Mathematically correct, or not

[Duece Three]

Down to heads-up in a 1 table tourney.

I have roughly T3600, leaving villain w/T3400

I have A/images/graemlins/heart.gif , 8/images/graemlins/heart.gif
Villain has J/images/graemlins/spade.gif , J/images/graemlins/diamond.gif

For arguments sake, lets say that I knew his hand.

I'll win the hand roughly 30% of the time, and cash for $100.
I'll lose that hand roughly 70% of the time, and cash for $60.

How do I figure out if the long term results are positive, or am I completely misinterpreting something that I read (somewhere)?

[LetYouDown]

Explain to me why you're not just folding if you know his hand?

[Duece Three]

Well, with even stack sizes, I suppose that I would fold every time (unless I felt like gambling was the only way I could beat the opponent)...

I guess that I am trying to find a way to justify to myself, that I wasn't too wrong by going in. /images/graemlins/crazy.gif

My read on this player was such that when he made a small-ish preflop raise, he had to have had a decent hand...ranging from a pocket pair down to at least a couple of broadway cards.

Blinds were up to 500/1000, so I don't think my all-in re-raise was too bad.

Anyway, I'm also trying to learn a little bit in regards to analyzing a situation like this statistically, so that I can apply some logic to the decisions I make at the tables.

Maybe this was not a good example.

[jba]

[ QUOTE ]
Down to heads-up in a 1 table tourney.

I have roughly T3600, leaving villain w/T3400

I have A/images/graemlins/heart.gif , 8/images/graemlins/heart.gif
Villain has J/images/graemlins/spade.gif , J/images/graemlins/diamond.gif

For arguments sake, lets say that I knew his hand.

I'll win the hand roughly 30% of the time, and cash for $100.
I'll lose that hand roughly 70% of the time, and cash for $60.

How do I figure out if the long term results are positive, or am I completely misinterpreting something that I read (somewhere)?

[/ QUOTE ]

I think what you're after is an EV calculation of calling which is:

EV=.3*100+.7*60=72

so your expectation of calling is $72. but the alternative is to fold (you aren't clear on the action, but I presume he went all in preflop or something??) which would appear to leaving you around even stack-wise, which means if you are about even skill-wise you should have a 50/50 shot to win this thing, so it makes your (tournament) expectation of folding:

EV=.5*100+.5*60=80

so folding is better than calling, assuming everything I just said is true ..

[LetYouDown]

Tournament implications aside. If the blinds are 500/1000, and he goes all in 3500 and flips his cards face up. It's 2500 to you to call. Pot is at 4500. So the pot is laying you 1.8 to 1. Quick EV calculation:

.7 * (-2500) + .3 * (4500) = -1750 + 1350 = -400

If you really thought he had pocket 8,8's or above, you should fold.

[Duece Three]

Thanks for the replies!

[college kid]

Let's just run through the math real quick here. For simplicity let's say you and Villian are of equal skill and that you both have the same stack size. Also, you will win/lose exactly 30/70, and no blinds are in the pot (even though they would actually very likely be high and a large factor at this point). It's just a bit easier that way and will help you see how to do this type of calculation.

So let's look at teh numbers, and see which one is higher.

EV of folding--Since you are both of equal skill, if you fold and lose no money, then you are both still at equal stack and you have a 50% chance of 1st and 50% of second, which means you get half of 100+60, which is $80.

EV of calling. You will win 100 dollars 30% and win 60 dollars 70% of the time. 100*.3 + 60*.7 = 30 + 42 = 72.

Clearly, 80 is better than 72, but given that the blinds are probably very high relative to the stack sizes and you did put in blinds, it should be a very marginal situation and you therefore didn't make too bad of a mistake, if one was made at all.

if you had about the same chips as him, then why would you go all in vs a vastly superior hand???