ha-he-ha!

sorry - i just posted this on the "texas hold'em general" forum by mistake - i meant it more as a "quiz" for the eggheads on this "poker general theory" forum, so please forgive me for making a duplicate posting:-


in my home game i find that there are often thirty second pauses in the action while someone shuffles, or goes to the can, or brings out sandwiches, or tells a joke, or something, and, as i'm sure you would agree, there is usually very little to do except count your and your opponents' chips


so, to fill the gaps, here's an interesting new game i have devised that you can play heads-up with a good friend during all those short breaks in the main game - it only takes a few seconds to play - in true sklansky tradition, i call it "haven hi-lo hold'em hands", or the more snappy "ha-he-ha!" for short


get your friend to deal out three pre-set hands face down: AA, KK, and AK, in any positions on the table - remember to explain all the rules to your friend and to emphasise that as you will be making all the choices it is vital that you do not know which hand is which, or which suited cards are used in each hand, to avoid any possible later argument that you could have cheated in any way - (in fact, it might be a good idea to type up the rules before introducing the game, and get your friend to sign that the rules were seen and understood pre-game - always carry several copies of the rules with you as you can play this game on the train, on the bus, on the plane, in the cafe, at the track, on the street corner, etc, etc)


now, first, your friend has to ante $10


you then choose any one of the three hands for your friend to play in the game by pointing at it - it is important that you do not touch their hand of cards


your friend turns over the top card of their hand, only


you then match the pot and choose either one of the remaining two hands, calling out that you are betting it to win the hand high or low, before you turn over your two cards


you turn over your two cards


your friend turns over their second card and the winner of the hand, high or low, as you have nominated, takes the $20 pot


for example: your friend reveals an Ace - (obviously, you know he can't have KK and it's 50%/50% whether he has AA or AK - if you happen to have picked KK for your hand then you would beat your friend's AK high or your friend's AA low - if you have picked AK you would beat his AA low - if you have picked AA you would beat his AK high) - in this example you decide to call "low" - you turn over KK - your friend reveals their full hand as being AK - so you lose, and your friend has to shout out "ha-he-ha!" to indicate that your friend has won the pot - (always encourage loud shouting as the louder the shouts, the more fun will be generated, leading to others queueing up to play with you)


i calculate that by using optimum strategy you should win over $3 per hand played, but, of course, you should throw in some strategically incorrect calls to try to cover your tracks for a while, before you are obliged to leave town


(i have used the term "your friend" throughout to be politically correct and gender-neutral - the one downside of the game is, naturally, that later, after your friend figures out what just happened, your friend ain't your friend no more


but then of course you have to remember that in the grand scheme of the gambler in the sky: $3 will always be $3 whereas friendship is only as of the blink of an eye)


what strategy would you suggest using in practice to keep your winnings to only $1 or $2 per hand, in order to prolong the game?

as there have been no replies to this quiz, although i did try my best to make it quite difficult for you to see where the "twist" is, obviously i must have made a mistake in attempting to dress the whole up into a humorous story, as this must have camouflaged the real strategy question beneath the excess flannel - sorry! - my mistake


in case you now wish to have an attempt at the math involved i will wait until tomorrow to tag the full answer on to this message, as, if i revealed the carefully hidden "twist", which is the whole basis of the problem, the answer would then be just a matter of some simple calculations

I can come up with an EV of $2.50 by calling high every time. What am I missing?


Also, consider shuffling the six cards and truly dealing them rather than arranging three different hands on the table. This will make it seem more like a game and less like a magic trick. Dealing this way does result in some distributions of (AK AK AK) but I do not know how often this will come up compared to (AA, AK, KK). I suppose you could have a rule that AK v. AK is a push and you keep anteing until someone wins. Bigger swings, but maybe the fish don't pick up on it so quickly. In addition, you could mix up your high and low calls when you see an A as long as you keep the number of each fairly even.


Looking forward to your results.


Matt

well it seems to me that you must have realised that "ha-he-ha" is really just a new poker-orientated variation of the old XX, OO, XO con trick - so therefore your profit with best strategy will be $3.33 per hand


but this is how you hope your friend sees the bet (perhaps with just a little bit of "help" from you!!):


"if he shows an Ace, he has AA or AK

so you have KK and AK or AA to choose from


if you pick KK and he has AK you need to call Hi to win

if you pick KK and he has AA you need to call Lo to win

if you pick AK and he has AA you need to call Lo to win

if you pick AA and he has AK you need to call Hi to win


therefore whatever you call you break even in the long run as every call is a 50%/50% shot when he shows an Ace


if he shows a King he has KK or KA

so you have AA and KK or KA to choose from


if you pick AA and he has KA you need to call Hi to win

if you pick AA and he has KK you need to call Hi to win

if you pick KK and he has KA you need to call Hi to win

if you pick KA and he has KK you need to call Lo to win


therefore if you call Hi every time he shows a King you win $20 every four hands in the long run


therefore in total you win $20 every eight hands in the long run


therefore you win $2.50 per hand in the long run"


hence, your overall best strategy is to tell your mark that instead of you matching his $10 bet YOU WILL BET$12.50 EACH HAND!


now he will think that the bet is evens in the long run and he will happily bet away at every opportunity, while you gradually milk him out of $0.83 per hand played, in the long run! this should work out at about five bets an hour profit for you - and, with a bit of luck, he might even suggest increasing the stakes after he has lost a hundred bucks or so, thinking his luck will change in this apparently even game


at this win-rate who needs hold'em when you have ha-he-ha in your armoury?


ha-he-ha!

you, sir, are a lateral-thinking genius in terms of the presentation!


because of your comment i have revised the rules somewhat, and have expanded the game to include your ideas - plus a further twist that you will love that will help even more!


i have it in pen on paper so far, and will post it above in a brand new thread in the very near future


thank you very much for the highly inspirational post