Here are my notes on this episode, I tried to correct everything that was wrong in the video and be more accurate with my rounding. thanks WoT, best series ever. If anyone see's any errors feel free to correct me.
Notes on Mathematics of NL Holdâ€™em episode4 by WiltonTilt
Video # 4 is all about EV Calculations.
Basic EV calculation setup:
EV = (Result of win) â€“ (Result of loss)
EV=(Our Equity) * (What we win) â€“ (Villainâ€™s Equity) * (What we lose).
Weâ€™re in the big blind with AsAc. The UTG player shoves with KhKd and folds to you. Itâ€™s $900 to call to win 1015 (stack+blinds) 5/10, $1000 stacks
Ev = (our Equity) * (What we win) â€“ Villainâ€™s equity) * (What we lose)
Ev = .81*1015 - .19 * 990
Ev = 822.15 â€“ 188.1
Ev = +634.05
Thus, every time this situation occurs we expect to profit $634.05
Ev = (Our Equity) * (Total pot) â€“ cost of our call
Ev = (.81) * 2005 -990
Both methods work, choose the one that seems to make the most sense to you. He prefers the first method because he thinks itâ€™s easier to build on, but itâ€™s essentially the same thing just a different way of thinking.
EV Calcs Vs Hand Ranges:
We have KsQc We have 3 bet this guy a lot, we are in position we 3 bet pf again he calls.
AK is not in his range because he would have 4bet. He checks the flop We bet 200 he jams for 875. There is 265 in the pot. The board is Kc9c8d
We assume he is check jamming here with at least 8 outs.
His range is KK+; 99,88, AcQc, AcJc , AcTc, Ac8c, QcJc,JcTc, 98s, 7c8c, JTs, 67s
.35(1075+265) - .65(675) = +30.25
#4 has how to do Tupac method at the table
This is not in the video but very valuable math.
One concern for me in NL Hâ€™E math is that most people finding Equity do it through poker stove which gives you your equity for seeing all 5 cards. This article can help you find your equity PFR to Flop and then you can recalculate for turn and river. I think knowing your equity based on the 3 flop cards and not just all 5 cards is one of the most under rated math concepts in poker.
Chance Of Overcards Hitting
Question: dear poker master,
i've been thinking a lot about this situation as it pertains to tourneys. what are the odds for the overcards hitting again? and how do you figure them out before the flop. i know that there is a 6 out of 47 and 6 out of 46 percent chance of hitting on the turn and river but how do you calculate for all three cards of the flrop?
Answer: To calculate the odds of hitting them on the flop you use a similar equation like you do for the turn and river. Let's do an example with KQ. You have 2 cards in your hand and that leaves 50 unseen cards for the first flop card. You have 6 outs for the flop cards (3 Kings and 3 queens). The next card you have the same 6 outs but this time only out of 49 cards. The last flop card gives us 6 outs out of 48. That looks like this:
6/50 6/49 6/48
Here is the tricky part. Whenever you have a situation when an event, hitting your card, can happen on more then one chance you figure out the odds of it NOT hitting and then subract it by one.
1 - [ ((Cards - Outs) / Cards) * ((Cards - Outs) / Cards) ... ]
Let's try that with our numbers:
1 - [(44/50) * (43/49) * (42/48)]
1 - [.88 * .8775 * .875]
1 - [.675] ----- this basically shows there's a 68% chance of us NOT getting our cards.
32% ---- this means that there is a 32% chance we WILL get our cards.
That seems like a high percentage until you think of it compared to the flush draw which seems like it never gets there. If you want to figure out how often AK will hit by the river then just add the turn and river cards to the equation:
6/50 6/49 6/48 6/47 6/46
Flip these again to cards that won't help us:
44/50 * 43/49 * 42/48 * 41/47 * 40/46
.88 * .8775 * .875 * .872 * .869
= 51% of the time it not getting there.
= 49% of the time it will hit by the river.