Playing perfect poker with the cards face up

[Henke]

My guess is that the hand would end up heads up between SB and BB. I think that most hands played (perfectly) with all the cards face up would end up heads up, because there would (almost?) allways be a preflop raise by the best hand.

This is because if all played perfectly, you could easily say that the biggest dog (if not in the blinds) would throw his hand away.

For example, the 6[img]/images/graemlins/spade.gif[/img] 5[img]/images/graemlins/spade.gif[/img] would have to assume that T[img]/images/graemlins/spade.gif[/img] T[img]/images/graemlins/diamond.gif[/img] would be thrown away, and after that A[img]/images/graemlins/heart.gif[/img] 3[img]/images/graemlins/diamond.gif[/img] and so on...

Disclaimer
My analysis is wrong in that it uses twodimes (and hence should require that all players that join the pot go all in), which creates a bias for KJ. A more correct analysis would require analysis of the flop vs. all possibilities of opponents instead.

Or am I far off?

[t_perkin]

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You may be thinking what is the point? if you can't calculate the answer then what is the point in knowing *how* to calcualte the answer? well I am afraid I am interested in things like this...


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and you replied

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I still don't see why this is particularly useful...If someone points out to me why it is, then maybe we can do something to reduce the complexity (it seems like the tree should be very suitable for significant pruning).


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so yes this is not an immediately applicable application to your friday night game. But then i did state this at the start of the post, and this forum is for poker *theory*.

But if you like I will now try and justify why *I* am interetested in this (and things like it).

First up I am an academic, and academics were put on this planet to think about things that are not immediately applicable to everyday life. You may not like it, but it pays the rent (unfortunately my poker play does not..) and I love it so that is me.

Secondly I think that by understanding the extremities of the game and the components of the game it makes me a better player (although still not a very good one).

so there we go.

Now as you state, this does look like a prime candidate for a pruning algorithm to reduce the search space. It may be that this becomes a very computationally feasible problem. Suddenly this would be the basis of a perfect player in real life poker. The other major component would be modelling opponents for two things - modelling the weaknesses in their game (to make you *optimise* your winnings) and model the way they play to help ascertain the cards that they hold.
SparBot - the best AI player in the world does something similar. Except that rather than searching the whole search space it uses monte carlo simulations (i think? or does it select simulations with a heuristic?) . It also plays a (nearly/maybe) world class heads up game and it *doesn´t* do *any* player modelling. They are attempting to make a perfect player, before they make it optimal. and just playing perfectly seems to be enough to make it almost world class. Just goes to show how valuable the mathematics of poker is.

Tim

[karlson]

Tim,

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Suddenly this would be the basis of a perfect player in real life poker

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But it wouldn't. Because the game is so much different with the cards face down, that this research could easily be absolutely inapplicable.

I am an academic too. We still try to work on problems that will somehow in the future be applicable. Approximations and simplifications are great, assuming that we can somehow relate it to the real thing later.

I find the research on Poki and Sparbot very interesting too.

Now, actually, you may be right. It may be that the right way to go about modeling real poker is actually to look through the entire, or almost entire, space, like we we talking about for the faceup model. In that case, the same pruning algorithm could apply (however notice we've increased the space size by several orders of magnitude), and we will have achived something. Or maybe once we figure out that we can't look at the whole space for face up play, we'll reject this idea for real poker. If this is the point of view you want to approach it from, great! However, saying that the solution, as is, is a guide to perfect play, is misleading.

Now, it seems that you are most interested in opponent modeling. If you want to work on opponent modeling in a sparbot-like system, this seems like both a feasible and applicable task. I thought about doing something similar myself, but have not found the time. I still have some ideas about it.

Victor.

[t_perkin]

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I am an academic too. We still try to work on problems that will somehow in the future be applicable.


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But what about all those economists!? [img]/images/graemlins/grin.gif[/img] - no really I am only joking.

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In that case, the same pruning algorithm could apply (however notice we've increased the space size by several orders of magnitude),


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yes absolutely - the search space increases considerably , but it is still the same algorithm.

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However, saying that the solution, as is, is a guide to perfect play, is misleading.


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Yes I am not suggesting for a minute that it is the "magic key" to a automated player (bot). But I think nobody would deny that *if* (big if) this could be accomplished then many of the key features of a solution to this could be applied to face down (normal) p#ker
Sorry if I was misleading though.

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Now, it seems that you are most interested in opponent modeling.


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yep! what I would *really* like to do is get hold of a pokerroom's database and do some serious data mining, would be great to try and train some neural nets or just generate some real life versions of the twodimes stats or a million other things. So many possibilities!

Would love to know your thoughts on player modelling, drop me a private message if you can be bothered.

Tim

[ACPlayer]

If all the cards are face up and every one played mathematically correctly (there is no psychology or mixed strategy here) the game would be a break even game (less the rake ofcourse).

[daryn]

why don't you just read my post? if every player played perfectly, the hand would play out as i described.

[Henke]

I think you put the two TT hands out of the picture too early. Yes, the T[img]/images/graemlins/spade.gif[/img] T[img]/images/graemlins/heart.gif[/img] wouldn't have odds to call, since it can only hope for a split pot, but the T[img]/images/graemlins/club.gif[/img] T[img]/images/graemlins/diamond.gif[/img] has already put money in from SB. If we include that hand in the twodimes analysis, we will see that 6[img]/images/graemlins/spade.gif[/img] 5[img]/images/graemlins/spade.gif[/img] would be a dog in this hand and wouldn't have odds to call. Yes, T[img]/images/graemlins/club.gif[/img] T[img]/images/graemlins/diamond.gif[/img] is the "worst" dog of all three, but if 6[img]/images/graemlins/spade.gif[/img] 5:spade would call, and if we expect K[img]/images/graemlins/diamond.gif[/img] J[img]/images/graemlins/diamond.gif[/img] to raise, it will just need to win more than 1.5/6=25%.

If we where to analyze favorable flops instead, I think the TT would be even more likely to call, since the KJ wouldn't get two "free cards" to pair one of his cards.