Doubt about an old BigFiszh post "Theory question in three bet pots"
Posted by Deactivated User
Posted by Deactivated User posted in Mid Stakes
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%.
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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