[jba]

[ QUOTE ]
Example 1:

There's $75 in the pot after your opponent bets $25. You have an OESD and have roughly %17 equity in the pot with one card to come. You opt to make a potsized raise, investing a $25 call + a $75, hoping to represent a set. How often does your opponent have to fold here for this play to be +EV?


[/ QUOTE ]

EV = P(fold) * 75 + ((1-P(fold)) * .17*150- .83*75)

In english this means "we will win $75 P% of the time because villain folded. when he doesn't fold, we win $150 (pot + turn call) 17% of the time and lose $75 (turn raise) 83% of the time".

to find break even we set EV = 0

P * 75 + ((1-P) * .17*150- .83*75) = 0
P = .327

so villain must fold nearly 40% of the time.

[ QUOTE ]

Example 2:

Same hand as example 1, except you intend to bet another $150 on the river if your opponent calls your 4th street raise if you hit or miss with your straight. How often does this play have to work in order to be +EV? How do I calculate this?

If someone could please explain to me the formula for calculating this, I would really appreciate it. Thank you!

[/ QUOTE ]

PT is probability villain folds to turn raise
PR is probability villain folds to river bet


EV = PT * 75 + ((1-PT) * (PR * 150 + ((1-PR)) .17*300- .83*225)

In english this means "we will win $75 PT% of the time because villain folds the turn. when he doesn't fold the turn (1-PT), then PR% of the time we win $150 (75 in pot plus 75 turn call). When he doesn't fold the river, we will win $300 (pot + turn call + river call) 17% of the time, and lose $225 (turn raise + river bet)

this last one is most useful if you first estimate PT, then solve for PR or vice versa. In other words "if villain folds only 20% of the time on the turn, how often must he fold on the river to make this sequence EV+"



edit to add disclaimer: i'm about 84% sure this is correct