[mykey1961]

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Ok here is what I just don't seem to understand.

You apply a formula, get an answer. But do you do anything else to verify it actually answers the question?

Your P1
[1,83] fold
[84,100] call

Your P2
[1,74] Check
[75,100] Bet

My P1
[1,56] Fold
[57,100] Call

My P2
[1,11] Bet
[12,78] Check
[79,100] Bet


My P1 vs Your P2
EV = -0.094545

Your P1 vs My P2
EV = -0.118182


My Strategy wins 0.011815 Ante's per hand from yours while rotating positions.



Maximal against your P1 "P1MO"
[1,65] Bet
[66,92] Check
[93,100] Bet

Maximal against your P2 "P2MO"
[1,83] Fold
[84,100] Call

Your P1 vs Your P2
EV = +0.023636

Your P1 vs P1MO
EV = -0.447879

P2MO vs Your P2
EV = +0.023636

Maximal would win 0.2357575 Ante's per hand from your strategies while rotating positions

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Mykey , you got to be kidding me . Why on earth would you restrict player one to check call with only 57-100 ?



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If P2 is playing optimal
[1,11] bet
[12,78] check
[79,100] bet

then P1 is indifferent to calling with [1,78] and calls with [79,100]

To find optimal for P1, you need to find which [x,78] x to maximize P1's EV against any strategy for P2.

x happens to be 57.

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If player two is betting [0,11] and [89,100], then player one "could" check-call with any number from [12,88] since he will always be able to beat 11 numbers and lose to 11 numbers .


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You can't fine tune a strategy to just one opponent (even if that opponent is optimal) and call it optimal against all.

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Your strategy for player one is NOT optimal !!

Here is a better strategy for player one than the one you proposed .

Player one check calls with [12-88] given that player two bets with [0,11] and [89,100] .

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Your P1 [12,88] Check else fold vs my P2 [1,11] and [79,100] bet else fold gives:
P1 EV = -0.226263

My P1 [57,100] call else fold vs your P2 [1,11] and [89,100] bet else check gives:
P2 EV = +0.090909

My strategy for P1 and P2 vs your's for P1 and P2
Your total EV = -0.067677 per hand when rotating positions

Can you find a strategy against my P1 which gives P2 an EV > 1/9?
Can you find a strategy against my P2 which gives P1 an EV > -1/9?