+ to the ev! math

+ to the ev! sent me a hand today. we were trying to decide if it was a +ev play or not. let me show you how to break down the math to decide. this math is only correct if were assigning correct hand ranges to the 2 opposing players.

heres the hand in question

Full Tilt Poker Game #5267299372: FTOPS Event #15 (39924392), Table 178 - 200/400 Ante 50 - No Limit Hold'em - 17:00:53 ET - 2008/02/15
Seat 1: Erich Kollmann (44,072)
Seat 2: monika13 (34,415)
Seat 3: LMB then GTFO (24,536)
Seat 4: Babooyah (8,815)
Seat 5: Rocknhrdplac (30,271)
Erich Kollmann antes 50
monika13 antes 50
LMB then GTFO antes 50
Babooyah antes 50
Rocknhrdplac antes 50
monika13 posts the small blind of 200
LMB then GTFO posts the big blind of 400
The button is in seat #1
rezdogz (Observer): dang!
*** HOLE CARDS ***
Dealt to LMB then GTFO [9d Td]
Babooyah folds
Rocknhrdplac folds
DeliveranAce sits down
DeliveranAce adds 8,842
Erich Kollmann raises to 1,650
monika13 has 15 seconds left to act
monika13 raises to 5,600
LMB then GTFO has 15 seconds left to act
LMB then GTFO has requested TIME
LMB then GTFO raises to 24,486, and is all in
Erich Kollmann folds
monika13 calls 18,886
LMB then GTFO shows [9d Td]
monika13 shows [Ah Kd]
*** FLOP *** [5h Ac 8d]
*** TURN *** [5h Ac 8d] [Jd]
*** RIVER *** [5h Ac 8d Jd] [2c]
LMB then GTFO shows Ace Jack high
monika13 shows a pair of Aces
monika13 wins the pot (50,872) with a pair of Aces

we assume that whenever the sb calls, the bb folds. it makes it a lot easier and only varies the answer by a very little




.55(7775) + .45((.15)(((.21)(30611) - .79(24486)) + ((.30(26861) - .70(24486))) =



725+1650+5400

7775



button calls 1.4/19.5 = .072 = 7.2%

sb calls 2.6/6.8 = .382 = 38.2%


.55(7775) + .45((.15)(-12915.63) + (.85)(-9081.9))



.21(30611) - .79(24486) .30(26861) - .70(24486)


6428.31 - 19343.94 = -12915.63 8058.3 - 17140.2 = -9081.9



.55(7775) + .45(-1937.3445 - 7719.615)


4276.25 + -4345.63 = -69.38




-69.38 > -450



heres how all that works. he has a 55% chance of taking down the pot without anyone calling him. and hes called by one of the players 45% of the time. in that 45% the sb called 15% and the bb called 85%. he has 21 percent equity against the buttons calling range, and 30% equity against the bb calling range. notice he wins more than his stack when hes called because of the extra money in the pot.

so this hand the way he played it has an expected value of 69.38 chips, about an ante.

this is a minus ev hand. but this is a +ev play. do you see why?


if he makes this play, hes losing 69 chips on average from his stack. but if he folds, hes losing 450 chips every single time. because of his blind and ante
so hes actually winning 1 bb on average with this play, because the money in the pot isnt his anymore.