theyen47

Hey memo bayes theorem relates conditional probabilities as follows

P(A|B) = P(A)P(B|A)/P(B) and [P(A)P(B|A)] / [P(A)P(B|A) + P(A#)P(B|A#)]

by using P(B) = P(AnB) + P(A#nB)= P(A)P(B|A) + P(A#)P(B|A#)

A#- not A

P(B|A)- the probability that B happens, given that A has happened

P(AnB)- the probability A and B happen

If we define events say

A- he has an 8

B- the board runs out 88

then

P(A)~=(4/5) or 80% (based on ilares range of 8x and 65s narrowed due to the action)

P(B|A)=(2/46)*(1/45)=(1/1035)

P(A#)~=(1/5) or 20%

P(B|A#)=(3/47)*(2/46)=(3/1081)

so

P(A|B) = P(A)P(B|A)/P(B)

=[(4/5)*(1/1035)]/P(B)

=(4/5175)/P(B)

=(4/5175)/[P(A)P(B|A)+P(A#)P(B|A#)]

=(4/5175)/[(4/5)*(1/1035)+(1/5)*(3/47)*(2/46)]

=188/323~=58.2%

pretty good article here about it if you're still confused :)

https://brilliant.org/discussions/thread/conditional-probability-bayes-theorem/

Ilares I think you might be overestimating how often you have quads, the fact that the board runs out 88 means it is much less likely you have an 8 doesn't it? 

I took your range where 80.95% of the combos contain an 8, saying 80% for simplicity, then used bayes theorem to work out the conditional probability that you have an 8 given that the board ran out 88 and it gave ~58%.

Plays seems fine to me, i'd for sure call. You don't have any better hands here, even though vs a passive fish he still will have some bluffs here e.g QJ with a diamond and very occasionally be value shoving worse like 55.