Using "Game Theory" in a common limit hand

[Aves]

Disclaimer:
- I use the term "game theory" to mean "optimum play", not sure if this is right or not

A common limit hand I encounter seems to go as follows: I raise in early position, only BB calls. He checkraises me on a T62 rainbow flop.

What I want to know is, what percentage of the times I don't have a pair should I be trying to bluff him off his presumable pair.

My Assumptions:
- My raising range is JJ+ and AJ+, meaning 24 combos of overpairs and 48 combos of A-high hands (range chosen for simplicity)
- BB checkraised with 1 pair, tens or lower
- The times BB improves his hand cancel with the times I improve my A-high hands; i.e. we can assume that neither BB nor I will improve our hands by the river

If I just call the flop checkraise and raise his turn bet, BB will be getting roughly 8:2 to call my turn raise and river bet. Therefore, I should be showing up with an overpair about 80% of the time to be "unreadable" when taking this line, correct?

If I 3-bet his flop checkraise, he'll be getting roughly 7:2 to check-call my turn and river bets. Therefore, to be "unreadable" when taking this line, I should show up with an overpair about 77.8% of the time, right?

It seems either line produces about the same percentage, so I'll just use 80% for simplicity. Since there are 24 combos of overpairs, I should only bluff with 6 of the 48 A-high hands, i.e. a frequency of 12.5%.

Does my logic for this example seem reasonable? Does anyone have any suggestions for adjusting the frequency i came up with, improving the example, or adding any variables/complications? Thanks for any replies.

[ocdscale]

[ QUOTE ]

- The times BB improves his hand cancel with the times I improve my A-high hands; i.e. we can assume that neither BB nor I will improve our hands by the river


[/ QUOTE ]

Not sure I agree with this. Villain has 5 outs to improve to 2 pair / trips and you have 6 outs to improve to a higher pair. This may be balanced against the times when he has you dominated, but I dunno.

That said, the rest of your calculations look spot on.

[Mike Gallo]

What I want to know is, what percentage of the times I don't have a pair should I be trying to bluff him off his presumable pair.

You need to balance this out by asking yourself what percentage of the time will villian fold.

If this hand takes place against someone who doesnt fold, game theory does not apply.

[juku]

Some comments:
1.) Recommended reading for this question:
"The Mathematics of Poker" (large part of the book deals with mixed strategies (including bluffs) which make the opponent indifferent from calling or folding) or the corresponding chapter in "The Theory of Poker"
2.) The basic idea is to make Your opponent indifferent from calling or folding.
Assume You bet in a 3 BB pot at the river as a bluff. Your oppenent is indifferent from calling or folding if the bluffing ratio (between value bets and bluffs) is the same as the odds You are laying.
With bluffing ratio ¼, if he always calls he gets -0,8 + 0,2 = -0,6
and always folding has expectation of -0,2*3 = -0,6 (if You bluff him).
3.) Game Theory always applies.
The advantage is that Your opponent cannot exploit Your strategy in any case.
If Your opponents see You folding 2/3 of the times You get check-raised on a T-high flop they could easily exploit You by always CR in this situation.
4.) I think one interesting question is to select the hands on the flop You plan to bluff with at turn or river.
In this specific scenario I would re-raise on the flop with some/maybe all of my suited hands with backdoor draws. This obviously dominates raising with offsuit non-pairs.