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Server Time: 11/23/2008 4:00:30 AM PACIFIC |
 Fun pot limit problem, Schuster, 29. Oct 2003 23:14 | ||
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| 2 players are playing pot limit hold'em. One player holds Ks Kc and the other holds Ad 4d. The flop is 8d 4h 9d. At this point, each player flips their cards face up. There is $100 in the pot from the preflop action. Assume each player plays perfectly and each has an equal stack. Is it ever correct for KK to bet? Or fold to a bet? Is it ever correct for A4 to bet? Or fold to a bet? How big would the stacks have to be in each situation? For reference, the A4 is a 51.6162% favorite and the KK is a 48.3838% favorite, assuming each hand went to the river. Lee | ||
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| Re: Fun pot limit problem, shorn, 30. Oct 2003 06:17 | ||
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| Not sure on your questions, but I would rather hold the A4 here as I have 12 outs (including the Kd) that give me the pot. And, since I have seen 7 cards now instead of five, my odds to call any bet have improved (since he doesn't hold the Kd). | ||
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| Re: Fun pot limit problem, Schuster, 30. Oct 2003 07:11 | ||
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| 14 outs really, nine flush cards, three aces, and two 4's. Lee | ||
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| Re: Fun pot limit problem, shorn, 30. Oct 2003 07:40 | ||
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| Good catch...missed the 4 on the board. Sorry. | ||
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| Re: Fun pot limit problem, Schuster, 30. Oct 2003 15:53 | ||
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| I submit that KK can always play the hand for a positive EV, whereas the A4 can only play it for a positive EV some of the time. Can you figure why? (Not many replies so far, so I'm tossing some hints around, hehe) Lee | ||
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| Re: Fun pot limit problem, Mark Barnett II, 30. Oct 2003 10:33 | ||
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| i think mathmatically its very clear only cause cards are face up kings bet the pot cause the other hand only has 14/45 to make the hand that makes the pot 300 assuming the kings fold if a winner comes *drawing to trips? dont think so* lose 150 14 times=2100 *assuming half the money is kings and half the other* turn comes blank bet the pot again making it 900 pot lose 450 14 times=6300 win 450 30 times=13500 expected value=5100 profit over 1378 possible outcomes *14 turn outcomes that dont see river plus 31 times 44 river outcomes* should be an EV of 3.7ish per outcome | ||
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| Re: Fun pot limit problem, Schuster, 30. Oct 2003 15:52 | ||
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| Is this always the case no matter how big the stacks are? Lee | ||
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| Re: Fun pot limit problem, mkpoker, 30. Oct 2003 17:06 | ||
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| OK Lee, I'll play--despite never having played PL HE before. IMO, this puzzle illustrates the difference between effective odds vs. odds to improve by the river. You are quite correct that A4 is a very slight favorite *with two cards to come.* But if a blank comes on the turn (which will happen more than two-thirds of the time) A4 becomes a huge dog and it'll be impossible for him to call a pot sized bet on the turn. This is especially true because having the cards face up destroys any extra value from implied odds. If, for example, an A comes on the turn, the KK will fold to any sizable bet since he now knows he's drawing to a 2-outer. So, even though A4 is the slight favorite to improve by the river, KK is actually in a MUCH stronger position. Bottom line: KK should make a pot sized bet on the flop. A4 has only a 7:3 chance of improving on the turn and the pot is laying 2:1. If A4 calls, it's a bad call. (It's a bad call because if he doesn't improve immediately, he can't possibly call another pot-sized bet on the turn). If A4 calls and the turn improves A4, KK should fold to any big bet (he should obviously call if A4 does something really stupid like making a $5 bet that gives KK the right odds to draw to a 2-outer). If the turn is a blank, KK should make another pot sized bet. Again, if A4 calls, it's a bad call. The pot is still laying 2:1, and A4 has only a slightly-better than 7:3 chance of improving. These guidelines would only change if either player can't afford to make a pot sized bet on the flop and again the turn. If A4 will be pushed all-in on the flop, he should call KK's bet, becuase then he gets to see the river for free. Similarly, if A4 sees that KK is short-stacked and has any way to push him on all-in on the flop (like by raising KK's flop bet), he should do so. The only way this hand is profitable for A4 is if he can find a way to see the river card either free or very inexpensively. So, professor, how'd I do? --matt | ||
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| Re: Fun pot limit problem, Schuster, 30. Oct 2003 23:45 | ||
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| You're on the right track mk, but not entirely there. Remember, part of the problem was to assume that both people played their hands mathematically perfectly, so no one is going to make a bad call, but each hand will maximize their EV. Should KK always bet the flop, and if not, when should KK check? If KK shouldn't bet the flop, does that mean that the A4 should bet the flop? I'll post my thoughts (which I am fairly certain are correct) on the problem in another day or two. I really enjoyed wrapping my head around this, but not everyone is a big math geek like me. I was just curious to see what people came up with. Lee | ||
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| Re: Fun pot limit problem, mkpoker, 31. Oct 2003 10:24 | ||
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| Here's my final answer: A4 can only play this hand profitably if either player holds less than a $400 stack (it's actually a few dollars less than $400, but I'm rounding). The reason (as described above) is that A4 must fold to any pot-sized bet on the turn, if he doesn't improve. Hence, if KK is able to keep enough $$ in reserve to make a pot-sized turn bet, his hand is +EV. However, if A4 can push either himself of KK all-in (or close to all-in) on the flop, he gets to see the river for free (or for cheap), which transforms the hand into a +EV play for A4. Of course, the only way to get all-in is if either of the players is short-stacked. There are three possible playing scenarios, which are entirely dependent on stack size (assuming, as you specify, that each player acts mathematically correctly): Scenario 1) Both players have big (600+) stacks. KK should make a pot sized bet on the flop. If A4 plays correctly, he must fold because he knows his odds of improving on the turn (7:3) are less than the immediate pot odds (2:1). Under normal circumstances, A4 might take these slightly unfavorable odds because his implied odds are a bit higher (because his improvement may be concealed). However, your hypothetical specifies that all cards are face up, so implied odds become a meaningless concept. Even though A4 is a slight favorite to improve with two cards to come, he's actually a dog overall, because of his effective odds, namely, the certainty that he'll need to call a big bet on the turn if he doesn't improve. Scenario 2) Either player has 400-600 KK should check /call the flop and make a pot-sized bet on the turn if A4 doesn't improve. If KK bets out on the flop, A4 will make a pot sized raise, pushing the players either all-in, or almost all in on the flop. With either KK or A4 not having enough money to make (or call) a pot-sized bet on the turn, A4 gets a free (or cheap) chance to improve on the river...effectively getting to see two cards for the price of one. This is the worst case scenario for KK. By check/calling, KK is holding back enough $$ for a pot-sized bet on the turn. BTW, A4 will also check, taking the free card. If the turn improves A4, he'll win the pot with any bet. If he doesn't improve on the turn (which will happen more than two-thirds of the time), KK will make a big bet and A4 will fold. Scenario 3) Either player has less than 400. Here, KK must check/fold. When he checks, A4 will make a pot sized bet. Calling will leave KK unable to make a pot-sized bet at the turn. If KK goes almost all-in at the turn, A4 will have the correct odds to call whatever turn bet KK can muster. An interesting puzzle (though I doubt I would have figured this out in 30 seconds at the table)! I'm off to vegas for the weekend to test out some of my new UPF-inspired skills. Will let you know how it went on Monday! Best --matt | ||
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| Re: Fun pot limit problem, Schuster, 31. Oct 2003 12:52 | ||
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| 1 and 2 are just about right. Scenario 3 is wrong though. The basic principle is that KK always wants to get as much money in on the flop as possible while still leaving enough for a turn bet that gives A4 improper odds. If this means that KK cannot bet the flop, then that's the way it goes. Note the scenario 2, where KK can't bet the flop, but the correct play for A4 would be to check it right back and see if he can pick up the 100 for free. Even if KK can only safely bet $5, it certainly should be bet. For very short stacks, KK should check and call regardless. Sure, A4 is the favorite, but the pot odds will be at least 5 to 4 for KK to put all his money in. For example, if each player has 200, KK should check and call, and then if A4 misses on the turn, bet whatever he has left. Note that the only time where A4 can even see the turn is if the stacks are short, and KK still has a +EV if they are. Lee | ||
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