Doubt about an old BigFiszh post "Theory question in three bet pots"

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Doubt about an old BigFiszh post "Theory question in three bet pots"

First of all sorry for asking questions about such an old post :-(, the post was this:

"I've struggled to see how our opponents bluffs preflop really "cost"
him anything since our opponents' expectations with his bluffs preflop
should be close to zero. "
That´s exactly the point, I really don´t know how to explain it in more detail. :)
@GTO: "There is no reason to believe that the "optimal" defense frequency
against 3-bets will make his "bluffs" breakeven just on preflop fold
equity alone" - you´re exactly right and it´s not what I meant, it´s obvious that our defense-frequency has to be higher than the calculated minimum defense treshold given by the odds Villain got on his 3-bet, because we allow him to see the flop when we call. Still, there has to be an optimal strategy, including a certain calling% (not "1-a") that makes his bluffs break-even pre, right?
OK, @OP, I´ll try to give a concrete example. Say you open to 3bb, I 3bet from the BB to 10bb, you call. When we ignore SB, I´m getting 4.5:9 on my bluff, which is 1:2. So, from the pure math point of view you had to defend 67% to make my bluff with 32o break-even. But (!!!) - I still have equity, so if you really folded 67% pre, I could 3bet my 32o and x/f everytime when I don´t flop at least a full house - and make immediate profit. If I´m more "risky", I could go down and continue with trips and two-pairs, but it´s up to me, it´s all cream on the cake, preflop I´m break-even. Agree so far?
OK, so let´s say you defend - maybe 36% (instead of 33%) which makes my bluff with 32o (let´s stick to that) break-even overall, so I don´t win money with that hand. That means, the rare times I flop "the nuts" (which is like 5%) are compensated by the fact that I lose some money preflop. Summarized I´m break-even. Cool. But now I cbet ANY SINGLE FLOP (I have no equity, so once you don´t fold, I´m done). I bet full pot - which means you have to call 50% to keep me from making profit, but you fold 55% instead (not a huge gap). Do you still think you can afford that?
Here´s the EV formula for preflop(!):
EV (3bet) = (0.64 * 4.5) + (0.36 * (0.55 * 11.5 + 0.45 * -29.5)
EV (3bet) = 2.88 + (0.36 * (6.33 -13.275))
EV (3bet) = 2.88 + (0.36 * -6.95)
EV (3bet) = 2.88 - 2.50
EV (3bet) = 0.33
Did you recognize btw. that I even ignored the 5% nut-chance for Hero? I calculated as if even my nuts are rubbish, once you don´t fold pre - and still I make profit, even though I´m losing money pre because you´re not folding enough.
If you argue now, that I won´t bluff any single flop - okay, I could change the formula and take into account that we´ll only bluff, say 50% and x/f the rest (still I´ll ignore our nut-chances!):
EV (3bet) = (0.64 * 4.5) + [0.5 * ( (0.7-9) + (0.5(0.55 * 11.5 + 0.45 * -29.5)))]
EV (3bet) = 0.01
Marginal, but still +EV. And still I ignored the 5% nuts. If I add the nuts to the formula (I won´t torture you with the entire formula, so I´ll just show the results), our EV will be +0.87bb when we bluff 100%, +0.53bb when we bluff 50% and 0.38bb when we only bluff 30%.

Do you believe me now? Or is there still doubt / sth. I didn´t cover or you meant differently?

I dont understand where do some numbers from the formula came from:
- First formula:
EV (3bet) = (0.64 * 4.5) + (0.36 * (0.55 * 11.5 + 0.45 * -29.5)
EV (3bet) = 2.88 + (0.36 * (6.33 -13.275))
EV (3bet) = 2.88 + (0.36 * -6.95)
EV (3bet) = 2.88 - 2.50
EV (3bet) = 0.33

Where does 11.5 and -29.5 came from? (11.5 is the pot we suppose to win when opponent folds the flop so i think it has to be 20 (10 of the 3bettor plus another 10 of the caller) and -29.5 i suppose that is the amount we are risking on the flop to win the pot (1P in this case)) Im a bit confuse with the numbers...

  • Second formula:
    EV (3bet) = (0.64 * 4.5) + [0.5 * ( (0.7-9) + (0.5(0.55 * 11.5 + 0.45 * -29.5)))]
    EV (3bet) = 0.01

I dont understand this: [0.5 * ( (0.7-9) + (0.5(0.55 * 11.5 + 0.45 * -29.5)))], can you explain a little bit to me please?

Thank you guys.

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