37%
Odds of (3) = (6/45 + 6/44) = about 27% (each of the three straight draws, given the flush draw) to make the straight
Odds of (4) = Re-draw on river to a boat or quads = [if J-J - no quads possible, needs 10, 5, or turn card for a boat = 2/44 + 3/44 + 3/44 = 0.18 or 18%] [if 10-10 - no quads possible, needs 5 or turn card for a boat = 3/44 + 3/44 = 13.6%] [if 5-5, can only get quads to win, 1/44 = 2.3%]
Odds of (5) = Re-draw to a boat = [can only get a 5 to win, 2/44 = 4.6%]
Based on my reads and the most likely hand combinations of (1) and (2) being present, 37 + 18 = 55% (I am only 45% to win) if both players call my all-in. Since player2 was likely to call an allin, this would make UTG player more likely to call another $80. Thus my odds of getting drawn out on are what we might say is a coin flip, which sucks for having only a $6 investment (actually $6 + $4) in the hand. This is another reason I folded. You can still argue against the fold as in my previous post.
But check out the re-draw winning percentages if the hands present were (2) and (3) - the flush draw and a straight draw. If both players call my allin, and these hands are present, I am now only 36% to win!! Let me repeat, this sucks for having a $10 investment in the hand, and another reason why I folded, since I was unsure if could get at least one player off the hand. And again, you can still argue against the fold. Of course in this case I was sure I was not up against both of these hands.
Any other combination I am quite the favorite, unless at least one player has the flush draw, then it really is close to even money.
CONCLUSION
In this type of betting action on the flop, when you're up against at least two other players and faced with an all-in decision on a pot in which you have a small investment, unless you are stone cold or have great reads in which you are quite sure you have a decided winning percentage with two cards to come, it is ok to fold what you are pretty sure is currently the best hand!
I think this topic is an advanced poker topic that warrants further discussion after this initial post.
Please read the previous post first to understand the hand in question in more detail.
What hands you can likely put your opponents on in this scenario:
1) A big overpair (QQ or KK or AA)
2) A flush draw
3) A straight draw (something like QK or 9Q or 89) [NOTE: The 89 is much less likely, as is the 9Q for the big re-raise.]
4) A set
5) Another two pair, like J-5 or 10-5 (most likely for UTG here)
As a side point, it is more likely for UTG check-raiser to have a made hand like (1) or (4).
First question -- What are the odds I am beat?
Answer: There is only one hand that beats my top two, and that's a set. As in the previous blog entry, the odds of someone having a set are about 0.37% here. As an aside, the odds of the other hands are:
Odds of (1) = 4/47 X 3/46 X 3 = 0.01665 = about 1.7% (of having any of the three overpairs)
Odds of (2) = 11/47 X 10/46 = about 5%
Odds of (3) = 4/47 X 4/46 X 3 = about 0.74% (of having any of the three draws)
Odds of (4) = See last post. About 0.37%
Odds of (5) = 2/47 X 3/46 X 2 = about 0.56% (of having any of the two choices)
And as it turned out, the most likely hands (1) and (2) were the hands that were being held by the other two players.
Second question -- What are the odds I could get drawn out on, if both players call?
Answer: We need to look at the winning percentages of each likely hand.
Re-draw winning percentages with two cards to come:
Odds of (1) = (1/45 + 1/44) = about 4.5% (any of the three overpairs, given a flush draw) to make a set + make a better two pair (can only make a 5) is 3/45 + 3/44 = 13.5% thus 18%
Odds of (2) = (8/45 + 8/44) = about 36% to make the flush (cannot make a 10 clubs) + make a better two-pair = (3/45 X 3/44 X 2) = 0.0091 or 0.91% + make a set of aces = (3/45 X 2/44) = 0.003 or 0.3%, thus total is 36 + .91 + .3 = about 37%
Odds of (3) = (6/45 + 6/44) = about 27% (each of the three straight draws, given the flush draw) to make the straight
Odds of (4) = Re-draw on river to a boat or quads = [if J-J - no quads possible, needs 10, 5, or turn card for a boat = 2/44 + 3/44 + 3/44 = 0.18 or 18%] [if 10-10 - no quads possible, needs 5 or turn card for a boat = 3/44 + 3/44 = 13.6%] [if 5-5, can only get quads to win, 1/44 = 2.3%]
Odds of (5) = Re-draw to a boat = [can only get a 5 to win, 2/44 = 4.6%]
Based on my reads and the most likely hand combinations of (1) and (2) being present, 37 + 18 = 55% (I am only 45% to win) if both players call my all-in. Since player2 was likely to call an allin, this would make UTG player more likely to call another $80. Thus my odds of getting drawn out on are what we might say is a coin flip, which sucks for having only a $6 investment (actually $6 + $4) in the hand. This is another reason I folded. You can still argue against the fold as in my previous post.
But check out the re-draw winning percentages if the hands present were (2) and (3) - the flush draw and a straight draw. If both players call my allin, and these hands are present, I am now only 36% to win!! Let me repeat, this sucks for having a $10 investment in the hand, and another reason why I folded, since I was unsure if could get at least one player off the hand. And again, you can still argue against the fold. Of course in this case I was sure I was not up against both of these hands.
Any other combination I am quite the favorite, unless at least one player has the flush draw, then it really is close to even money.
CONCLUSION
In this type of betting action on the flop, when you're up against at least two other players and faced with an all-in decision on a pot in which you have a small investment, unless you are stone cold or have great reads in which you are quite sure you have a decided winning percentage with two cards to come, it is ok to fold what you are pretty sure is currently the best hand!
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