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Server Time: 3/16/2010 4:08:31 PM PACIFIC |
 A hold'em proposition, Mark Gregorich, 7. Oct 2003 10:37 | ||
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| Here's a hold'em prop that came up a couple years ago that I think provides an interesting scenario: You and a buddy decide to play some heads-up limit hold'em. However, he suggests that rather than deal out two random hands every time, one of you will always start with the AK of spades. The other one will have a random hand. You will play $4-8 limit, with the blinds of $2-4. He gives you your choice as to whether you get the AK or the random hand. Which would you prefer? | ||
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| Re: A hold'em proposition, 4 POKER, 7. Oct 2003 10:49 | ||
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| on 7. Oct 2003 10:37 Mark Gregorich wrote: > Here's a hold'em prop that came up a couple years ago that I think provides an > interesting scenario: > > You and a buddy decide to play some heads-up limit hold'em. However, he > suggests that rather than deal out two random hands every time, one of you will > always start with the AK of spades. The other one will have a random hand. You > will play $4-8 limit, with the blinds of $2-4. He gives you your choice as to > whether you get the AK or the random hand. Which would you prefer? > Well if he knows that you're holding the AK of spades, (or vice versa), then I would chose the random hand. (that's if I'm reading you correctly here). Sure AK suited heads up is a great hand, and will win many pots, but that won't matter as much (or factor into it) if you have it and I "know" you have it. 4P- | ||
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| Re: A hold'em proposition, Lou Krieger, 7. Oct 2003 11:10 | ||
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| on 7. Oct 2003 10:49 4 POKER wrote: "Well if he knows that you're holding the AK of spades, (or vice versa), then I would chose the random hand. (that's if I'm reading you correctly here). Sure AK suited heads up is a great hand, and will win many pots, but that won't matter as much (or factor into it) if you have it and I "know" you have it." Of course, if he knows that you know he's holding A-K, then he MUST determine how often you'll bluff with hands that can't bet A-K, or else you'll seldom be called when betting hands that can beat big slick. Lou Krieger Raise your game with Lou Krieger, author of "Poker For Dummies" and five other books about poker, at Royal Vegas Poker http://www.royalvegaspoker.com/lou | ||
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| Re: A hold'em proposition, mkpoker, 7. Oct 2003 11:05 | ||
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| I'm sure you'll tell me why this is the wrong answer, LOL, but I'd take AKs. My strategy would be to bet/raise every hand pre-flop, bet/call every hand on the flop and turn, and check/call every hand on the river. I'd do this regardless of the cards on the board and regardless of my opponent's action. Obviously, AKs is far superior to most hands. It is a coin flip with most pairs, and is dominated only by AA and KK. Hence, the only way to win in your scenario with two random cards is bluff with enough frequency to force AKs to throw away better hands and/or to score big pots when you're lucky enough to make a winning hand. I'd counteract these possibilities by playing my AKs blindly (I'd play every hand to the river, regardless of the situation). This would eliminate the possibility that I could be "outplayed" by skillful bluffing AND I'd avoid getting sucked into losing a huge pot when beat (since all pots would be close to the same size when called to the river). If a player tried to "beat" my strategy by never bluffing and only playing with what he knew to be a winning hand (by playing only pairs, for example), he'd fold so much that my picking up the blinds would more then compensate for the pots I'd lose at showdown (Indeed, I'd expect to lose most hands at showdown, because it's unlikely my turn bet would be called unless I was beat or my opponent was on a good draw). I'm sure there's a mathematical answer to this question, but I'd bet that my AKs would be impossible to beat over the long term using the strategy I've outlined. | ||
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| Re: A hold'em proposition, Barry T, 7. Oct 2003 16:21 | ||
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| Hi,. MK: OK, I'll try to point out why you are wrong. If you decide to play predictably (we all know itis the goal of every poker player to get their opponent to play predictably),. then oyu opponet will adopt the folowing plan: 1- Always call preflop. 2 - On the flop, fold with nothing, raise whenever ahead. There might be some draws worth playing as well. 3 - On the turn, cap with any hand that is leading, alost always fold with any hand that is now trailing. (Pot ods will be considered). 4- On the river, bet every hand that is ahead, check all others. BarryT "who would always take the ranom hand...I will happy to spot my opponent a lead in exchange for my ability to play nearly perfectly." | ||
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| Re: A hold'em proposition, mkpoker, 7. Oct 2003 17:03 | ||
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| on 7. Oct 2003 16:21 Barry T wrote: > Hi,. MK: OK, I'll try to point out why you are wrong. If you decide to play predictably > (we all know itis the goal of every poker player to get their opponent to play > predictably),. then oyu opponet will adopt the folowing plan: > 1- Always call preflop. 2 - On the flop, fold with nothing, raise whenever ahead. There might be some draws worth playing as well. 3 - On the turn, cap with any hand that is leading, alost always fold with any hand that > is now trailing. (Pot ods will be considered). 4- On the river, bet every hand that is ahead, check all others.> > BarryT Barry, I'd love to see a computer simulation of the MK vs. Barry T strategy...I'm not ready to abandon my case. Remember that my strategy is to bet/call the turn, so there's no way you could cap the betting if ahead. If you played optimally (and you surely would), you'd check-raise the turn (and flop) when ahead. Also, remember that my plan is to check/call the river, so you'd get a maximum of 1 BB from me there. In fact, each hand would have exactly the same betting pattern played under the MK vs. Barry T strategy, assuming Barry T is ahead (if you were behind at any point, you'd fold): Pre-Flop: 2BB (MK raises and Barry T calls) Flop: 2BB (Barry check-raises, MK calls) Turn: 4BB (Barry T check-raises, MK calls) River: 2BB (Barry T bets, MK calls) Hence, the real (basic version) of the question is this: Will MK win more than 5 hands (folded on the flop) for every 1 that Barry T wins (at showdown)? If so, then MK will come out ahead. BUT, there's another factor that's to my advantage: MK has a reasonable shot at outdrawing Barry T on the turn or river. That's because Barry T will raise on the flop with 1-pair (and no A or K on the flop), which means an A or K on the turn or river will cost Barry T dearly (it's the most likely way MK could win a big pot in this battle). Drawing to a 6-outer isn't great, but it means that MK will outdraw Barry T a good 15-20 percent of the time, which will add up. I'll also draw a few nut-flushes and straights to outdraw Barry when Barry gets lucky on the flop. Another factor (as you note) is that you'll call on any draw giving you favorable pot odds, which I believe would be any open-end straight (unless 2 spades are on board) or any non-spade flush draw. This will increase Barry T's return slightly. A final (and more important) factor to consider is the impact of Barry T holding any pocket pair. In those cases, Barry T should probably cap the betting pre-flop, since he's ahead (albeit very slightly). This should increase your return moderately. Also, when Barry T has AA or KK, he'll cap pre-flop for sure! So like I said, I'd love to see a computer simulation of the MK vs. Barry T strategy. In fact, I might take a crack at developing a probability model myself (though I doubt I have the ability). I still think I might come out ahead! ...and finally, the real item we're measuring here is the relative value of a head start (being dealt AKs) vs. optimal play. It's simply not true that "great play" will always overcome a head start. What if the proposition was to start with AA (instead of AKs) vs. two random cards? No matter how well you play, AA will be the a long-term winner. --matt | ||
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| Re: A hold'em proposition, mkpoker, 7. Oct 2003 21:32 | ||
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| I’ve now spent WAAY too much time trying to figure out these probability equations. The bottom line is that it’s ALMOST a draw between the Barry T. and MK strategies for playing this proposition…But Barry comes out ahead! I figure that using the Barry T. vs. MK strategy: Barry will fold on the flop 70% of time (usually because his hand doesn’t improve or because an A or K trumps his lower pair) Barry will fold on the turn approximately 5% of the time (because an A or K hits when Barry has 1-pair OR because a flush or straight hits MK) Barry will fold on the river approximately 4.5% of the time (or Matt will win a check-check showdown, for the same reasons) Barry will win approximately 20.5% of all hands at showdown. However, the pots MK wins would be far smaller than those Barry T would win. If we played 1,000 hands heads up, MK would win pots totaling $7,840; Barry would win $8,200. So, my best guess is that Barry would take $180 of my money after playing 1,000 hands. I know my numbers aren’t perfect, so I’d encourage anyone with a better mind for probability to test this strategic matchup. --matt P.S. I stopped figuring when I recognized a simple way to refine the “Barry Strategy” to improve its performance: Barry should fold Ax and Kx instead of calling MK’s pre-flop raise. I suspect that adding making this one modification would change the matchup in Barry’s favor significantly. P.P.S. Regardless of the outcome…wrestling with these numbers was a fun challenge. Thanks Barry! | ||
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| Re: A hold'em proposition, Stevolley2, 7. Oct 2003 11:36 | ||
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| The random hand will win for the same reason, semibluffing works. You never know when to call, raise or fold. | ||
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| Re: A hold'em proposition, Allyc, 7. Oct 2003 12:09 | ||
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| An analogous situation would be: Player 1 plays with cards face up. Player 2 plays with cards face down. Who would choose to be Player 1? Player 1 can never bluff. Player 2 can bluff and as 100% information at all times. Player 2 must have the overwhelming advantage. | ||
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| Re: A hold'em proposition, GambleAB, 7. Oct 2003 13:06 | ||
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| No, thats not the same at all. In the given scenario, there is no chance of the player with the "face up" hand having 27o or 38o, he will always have AKs, which will beat most other hands a high percentage of the time. | ||
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| Re: A hold'em proposition, Schuster, 7. Oct 2003 14:09 | ||
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| After a lot of thinking, I still don't know. But I'll throw down my thoughts so far to add fuel to the debate. First, I believe it would be a mistake for the AKs to raise preflop every time. Even if the random hand just calls from the small blind and AKs raises from the big blind, the random hand is getting 10 to 6, or 1.66 to 1 to see the flop. The odds are 3 to 1 when AKs raises out of the small blind. Given that you know your opponents hand, I have a hard time thinking that it would ever be correct for the random hand not to see the flop. If the AKs does raise, the random hand will be getting 5 to 1 to call a flop bet. With 6 (unless you are in a dominated situation) outs, you would normally need about 7 to 1, but the implied odds are clearly there when you know your opponents hand. If the AKs doesn't raise, the random hand is only getting 3 to 1, and will need to make up a full 2 big bets in implied odds in order for calling to be correct. That is a bit tougher. As far as the overall puzzle is concerned, I think it would be better to be the random hand. I don't have my copy of TTOP on me, but my recollection of the game theory chapter is that if you bluff with the proper mathematical frequency, you will make money whether your opponent chooses to call or fold. Even if you tell him your exact strategy, you will make money, even if your opponent is a better player than you. Given that you can figure out how often you will hit your hand and AK will miss on the flop fairly easily, using game theory will allow you to bluff at it with the proper frequency. I'm not sure if I'm on the right track here or not. Intuitively, I really think that it would be better to be the random hand, I just can't really pinpoint why. Lee | ||
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| Re: A hold'em proposition, ICIP, 7. Oct 2003 14:52 | ||
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| I think most people would take the AK, but the biggest problem is that your opponent knows what you have. That is the "catch" with this proposition. There is more money to be made with the two random cards. The AK is going to have to do a lot of calling, if they miss, which can be risky business. Even if they hit, the two random cards definately knows when they are beat and when they are not, so making the correct call is a lot easier. Plus you can punish the AK when they hit a Ace or King and you hit either trips or two pair. AK has a good edge, but have knowledge on your side is much more powerful. Plus it also depends on your opponent and their skills. Are they able to pull off a good bluff or do they like to call a lot. It would be an interesting game. | ||
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