[nunrg]

First: VOCABULARY
NP: Number of player
NL: Number of limpers
P: My position (1<P<=NP)
Z: Number of hand possibilities
V: The power of my hands (1 is the worse, Z is the best)
X: Ants
Y: A bet

F is the probability to be confronted to a better value for the people AFTER ME:
F = (1-((V/Z)^(NP-P))
This is the 1-the proba of having not a better hands than me
(the proba is my ranks divide by the number of total hands multiply N times, N = number of people after me)
G is the probability to be confronted to a better value for the people who has limped BEFORE ME
G = ((Z/(2*NP))*NL)/(Z) = (0.5*NL)/NP
It's 0.5 (the ration of hands better than the average) multiplied by the number of limpers and divided by the number of players.

The probability to loose: H=F+G
If H >= 1, you don't BET !!!!!!!!
The probability to loose money is H*(X+Y)
The probability to win is I=(1-H)
The probability to win money is I*(NP*X+NL*Y)
if WonMoney-LooseMoney>0, you need to bet [img]/images/graemlins/wink.gif[/img]

Some numeric application.
10 players, Y=5*X, 100 possible hands.

Case1.
I'm on the button, my hands ranks is 70, everybody folds.
F = (1-((70/100)^(10-8))=1-(0.7)^2=0.51
G = 0
H = F+G = 0.51
Loose money (0.51)*(X+Y) = 0.51*(6X)=3.06X
Won Money = (1-0.6) = 0.4*10X=4.0X
So your profit is +0.94X, you need to BET.

Case2.
I'm in position 5 with 75, 2 limpers.
F = (1-((75/100)^(10-5))=1-(0.75)^5=0.864
G = (0.5*2)/10 = 0.1
H = F+G = 0.964
Loose money H*(X+Y)=0.964*6X=5.784X
I = 0.044
Won money = 0.044*(10X+2Y)=0.044*20X=0.88X
You don't bet !!!!

Cas3: Like Cas2 but you have 92 ranked and 3 limpers
F = (1-((92/100)^(10-5))=1-(0.92)^5=0.34
H = (0.5*3)/10 = 0.15
H = F+G=0.49
Loose money: 0.49*6X=3.0X
Won money: 0.51*(10X+3Y)=0.51*25X=12.75X
YOU NEED TO BET [img]/images/graemlins/laugh.gif[/img]

Case4: You are first with 85
F = (1-((85/100)^(10-1))=1-(0.85)^9=0.80
G = 0
H=0.80
Loose money: 0.80*6X=4.8X
Won Money: 0.20*10X=2.0X
You don't BET

Case5: You are in position 9 with 52, 1 limpers
F=1-0.52=0.48
G=0.05
Loose money=0.53*6X=3.18X
Won money=0.47*(10X+Y)=0.47*15X=7.4X
So you BET