TD last-draw strategy tool

[DeathDonkey]

Optimum for whom? I'm out of my element in game theory discussions but this tool seems most useful for establishing a benchmark set of plays for one opponent and then figuring out how to best beat them. Basically what I am trying to learn at the table is how do each of my opponents play their good rivers, pairs, A/K highs, etc. so I can figure out how to play the river myself. This tool makes sure if I can do the first part I get the second part exactly right.

-DeathDonkey

[AffleckKGB]

Can someone explain why the expected values add up to 5.5 if additional bets might be going in on river?

[MarkGritter]

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Can someone explain why the expected values add up to 5.5 if additional bets might be going in on river?

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Any bets gained by one player must be lost by the other. If I find a bet or raise that increases player B's expectation, it must be because player A loses more.

[MarkGritter]

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FYI, the dates at the bottom of the page say '05, not '06

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I am so not ready for 2007 to start.

[AffleckKGB]

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Quote:
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Can someone explain why the expected values add up to 5.5 if additional bets might be going in on river?


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Any bets gained by one player must be lost by the other. If I find a bet or raise that increases player B's expectation, it must be because player A loses more.

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In the situation where player A check/folds every card except where he pairs an 8 and then he will bet/call, and meanwhile, B is betting every card, shouldnt player B's EV be greater than 5.5?

[MarkGritter]

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In the situation where player A check/folds every card except where he pairs an 8 and then he will bet/call, and meanwhile, B is betting every card, shouldnt player B's EV be greater than 5.5?

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Yes, A's strategy would have negative expectation since he would never win the pot, only lose money:

2KF 3KF 4KF 5KF 6KF 7KF 8BC 9KF TKF JKF QKF KKF AKF : -0.143
2kBF/bRC 3kBF/bRC 4kBF/bRC 5kBF/bRC 6kBF/bRC 7kBF/bRC 8kBF/bRC 9kBF/bRC TkBF/bRC JkBF/bRC QkBF/bRC KkBF/bRC AkBF/bRC : 5.643

But the total EV is still 5.5 big bets, because the extra bets that A loses is exactly balanced by the extra bets that B wins.

In every possible case, somebody wins the 5.5 bets in the pot plus an additional N bets (possibly N=0) while the other player loses N bets. So EV(A) + EV(B) = 5.5 + N + (-N) = 5.5 in each individual case, and thus must equal 5.5 for the weighted sum of probabilities as well.

[AffleckKGB]

If Player A has KF for a certain card, then it is irrelevant whether Player B has bF or bC or bRF for that card, right?

[MarkGritter]

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If Player A has KF for a certain card, then it is irrelevant whether Player B has bF or bC or bRF for that card, right?

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No, because each player makes his decision based on the card he receives--- there are two cards dealt.

If player A has KF for all cards then player B's bXXX decisions are irrelevant, but if player A has at least one Bxx line then all of player B's bXXX choices will be used.

[gergery]

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Optimum for whom? I'm out of my element in game theory discussions but this tool seems most useful for establishing a benchmark set of plays for one opponent and then figuring out how to best beat them. Basically what I am trying to learn at the table is how do each of my opponents play their good rivers, pairs, A/K highs, etc. so I can figure out how to play the river myself. This tool makes sure if I can do the first part I get the second part exactly right.

-DeathDonkey

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Optimal from a game theory point of view. If I were player A and forced to tell you my strategy ruleset and I knew you would find the optimal way to play against me, then I could adjust to that style you are using, and then you adjusted again to me, then we would eventually reach equilibrium fairly close to the ruleset I posted above (assuming pure strategies; using mixed strategies will change things a bit).

Essentially, it mimics the decisions that two excellent players will end up using against each other over the long run, as it minimizes how exploitable you will be.

However, you don't always play against excellent game-theoretically perfect opponents, and so deviating from the game theoretic equilibrium usually can improve your profit as you shift strategy to capitalize on the specific mistakes your opponents make. I'd guess that most opponent are too passive and fold too much at a first go round with the tool, in fact.

And I completely agree that the tool is outstanding for this purpose, and of greater value here than in game theory. But the game theory is a good starting point.

-g

[SellingtheDrama]

And that's why randomization of your actions within the decision matrix is a good thing [img]/images/graemlins/smile.gif[/img]

Generally if I have two actions that I feel are relatively equal in EV terms, I'll elect to go with the one that either a)fits the line of a hand I'm trying to represent (whether or not I have it) or b)is more likely to confuse my opponent.