How to calculate most profitable move???

[Jailblazers]

How do some of you guys solve this problem? This is a made up hand.

You have: 33
Villains range: 22, 66, 77, JJ+, J2o+, 32
# of hands you beat in villains range: 156/165 (may be a little off)

Board: 2-J-3-6-7 (rainbow)

Your opponent bets out $75 into a $125 pot. You both have $500 left in your stacks after the river bet. Right now the pot is $200.

So your options are:

MinRaise to 150: Villain calls with every hand in his range, and will re-raise all-in with 22, 66, 77 and JJ.

Raise to 200: Villain folds J4, J5, J8, J9, and JT. Re-raises all-in with 22, 66, 77, and JJ. Calls with every other hand.

Raise to 300: Villain folds J4, J5, J8, J9, JT, JQ, JK, AJ.
Re-raise all-in with 22, 66, 77, and JJ. Calls every other hand.

Raise all-in to 500: Villain folds J2, J3, J4, J5, J8, J9, JT, JQ, JK, AJ, 32, and QQ+. Villain calls with J6, J7, 22, 66, 77, JJ.

1. Can somebody do the math to find out how much profit (or negative profit) each move would make? Showing work would be GREATLY appreciated.

2. Also, for you high stakes players. Do you do this kind of math in your head for every hand? every street? It seems like this would be a ton of stuff to calculate in your head, but if done right, it would create a ton of profit.

Edit: If no one wants to solve this, just show the equations and the "tools" to do this and I will be satisfied.

[Sushiglutton]

If this existed it would help.

[Jailblazers]

Wait, so are you saying it's not even possible to do this?

Are you better off just trying to guess what is the most profitable?

[Born2Run]

Jail, you are into some deep thinking posts. I don't have an answer to your question but if I did I am not sure how you would apply it in a live game without grinding your hands played way donw.

[jay_jaywalk]

I think this article is dealing with the questions above:

http://www.cardplayer.com/magazine/article/15295

[Dromar]

[ QUOTE ]
Wait, so are you saying it's not even possible to do this?

Are you better off just trying to guess what is the most profitable?

[/ QUOTE ]

Can it be solved? Of course.
Can I solve it? Yes.
Is it too much work? Of course.

Are you better off guessing the best line? At the table, yes. If you sit there thinking about this stuff for five minutes, your opponent (and the rest of the table) will notice this.

Since no one else wants to actually answer your question, I'll give directions on how it could be solved:

Examine each case independently (r150, r200, r300, AI). Based on the ranges you've given, calculate %fold, %call, %raise of your opponent's actions (%raise only applicable when you didn't go all-in obv). Since your opponent might raise, the calculation gets more complicated. Given his raising range, you have to determine whether or not you're going to call his raise (based on pot odds and your odds to win given his raising range). Now the calculation is done:

EV = (%fold)(potsize) + (%call)(potsize + betsize)* + RAISEPART

where
RAISEPART = (%raise)(potsize + betsize)(chance you win - chance you lose) [this assumes you will call his AI, and btw betsize = 500 in this case]
or
RAISEPART = (%raise)(-betsize) [if you fold. here, betsize is however much you bet on the river. It's negative because you always lose when you fold, which is a simplification of the above equation for RAISEPART]

*the calling part of the equation could be more complicated, except that, in this case, you win 100% when he calls, since he'd raise with every hand that beats you.


So, once you've calculated your EV for a given action, calculate it for the other 3 possibilities, and see which one has the greatest EV.

It's pretty early, but I think those equations are right. Maybe someone can proofread them.

Tools: Any calculator, and Pokerstove.

[BlueBear]

Yes, this is solvable, but I don't anybody is going to do it for free. Like Dromar says, you need a calculator, Pokerstove and use lots of "probability trees".

[_D&L_]

But your problem isn't completely defined yet.

First, even though u listed the range of hands you believe your opponent is on, you haven't said whether u think that each one of those cominations is equally likely in your mind.


Example 1: more ways to make J2 than 66 so, J2 more weight? Or is he less likely to play/hang in their with J2 despite more ways to make J2o

Example 2: Same number of ways to make JJ as 22, but equal weight? Again, same number of ways to make J2o as JQ off, but again, equal weight?

The second piece of information missing is how you play your other hands. That's why its hard to solve. Maybe we can simplify, and you can simply state your beliefs on whether he will fold or call to your bet. But are your beliefs justified? That depends on how you play your other hands. What other hands could u be holding, and betting with at this point?

P.s. i have a self-written program that takes as input beliefs about two players holdings on the river, and calculates near-optimal play (meaning if you could solve the nash equilibrium, its probably 95% efficient). Work in progress to get it to 100% efficiency.

[Perestroika]

[ QUOTE ]
I think this article is dealing with the questions above:

http://www.cardplayer.com/magazine/article/15295

[/ QUOTE ]

I think this is a very bad argument from this player. "Analyzing extremely close decisions is a waste of time." BEERP Wrong.

[GeeBeeQED]

What was the preflop, flop and turn action? So much of this depends on the quality of the player, his style, his susceptability to getting all in with a lower value hand and etc. Not enough information really.