How About This Game Theory Problem

[creedofhubris]

Consider showing a seven after you move in with A7, K7s, or 77, or a deuce after you move in with A2s, if that play is legal.

[creedofhubris]

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Consider showing a seven after you move in with A7, K7s, or 77, or a deuce after you move in with A2s, if that play is legal.

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Turns out this is a bad idea; the extra money you win when he calls your decent hands with just about any 2 do not make up for the amount of money you lose when he calls your 72o with just about any 2.

[eviljeff]

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Consider showing a seven after you move in with A7, K7s, or 77, or a deuce after you move in with A2s, if that play is legal.

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Turns out this is a bad idea; the extra money you win when he calls your decent hands with just about any 2 do not make up for the amount of money you lose when he calls your 72o with just about any 2.

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um, so don't show any cards when you have 72

[seemorenuts]

btw, 72 vs 72 wins $200 from each player, just another reason to play 72. A chopped pot is a win, but not always e.g. with a (better) made flush.

[RobNottsUk]

Not really Game Theory as I'm not presuming perfect play by opponent, but as noone mentioned this so far.

The abscence of prior raises implies 72 has not been dealt to other players. So the BB is slightly more likely to have 72 than usual, but on other hand there's no 'real' hands out there either it seems,so does this balance out? I've no idea [img]/images/graemlins/smile.gif[/img]

If we fold, then there's (2x4x4) 32 'fatal' combo's out of 2652 which cost us $200, beyond the $25 surrended.

Assuming we do not have a 7 or a 2 in our hand, there's actually 32/2450 'kills'. So I think folding, 'costs' $2.61 more than usual.

So if we know, against that player (remember they might call or fold more frequently than theoretically correct), our expecation neutral hands, are going to include all the ones that would 'cost' $2.61 as well as the break evens and up (taking into account rake).

[jogsxyz]

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Not really Game Theory as I'm not presuming perfect play by opponent, ....

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Where does it say that exploitive strategy is not part of game theory? Many 2+2'ers seem upset when anyone suggests one should deploy a non-optimal strategy.

[RobNottsUk]

It doesn't there, but I have read elsewhere that "Game Theory" seeks winning strategies against optimal play by opponents. Obviously I do not want to upset anyone, and so discretion is the better part of valour etc. But practical effect on play, is interesting to me.

According to my approximate calcs, with 8 opponents there'll be a '72' killer hand, around 10% of time, which benefits from invisibily inflated pot (to tune of $1,600).
Rather than focus on well covered details, I was chucking an idea out, and see if anyone could make anything of it, from a different angle.

As mentioned, a Ueber-Dominating pair of 7's is not going to gain much value in practical terms, as a set is very unlikely when you most need to win, so 72o will be a superior hand, under non-Push conditions. Obviously, folding a pair 7's will be easier than 8's as you will face 72o far less often! :lol:

[Justin A]

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Obviously you should move in with 72 now.

Your opponent should only add A9o to the calling hands. He cannot call with 72.

I assume that if your opponent only calls with 12 more combos that it should barely change the move-in hands if at all. So no, the $1600 bonus does not change that to a significant degree, other than moving in with 72 of course.

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of course you call with 72

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If your goal is to lose money, then sure, call in the BB with 72.

[Robk]

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Thats weird how A9o went over the threshold and not A7s, you would think you'd rather play a hand that dominates the only other hand that would supposedly be played.

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when you have the A,7 it decreases the chances your opponent has raised with 7,2. (because he can only have 12 combos of 7,2 rather than 16.)

[Spence]

ahh that makes perfect sense, thank you robk.