COTW: The Mathematics of Poker
09-02-2010
, 07:17 PM
This is excellent. My math skills are weak and the concepts do not come easily to me, so I appreciate the step-by-step explanations and "homework" as well as the discussion and input from others (like math-whiz Cangurino 
). I will work through this COTW slowly and most likely multiple times to completely gain a proper understanding of the concepts.
Thank you so much for this COTW.
). I will work through this COTW slowly and most likely multiple times to completely gain a proper understanding of the concepts. Thank you so much for this COTW.
09-02-2010
, 09:39 PM
09-02-2010
, 11:00 PM
I've always thought that this kind of thing is better described graphically.
First, we are only concerned with the smaller rectangle comprised of colored boxes (and not including the large white box on the left), since we are looking to find the EV of raising.
Straight up profitable boxes (villain folds) are shaded green; straight up unprofitable boxes (we fold) are in red; and boxes where there are no folds preflop are shaded yellow.
As an example, if villain has a hand that he will 3b with but fold to a 4b, and we have a hand that will 4b with but fold to a 5b, then what will happen?
1. We raise
2. Villain 3bets
3. We 4bet
4. Villain folds,
so that particular small box (villain = 3b but fold to 4b, us = 4b but fold to 5b) should be colored green.
Finally, the total EV is the sum of the net gains and losses in each of the boxes (weighted by the area/probability of each box).
*****
One possibly confusing final note: the q I use is the same as the q Cangurino uses, but the b I use is actually the b/q Cangurino uses - I thought it detracted from the main point, and looked cleaner/less confusing written down.
The difference is this - are you considering your 4bet range as a fraction of your raising range? If so, then your b is the same as Cangurino's. If you are considering your 4bet range as a fraction of all possible hands, then your b is the same as mine.
edit: ack, the bottom right corner of the graphic should say "raise, 4b to 3b, call 5b" instead of "raise, 4b to 5b, call 5b".
First, we are only concerned with the smaller rectangle comprised of colored boxes (and not including the large white box on the left), since we are looking to find the EV of raising.
Straight up profitable boxes (villain folds) are shaded green; straight up unprofitable boxes (we fold) are in red; and boxes where there are no folds preflop are shaded yellow.
As an example, if villain has a hand that he will 3b with but fold to a 4b, and we have a hand that will 4b with but fold to a 5b, then what will happen?
1. We raise
2. Villain 3bets
3. We 4bet
4. Villain folds,
so that particular small box (villain = 3b but fold to 4b, us = 4b but fold to 5b) should be colored green.
Finally, the total EV is the sum of the net gains and losses in each of the boxes (weighted by the area/probability of each box).
*****
One possibly confusing final note: the q I use is the same as the q Cangurino uses, but the b I use is actually the b/q Cangurino uses - I thought it detracted from the main point, and looked cleaner/less confusing written down.
The difference is this - are you considering your 4bet range as a fraction of your raising range? If so, then your b is the same as Cangurino's. If you are considering your 4bet range as a fraction of all possible hands, then your b is the same as mine.
edit: ack, the bottom right corner of the graphic should say "raise, 4b to 3b, call 5b" instead of "raise, 4b to 5b, call 5b".
09-02-2010
, 11:10 PM
