slapdash Posted May 1, 2007 Share Posted May 1, 2007 ... from Bill Chen and Jerrod Ankenman's "The Mathematics of Poker". Three players. Everybody starts by anteing $10. Each player is dealt just one card. If it comes to a showdown, aces and kings win: the pot is shared between all players with an ace or a king, and if nobody has one then the pot is shared between all players who haven't folded. Starting to the left of the button, there is just one betting round. The only bet size allowed is $10, and when somebody has bet, nobody else can raise, they can only fold or call. Button rotates as usual, so in the long run nobody has any advantage or disadvantage that cames from being first or last to act. OK, a nice simple game. Now suppose you know exactly what your opponents' strategies are: to your left is a rock, who will never make the first bet and will only call with an ace or a king; to your right is a maniac who will always bet if nobody else has, and will always call if somebody has bet. What is your expected win rate if you play optimally against these strategies? How about some guesses before somebody does the calculation? Quote Link to comment Share on other sites More sharing options...
GaF Posted May 1, 2007 Share Posted May 1, 2007 Re: Another interesting game ... Gut feel is your win rate is microscopically small :unsure In fact, I'm not certain you can get an edge at all..... (though instinctively you must be able to if you know the exact way they play.....) Quote Link to comment Share on other sites More sharing options...
Tweetypie05 Posted May 1, 2007 Share Posted May 1, 2007 Re: Another interesting game ... Hmmmm... absolutely no idea! As a guess I would think it is around 10%? Looking forward to hearing how this works though... think I need to go back to school to do some more maths!! Quote Link to comment Share on other sites More sharing options...
slapdash Posted May 1, 2007 Author Share Posted May 1, 2007 Re: Another interesting game ... And what if the rock is on your right and the maniac is on your left? Quote Link to comment Share on other sites More sharing options...
Tweetypie05 Posted May 1, 2007 Share Posted May 1, 2007 Re: Another interesting game ... If the rock is to your right I would expect your edge to increase as you know when he calls before you the best you will do is split the pot. In this instance I would check everything apart from an A or K and call (with 9 up) when only the maniac bets (no call from the rock). I think I'm talking rubbish... :eyes Quote Link to comment Share on other sites More sharing options...
slapdash Posted May 1, 2007 Author Share Posted May 1, 2007 Re: Another interesting game ... Since you know the maniac will bet, you may as well check if you have to act before him. If you have an A or K, you obviously call. If you don't, you have no information from the rock, if he's on your left, so you have to decide whether to put your money in without any information. So effectively, you only have two choices: play like a rock (fold your non-AK's) or play like a maniac (bet them). If there are two rocks and one maniac, it turns out that the maniac wins about $9.52 per hand, and each of the rocks loses about $4.76. If there is one rock and two maniacs, it turns out that the rock wins about $2.47 per hand, and each of the maniacs loses about $1.23. So you have NO WINNING STRATEGY, even though the rules are the same for all three players and you know how your opponents will play. Effectively, by playing the way they do, your opponents are implicitly colluding against you: you can't win, all you can do is decide how much money to give them and who to give it to. As Tweetypie pointed out, if the rock is to your right it's different. You can wait to see what he does before making your decision. If he puts money in, you know he has a winning hand, so you obviously fold if you don't have one yourself. If he folds, it turns out that you should always call the maniac. Following this strategy, you win a small amount per hand. Quote Link to comment Share on other sites More sharing options...
Tweetypie05 Posted May 2, 2007 Share Posted May 2, 2007 Re: Another interesting game ... Cheers for that Slapdash! I told you I know nothing... can't believe the odds though... would have thought there could be a way to maximise your wins. Obviously in the 2 maniac scenario there does not appear to be a good outcome. How could you play this and win? What cards would you need to call with? T-A? J-A? Or is there really no winning strategy...???? My maths is isn't up to this!!! :ok Quote Link to comment Share on other sites More sharing options...
GaF Posted May 2, 2007 Share Posted May 2, 2007 Re: Another interesting game ... The kicker doesn't play mate - If you have an A or K you have the best hand (the ABSOLUTE nuts). If you don't you have the absolute worst hand......There are effectively only 2 hands....it's almost like tossing a (biased) coin, wiyh a known bias (Unless I've totally misunderstood) If you have any A or K, you should not fold under any circumstances - you should raise under all circumstances - at worst case you split the pot.... Quote Link to comment Share on other sites More sharing options...
Jimany Posted May 2, 2007 Share Posted May 2, 2007 Re: Another interesting game ... What cards would you need to call with? T-A? J-A?The kicker doesn't play mate Three players. Everybody starts by anteing $10. Each player is dealt just one card.I may write a program later when I'm boggled before the Milan game to see if I can find out some rough average winnings over # of hands for a few seating arrangements/player types. I would imagine the Maniac will have the best of it however with the constant betting Quote Link to comment Share on other sites More sharing options...
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