Applying Elindaur's Concept

[elindauer]

[ QUOTE ]
I like the way you're applying this. Rather than giving our specific hand a range of options, we give our range of hands an option and then see where our specific hand falls. This approach probably makes progressively less sense as we approach the river, but since both players know very little about each others' hands, it's nice to think about this taking villian's limited knowledge into consideration. Once the range is complete, we have to make sure that villian cannot exploit our new strategy if he knows it.

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This last line is critical. I think what you'll find is that to prevent being too predictable in which hand types we raise and which we call, we're going to have to keep shuffling parts of each hand back and forth. Eventually, I suspect that all the hands will be best handled by a mixed strategy. We have to move some draws out the raise into the call, but then we have to move some more hands from the call ot the raise... there just aren't that many hands to go around. See vkh's specific thoughts on how this could happen to KQ for more details.

-eric

[elindauer]

I haven't checked your numbers, but I wrote my post quickly so I'm sure you're right. The 228 total numbers implies that we need to add 14 combos to the raise category, and 4 to the call category.

More to the point, your analysis suggests that when we do chose to play, our opponent still has a fair amount of equity in the pot. I'm not sure exactly how this effects our overall fold, call, raise mixed strategy, but I'm guessing it means we have to call more and raise more, perhaps even more than I'd initially suggested. Perhaps not though. Maybe somebody with some math experience can help us here. Calculating the optimal numbers for our overall strategy is crucial.

thanks,
Eric

[DeeJ]

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The big blind is getting 4:1 to bluff, so we're going to need to continue quite often to stop him from making more money than he deserves from a bet-every-time strategy.

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Nice post, but aren't you making a big assumption that villain is betting here every time? If he is, sure, we can exploit that by knowing our chances pretty precisely through probability/game theory. But if villain is betting half the time and checking half the time, and that action is based on his hand holding and the flop, this all becomes far more meaningless? Or have I totally misunderstood?

[elindauer]

[ QUOTE ]
[ QUOTE ]
The big blind is getting 4:1 to bluff, so we're going to need to continue quite often to stop him from making more money than he deserves from a bet-every-time strategy.

[/ QUOTE ]

Nice post, but aren't you making a big assumption that villain is betting here every time? If he is, sure, we can exploit that by knowing our chances pretty precisely through probability/game theory. But if villain is betting half the time and checking half the time, and that action is based on his hand holding and the flop, this all becomes far more meaningless? Or have I totally misunderstood?

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In a perfect game theory solution, it won't matter what frequency villian bluffs. I only use the case that the villain always bluffs it provides such an interesting bound to the problem.

In other words, if our solution has us folding enough that it would be always correct to bluff, it's clear that we haven't reached a game-theory-optimal solution.

On the flip side, if we play so much that it is never correct to bluff, we've gone too far. This only tells us that we must fold sometimes though, which isn't nearly as interesting as knowing that we must play at least 80%.

thanks,
eric

Hi Deej,

You are correct. This is what I was getting at in my other post. Let's say that somehow you know that the big blind only bets with top pair or better. The game theory solution is then sub-optimal, as you should be folding many of the hands that we had advocated calling or raising with. If he only bets TPTK or better, then the game theory solution gets even worse. It may turn out that most players you play with tend to bet far too little on the flop in the situation presented in this thread. If you're in that type of a game, you'll be doing far worse than you could if you play the game theoretic optimal strategy. But if you don't know your opponent's betting tendencies, and/or he's a good player, the game-theoretic optimal solution is an attractive option. At the very least it's a good starting point strategy against an unknown player who appears to be good.
It's the least exploitable strategy and will usually not be too far off.

But yes, if you want to maximize your earn in practical poker situations you can and should do better by knowing your opponent and adapting your strategy accordingly.

-v

[elindauer]

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It's the unexploitable strategy and will usually not be too far off.

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FYP, I believe.

It may sometimes be well short of the optimal solution that makes the most money given your poor playing opponents' mistakes though. A solid player should know the game theory solution so he can play in bigger games. A good player will know the optimal solution that takes advantage of a typical opponent's mistakes. A great player will know both.

-eric

[Phogster]

[ QUOTE ]
The poster wanted to know what to do with KQ. I've tried to show how we can use game theory to get at the answer, a very complete, basic-strategy-like answer which would be great against unknowns and against good players who can adjust to our play. I suggest:

FCR {38, 19, 43}

specifically,

raise: KcQc, KcQh, Kc Qd, Kc Ks, Kh Qc, Kd Qc, ks Qc
call: Kd Qh, Kd Qs, Kd Qd
fold: Kh Qd, Kh Qh, Kh Qs, Ks Qd, Ks Qh, Ks Qs


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I know he asked for KQ, but mixing suited KQ with the unsuited doesn't look right. e.g. i'd rather see Ks Qs in the raise group and Kh Qc in the fold group, if anything.