Join Date: Sep 2012
Posts: 100
Hi - I'm re-reading this article by Matrix on EV (see below)/
"Poker Stars
No Limit Holdem Ring game
Blinds: $0.10/$0.25
6 players
Stack sizes:
UTG: $27.85
UTG+1: $24.65
CO: $28.95
Button: $23.95
Hero: $25.15
BB: $27.80
Pre-flop: (6 players) Hero is SB with 2 2
UTG calls, 2 folds, Button calls, Hero calls, BB checks.
Flop: J 2 5 ($1, 4 players)
Hero bets $1, BB raises to $3, UTG folds, Button calls, Hero raises to $8, BB raises all-in $24.9,Button folds, Hero calls.
Turn: 9 ($53.8, 1 player + 1 all-in - Main pot: $53.8)
River: 9 ($53.8, 1 player + 1 all-in - Main pot: $53.8)
Results:
Final pot: $53.8
- it's the flop action I am interested in here.
In real life we don't know what sepcific hand we are facing at the point in time where we make a decision. What hand does BB have here? is my hand strong enough to call his all-in? and how do we work out the EV of this play??
The answer is to put BB on a range of hands - if we re-run this hand 1000 times say sometimes he has AA and we are a huge favourite, sometimes he has 55 and we are a huge underdog, he might also have JJ-KK, AJ,KJ,J2,52,J5, Ax, or he might be bluffing. In this particular case his range is wide because there was no preflop raise. Also we are not saying htat he will always play every hand in this range exactly this way - but that he isn't playing any other hand apart from the ones in this range in this fashion.
Against most of these hands I am a favourite, and against some of them I am an underdog. I have no way of knowing what hand he has and certainly don't have time at the table to put the numbers into Pokerstove so we just make an educated guess.
I play using the general rule that I should never fold a flopped set for ~100BB. The reason being that no matter the flop if we can get all the money in on the flop we are almost always a favourite to win the hand at the showdown vs our opponents range of hands.
So I happily call his all-in. But have I made a +EV play and will this earn me money in the long run???
Lets put his range and my hand into pokerstove and see...
Board: Jc 2h 5h
Dead:
equity (%) win (%) tie (%)
Hand 1: 78.7155 % 78.72% 00.00% { 2d2s }
Hand 2: 21.2845 % 21.28% 00.00% { JJ+, 55, AhKh, AJs, J5s, J2s, Ts7s, 52s, AJo, J5o, J2o, 52o }
(T7ss is included in this range to represent a bluff)
and the numbers say that on this wide range of hands my play is +EV and that calling his all-in here means that vs that range I expect to win ~79% of the time.
The actual results don't matter, as long as my range is accurate, and what cards come on the Turn or on the River don't matter either (as the decision is already made by then) if I make this play everytime it is +EV and in the long run I expect to win ~170BB everytime I make this play. As this play costs me 100BB to make I make a profit everytime here of 70BB, whether BB shows me JJ for top set or A 8 for a busted flush draw I still "gain" ~70BB everytime I make the play.
I just need a little help regarding the last paragraph of the extract i have pasted into this thread.
I just want to know how he comes to the solution of earning 170BB everytime he makes this play (70BB of that profit), as i am having trouble trying to work it out.
Thanks.
