how do I work out % of times I need to win to justify a call in NL

[Necromancer]

This hand was posted here http://forumserver.twoplustwo.com/showfl...;gonew=1#UNREAD
if you want to see the original.

A poster pointed out that you need to win 38% of the time for a call on the turn to be +EV.

Can you show me the maths to work this out?



Party Poker No-Limit Hold'em, $ BB (6 handed) Hand History Converter Tool from FlopTurnRiver.com (Format: 2+2 Forums)

SB ($49.75)
BB ($83.69)
UTG ($81.95)
MP ($68.05)
Hero ($50)
Button ($54)

Preflop: Hero is CO with Q, Q. SB posts a blind of $0.25.
UTG calls $0.50, MP calls $0.50, Hero raises to $3, 3 folds, UTG calls $2.50, MP folds.

Flop: ($7.25) 5, 7, 4 (2 players)
UTG checks, Hero bets $5.5, UTG raises to $11, Hero calls $5.50.

Turn: ($29.25) 4 (2 players)
UTG bets $40, Hero folds.

Final Pot: $69.25

[Catyoul]

To call : $40
Total pot when you have called : $29.25 + $40 + $40
Neutral EV point : (to call) / (total pot) = 40/(29.25+40+40) = 36.6%

Why ?
Let's say you win x% of the time.
EV = -(to call) + x*(total pot)
0 Ev point : 0 = -(to call) + x*(total pot)
Thus x = (to call) / (total pot)

[Necromancer]

thats great. thanks for that. I will try to put it to good use.