2nd scenario:
[22+, A2s+, A2o+, K2s+, K2o+, Q2s+, Q5o+, J6s+, J8o+, T7s+, T9o, 98s] each >50% equity vs. random
[22+, A2s+, A2o+, K2s+, K2o+, Q2s+, Q5o+, J6s+, J8o+, T7s+, T9o, 98s] collectively 58.130% equity vs. random
1326 total Holdem starting hand combinations
winning hands
combinations
22+ = 6*13 = 78
A2s+ = 4*12 = 48
A2o+ = 12*12 = 144
K2s+ = 4*11 = 44
K2o+ = 12*11 = 132
Q2s+ = 4*10 = 40
Q5o+ = 12*7 = 84
J6s+ = 4*10 = 40
J8o+ = 12*3 = 26
T7s+ 4*3 = 12
T9o = 12
98s = 4
sum = 664
losing hands
the rest each <50% equity vs. random
the rest collectively 46.081% vs. random
Q4o = 12
Q3o = 12
Q2o = 12
J5s = 4
J4s = 4
J3s = 4
J2s = 4
J7o = 12
J6o = 12
J5o = 12
J4o = 12
J3o = 12
J2o = 12
T6s = 4
T5s = 4
T4s = 4
T3s = 4
T2s = 4
T8o = 12
T7o = 12
T6o = 12
T5o = 12
T4o = 12
T3o = 12
T2o = 12
87s = 4
76s = 4
65s = 4
54s = 4
43s = 4
32s = 4
sum = 662
We pick that we will win when we hold one of the "winning hands". We will get such a hand 664/1326 times, or 50.08% of the time. When we have a "winning hand" on average we have 58.13% equity.
We pick that we will lose when we hold one of the "losing hands". We will get such a hand 662/1326 times, or 49.92% of the time. When we have a "losing hand" on average we have 46.081% equity, which is the equivalent of having 53.919% equity in the bet.
Chance we have winning hand * equity + Chance we have losing hand * equity = total equity (chance of winning)
.5008*58.13 + .4992*53.919 = 56.028% chance to win
Chance to win = 56.028%
Edge = 56.028:43.972 = 1.274:1
ROI = 12.056%
This post was edited by katharsis on Oct 26 2013 06:22pm