The No Limit Paradigm

[Pokey]

[ QUOTE ]

------------------------

villain raises 1.75$
hero reraises to 4.75$
villain calls 3$.
blinds: .75$

pot: 10.25$ - .5$ rake

pot: 9.75$

hero leads 4$.


gets called 60% of the time: -240$
gets folded 40% of the time: +390$

EV: +1.50$

--------------------------------------

villain raises 1.75$
hero reraises to 4.75$
villain calls 3$.
blinds: .75$

pot: 10.25$ - .5$ rake

pot: 9.75$

hero leads 3$.


gets called 60% of the time: -180$
gets folded 40% of the time: +390$

EV: +2.10$


---------------------------------------

villain raises 1.75$
hero reraises to 4.75$
villain calls 3$.
blinds: .75$

pot: 10.25$ - .5$ rake

pot: 9.75$

hero leads 6$.


gets called 60% of the time: -360$
gets folded 40% of the time: +390$

EV: +.30$


------------------------------------


suffice to say, if i've done this right (PLEASE SAY SO) the 3$ bet seems to be the best. it yields 2.1$/per play (on 100 trials).

[/ QUOTE ]

Yes, but we can do even better!

villain raises $1.75
hero reraises to $4.75
villain calls $3.
blinds: $0.75

pot: $10.25 - $0.50 rake

pot: $9.75

hero leads $0.25.


gets called 60% of the time: -$15
gets folded 40% of the time: +$390

EV: +$3.75!

Even better, we could three-bet to $24.75 preflop and then bet $0.25 on the flop. When villain calls 60% of the time we still lose $15 but when he folds 40% of the time we now win $1980, for a net win of $19.65 per hand!

See, there's a problem with your assumption: when you change your bet size (as a fraction of the pot) you also change your opponent's calling range. A smaller bet gets called more often, so the $3 bet won't have the same folding and calling ratios as the $6 bet. Which bet is EV-maximizing will depend on the specific flavor of opponent you're facing; trying to mathematically optimize this in a vaccuum is very hard, and your assumption of constant folding equity is so terribly wrong that it leads you to horribly incorrect and expensive conclusions. Don't put faith in this theory because it will lead you astray.