equity problem, help me out

[Roswell]

Let's say $200 in the pot preflop.

Both players have $1000 left.

The flop comes down. Player 1 bets the pot $200. Player 2 looks at his cards and figures he has a 12-outer, or a 45% chance to win. He decides he's going to raise.

How do I figure (algebraically) player 2's equity upon raising?

also: let's say player 2 goes all in every time. If player 1 will call every time, at what size stack does player 2's all-in raise become unprofitable?

[jay_shark]

Hey Roswell , maybe this will help .

Player two goes all in and bets 1000 into a pot containing 400 . Therefore player one is getting 1400:800 or 7:4 on the bet . If he folds 100% of the time , he is down to 800 . If he calls , then he is a 55% favorite .

EV if player one folds is 0 . EV if he calls is 1400*0.55-800*0.45=410 . Or 2200*0.8 - 800 =410 .

Suppose player one folds x% of the time on the flop and thus loses his $200 bet . Then he loses 200*x%/100 but he wins (1-x)*410/100 . Therefore it's positive EV for player one if the following is true .

410*(100-x)/100 -200x/100>=0 solve for x you get .
After multiplying both sides by 100 you get
41000-410x-200x>=0
41000>=610x
67>=x

So it's positive EV for player two if player one folds more than 67% of the time .

Second question : Player two bets x amount knowing that player one will always call on the flop and will be a 55% favorite . Player two is essentially getting pot odds of (x+200):x which means that we want x/(x+x+200) =0.45
solve for x and you get x=900 which means that if player two bets more than 900 than it becomes negative EV .

[jogger08152]

[ QUOTE ]
Let's say $200 in the pot preflop.

Both players have $1000 left.

The flop comes down. Player 1 bets the pot $200. Player 2 looks at his cards and figures he has a 12-outer, or a 45% chance to win. He decides he's going to raise.

[/ QUOTE ]

[ QUOTE ]
How do I figure (algebraically) player 2's equity upon raising?

[/ QUOTE ]
His equity is simply (45+ (.55F))% of 1400 dollars, where F is the probability, expressed as a percentage, that Player 1 will fold.

[ QUOTE ]
also: let's say player 2 goes all in every time. If player 1 will call every time, at what size stack does player 2's all-in raise [Note: this isn't a raise, it's a bet. -Jogger] become unprofitable?

[/ QUOTE ]
Player 2's push will always be profitable given the stipulated stack sizes.