Really simple questions

Mr. Pozzer · #1 08-26-2007, 05:54 AM

PokerStars No-Limit Hold'em, $0.50 BB (9 handed) Hand History Converter Tool from FlopTurnRiver.com (Format: 2+2 Forums)

MP1 ($60.70)
MP2 ($31.20)
MP3 ($16.65)
Hero ($58.85)
Button ($31.15)
SB ($9.50)
BB ($31.75)
UTG ($27.45)
UTG+1 ($70.35)

Preflop: Hero is CO with 9[img]/images/graemlins/club.gif[/img], A[img]/images/graemlins/club.gif[/img].
5 folds, Hero raises to $1.5, Button calls $1.50, 1 fold, BB calls $1.

Flop: ($4.75) T[img]/images/graemlins/heart.gif[/img], 6[img]/images/graemlins/club.gif[/img], J[img]/images/graemlins/club.gif[/img] (3 players)
BB checks, Hero bets $3.5, Button raises to $10.5, BB folds, Hero calls???

Assume the hand ends when I make my call. Can you show me the equation of how to get how much real $$$ I can call up to, to make this call profitable against a range that I have .310 equity against.

I got that I can call up to $5.81 to break even on my call. Is this right? (.31)*(18.75)? 18.75 is the pot before I call.

Seeing that my immediate odds are 2.68:1 I would guess that I'm very off here, please help me.

jay_shark · #2 08-26-2007, 10:59 AM

There is 4.75+3.5+10.5 =18.75 in the pot before it's your turn to act .

These are pot odds of 18.75/7 = 2.678:1 which means you need to win 1/(3.678) = 27.18% of the time to show a profit . Since you have a 31% equity against this hand , the call is a profitable one .

Suppose the button raised an amount X and knows that you have a 31% equity against his hand . The amount he should bet so that calling is neutral EV is :

If he bets x , then you're getting pot odds of (8.25+x)/(x-3.5) . We want (x-3.5)/(8.25 +x+x-3.5)=.31
(x-3.5)/(4.75 +2x)=0.31

Solve for x and you should get 13.08... which is the maximum amount you can call .

mykey1961 · #3 08-26-2007, 01:40 PM

It may be profitable, but just barely.

The the combination of a $1.5 call preflop and a raise to $10.5 on the flop screams a set.

If the button had JJ, TT, or 66 and assumed he was behind, he would need to profit $13.04 each time he flopped a set to justify calling $1.5 preflop.

He has invested $12 into a $25.75 pot (if called). That would net a $13.75 profit.

Assuming the button has JJ, TT, or 66, the Hero has 0.27374 pot equity.

25.75*0.27374 - 7.0 = 0.048805

And that assumes no rake.

Mr. Pozzer · #4 08-26-2007, 07:08 PM

[ QUOTE ]
It may be profitable, but just barely.

The the combination of a $1.5 call preflop and a raise to $10.5 on the flop screams a set.

[/ QUOTE ]Yeah the range I gave him to come to .31 equity was JJ/TT/66/JT. He had JJ. My plan was to call and fold UI on the turn and try to figure out how good/bad my call on the flop is if I hit and I'm against a set. I didn't hit but I am curious. For this I was going to include implied odds though.

Mr. Pozzer · #5 08-26-2007, 07:25 PM

Jay, thank you for all that math. I'm still trying to digest all of it so I can put it to use in future hands. Can you explain something to me though, please?

If (.31)*($25.75(pot after I call)) = $7.98 it would seem to a math novice like me that only a call of $7.98 (11.48 total) would make me break even since this is my equity if I call. Can you tell me why this is wrong please. I'm not doubting your answer at all I'm just trying to figure all this out.

Does the above equation also say that I'm making $.98 if I call the $7 raise if the hand ends now?

jay_shark · #6 08-26-2007, 08:10 PM

Let me just add that my answer assumes that you will see two cards for that price . This isn't always true as your opponent may continue to bet on the turn .

So for simplicity , lets assume that you only have $7 left to call the bet . If this is the case , then you make $ 0.98 which agrees with your thought process [img]/images/graemlins/smile.gif[/img]

mykey1961 · #7 08-26-2007, 11:00 PM

[ QUOTE ]
Jay, thank you for all that math. I'm still trying to digest all of it so I can put it to use in future hands. Can you explain something to me though, please?

If (.31)*($25.75(pot after I call)) = $7.98 it would seem to a math novice like me that only a call of $7.98 (11.48 total) would make me break even since this is my equity if I call. Can you tell me why this is wrong please. I'm not doubting your answer at all I'm just trying to figure all this out.

Does the above equation also say that I'm making $.98 if I call the $7 raise if the hand ends now?

[/ QUOTE ]

Under the assumption you have .31 pot equity:

(4.75+3.5+10.75+7.25)*0.31 -7.25 = +0.8875
(4.75+3.5+11.00+7.50)*0.31 -7.50 = +0.7925
(4.75+3.5+11.25+7.75)*0.31 -7.75 = +0.6975
(4.75+3.5+11.50+8.00)*0.31 -8.00 = +0.6025
(4.75+3.5+11.75+8.25)*0.31 -8.25 = +0.5075
(4.75+3.5+12.00+8.50)*0.31 -8.50 = +0.4125
(4.75+3.5+12.25+8.75)*0.31 -8.75 = +0.3175
(4.75+3.5+12.50+9.00)*0.31 -9.00 = +0.2225
(4.75+3.5+12.75+9.25)*0.31 -9.25 = +0.1275
(4.75+3.5+13.00+9.50)*0.31 -9.50 = +0.0325
(4.75+3.5+13.25+9.75)*0.31 -9.75 = -0.0625