How About This Game Theory Problem
 

So today when I got into the 25-50 blind no limit, nine handed game at the Bellagio they told me there was a seven deuce bonus. Win the pot with 72, even without a flop and every player must give you $200. Which brings up this question.

Seven players fold to you in the small blind. You have 2000 more in your stack and must move all in or fold. With what hands should you? What should the big blind call you with? If I'm reading the chart in the Mathematics of Poker correctly, the move in hands would normally be any pair, any ace suited, K7 or better suited, Q8 or better suited, J9 or better suited, T8 or better suited, 98suited, 87 suited, A7 or better offsuit, KT or better offsuit, QT or better offsuit, or JT offsuit.

The calling hands would be fives or better, A8 or better suited, KJ or better suited, AT or better offsuit, and KQ offsuit.

Does the $1600 bonus (plus your extra $200 risk) change that to any signicant degree?

Re: How About This Game Theory Problem
 

I'll take a swing at this. Add in 27 and 97s for raising all in. throw in 33-44 (not too sure about this), A7s, and 27 for calling.

Re: How About This Game Theory Problem
 

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.

Re: How About This Game Theory Problem
 

I was incorrect about calling with 72, wouldn't be getting the pot odds even with such a wide range, but yes move all-in with 72, and add A7s to call list, why add A9o but not A7s?

Re: How About This Game Theory Problem
 

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I was incorrect about calling with 72, wouldn't be getting the pot odds even with such a wide range, but yes move all-in with 72, and add A7s to call list, why add A9o but not A7s?

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I ran sims on PokerStove and A9o got over the threshold as a call hand but A7s did not.

Re: How About This Game Theory Problem
 

I assume you have only 200$ in your stack, not 2000$ as I still dont see why must you must move all in or fold?

Am I missing something?

Re: How About This Game Theory Problem
 

It's a hypothetical situation, you have 2k, and some rule says it's folding or shoving only.

(right?)

Re: How About This Game Theory Problem
 

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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

Re: How About This Game Theory Problem
 

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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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I assume you mean that your opponent in the BB will of course call with 72off. This is retarded.

* He doesnt get the money unless he wins!

Re: How About This Game Theory Problem
 

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. I did not use any programs etc to come to my decision (which is an error in itself) I used logic. I made a mistaken with calling with 27 without doing a quick run of pot odds, which you would not be getting enough of.

Re: How About This Game Theory Problem
 

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.

Re: How About This Game Theory Problem
 

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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.

Re: How About This Game Theory Problem
 

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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

Re: How About This Game Theory Problem
 

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.

Re: How About This Game Theory Problem
 

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).

Re: How About This Game Theory Problem
 

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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.

Re: How About This Game Theory Problem
 

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:

Re: How About This Game Theory Problem
 

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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.

Re: How About This Game Theory Problem
 

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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.)

Re: How About This Game Theory Problem
 

ahh that makes perfect sense, thank you robk.

Re: How About This Game Theory Problem
 

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

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How much is the extra $1,600 to win on top of the $2,000, from an outdraw worth?

Say you expect to call and win 1/3 times, then it indeed would cost you $4,000 before you pick up $3,600.

Is the basket of raising hands, going to make you that much of a dog, that often though?

Re: How About This Game Theory Problem
 

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

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How much is the extra $1,600 to win on top of the $2,000, from an outdraw worth?

Say you expect to call and win 1/3 times, then it indeed would cost you $4,000 before you pick up $3,600.

Is the basket of raising hands, going to make you that much of a dog, that often though?

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Plug it into a calculator. PokerStove, specifically.

Re: How About This Game Theory Problem
 

So the calculator will tell me the basket of raising hands?

You know this is funny, it's meant to be a game theory thread, a question gets asked, answer is plug it into a black box ie PokerStove. I read to, that actually it shouldn't change things much, but all in all, the answer's aren't really illuminating.

So the answer to my question is actually, yes you are too big a dog, on average. The tempting proposition is going to marginally loosen up play, but may unduly influence players into mistakes.

Hopefully asking the question, cleared things up for someone though. Understanding it, is fundamental for understanding starting hand guides.

But, if a player is short-stacked....

So is there a way to make more money out of 72o, by being shallow stacked and having it as a calling hand, not just a raising hand?

Re: How About This Game Theory Problem
 

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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:

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You must play 77. It's going to cost you $200 if 72 wins. You must stop 72 from winning.

Re: How About This Game Theory Problem
 

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So the calculator will tell me the basket of raising hands?

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The original post tells you the basket of raising hands.

Re: How About This Game Theory Problem
 

Justin, you and Spence have PokerStove, and it's 'obvious' to you about that normal basket of raising hands. Other ppl with less info than you, but read the thread, so actually just saying "A9 or A7s and 72o" added is not going to help everyone, as much as you may assume.

If a question is theory, not a purely practical playing one, it'd be nice to see more working and explanation. Your posts are not going to be as clear to everyone, as you might hope, even if the 'stalwarts' know exactly.

I've re-read the early posts, and I do not see, the full compliment of raising hands, only candidate additions.

Also, actually it'd be interesting to know the averaged out odds over basket of hands, as it tells you what stack size, 72o becomes a call with.

Obviously telling someone to re-read previous is simpler than answering simple questions. Perhaps knowing answers is more important than thinking? But then why would David phrase the question as "Game Theory" problem, rather than a practical adjusting to game. Apolgies in advance, if I have misunderstood the point of the forum.

Re: How About This Game Theory Problem
 

If I had Sklansky's reputation for being a squeeze bunnel, I'd move in with 7,2. It would work.

Re: How About This Game Theory Problem
 

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You know this is funny, it's meant to be a game theory thread, a question gets asked, answer is plug it into a black box ie PokerStove.

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computer simulation is the answer precisely because it is a game theory thread.

pokerstove on its own isn't quite enough unless you do a lot of extra work by hand.

you add 72o to your pushing range. the big blind adjusts and adds A9o to his calling range. now you probably have to remove A7o from your pushing range. etc. etc. etc.

the method is pretty simple, but its a lot of work without a specialized program for it. (unless the ranges change very little, which might be the case)

justin, did you check to see if A7o should be removed from the pushing range?

Re: How About This Game Theory Problem
 

also, the fact that sklansky said that you have $2000 more in your stack (for a total of 40.5 big blinds) suggests that he's actually done the math and A7o would have to be removed from the pushing range... theres might be some kind of chain reaction there that actually changes the ranges a lot more than one might expect. i might write a program to calculate this over the next few weeks. i'll report back if i do.

Re: How About This Game Theory Problem
 

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If I had Sklansky's reputation for being a squeeze bunnel, I'd move in with 7,2. It would work.

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not pushing with 72 would be terrible, regardless of your reputation.

Re: How About This Game Theory Problem
 

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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:

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You must play 77. It's going to cost you $200 if 72 wins. You must stop 72 from winning.

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Agreed when you're pushing. The comment about 7's losing value was for "non-Push" conditions, normal practical play.

Re: How About This Game Theory Problem
 

Now that's interesting! I do agree, that a tool to crunch the numbers is useful. I'll list the "pushing range". Also the Pokerstove 'odds' for 72o against the anticipated pushing range.

The reason to ask verbal questions, is to try and get to heart of it, and learn from the question some understanding that may be applicable in other situations.

So we have from David's quote of Maths of Poker :

AA.22
Axs
KQs..K7s
QJ..Q8s
JTs..J9s
T9s..T8s
98s..87s
AKo..A7o
KQo..KTo
QJo..QTo
JTo

Added : 72s, 72o ; Spence Suggests 97s

Calling Hands are stronger, as per Gap Concept

AA..55
AKs..A8s
KQs..KJs
AKo..ATo
KQo

Added: A9o


So why isn't K7o a Push?

As I understand it, because 72o is not a call, Dominating 72o has no special value.

But, becayse the BB may have 72o, then we lose approx. an additional $2.61 every time we fold. That means raggy hands holding a 7 or a 2, are safer folds, than non 7 hands (reduced chances of running into 72o).

That explains why A9o becomes a call. It argues against 97s becoming a Push. Does a hand like K9o, cross the threshold from marginal loss into 'crying' Push land?

It is actually still pretty unlikely that the BB will hold 72, about 1.3% by previous calc.

Now if the BB was shorter stacked, and 72o became a calling hand, that might not affect things much really, because Push hands with 7 or 2, would be Dominated more often than they Dominate 72.

Probably I've missed some candiate hand or something, please point it out!