Calculating equity as the aggressor...

[galahad_187]

I'm not certain how to word this, but hopefully my hypothetical hand example can help eplain my question.

playing .5/1nl
your heads up in posistion on the turn w/ As5s on a board of 10 6 4 2 with two spades the pot is 10$. villian checks you shove with 10 bucks. this example is ment to help determine my equity in double barreling spots where i pickup more outs. i know in those situations theres typically money left on the river, but i understand how to include my implied odds when determining my equity.

my outs are 3 Aces, 2 threes, and 9 spades. 14 outs = 28%. given the amount of the pot bet, how often does your opponent have to fold in order to make this bet profitable. And please give me the lengthy math answer so that i may learn to calculate it myself under varying circumstances.

thanks alot,

galahad

[sixhigh]

Assumptions: he only calls you with a hand you beat; all your outs are clean; your only option is to push.

Variables: potsize before the push (p); equity when called (e); amount to push (s); foldequity (f).

1st case: he folds, you win +p.
2nd case: he calls, you win (p+s)*e - (1-e)*s
(this means in e% of the cases you win the pot and the amount he has to call and in the remaining (1-e)% cases you lose the amount you pushed with)

1st case happens whenever he folds (f% cases), 2nd whenever he doesn't fold (1-f)%.

So the whole ev of pushing is

ev = f * p + ( 1 - f ) * ( ( p + s ) * e - s * ( 1 - e ) )

= f * ( p - ( p + s ) * e + s * ( 1 - e ) ) + ( p + s ) * e - s * ( 1 - e )

= 0

<->

f = { - ( p + s ) * e + s * ( 1 - e ) } / { p - ( p + s ) * e + s * ( 1 - e ) }

= { e*(p+2s) - s } / { e*(p+2s) - p -s }


For your example we get the following value for f (lets say your equity is 30%)

f = { 30% * 30 - 10 } / { 30% * 30 - 20 }
= 1 / 11.

[DrVanNostrin]

It depends on what the river action will be if you check the turn. I'll assume that:
-you will never bluff the river if you check the turn
-if you spike one of your outs it will always be good
-you will either stack your opponent if you hit on the river of get nothing more; the probability of stacking your oppoenent is p when you hit on the river

The EV of checking would be:

EV_c = p*0.28*$20 + (1-p)*0.28*$10

If the probability that your opponent will call your turn bet is q the EV of betting is:

EV_b = q*0.28*$30 + (1-q)*$10 - $10

The tough part is estimating p and q.

[Petri]

Hello!
Thanks for great posts, I just became curious about everything you can calculate during poker game, and wanna learn everything possible.
What other formulas are there that you can use, exept the basic pot odds and implied odds, like those you showed?

By the way, I figured out a way to calculate how big implied odds must be to you to call, is this correct:

flush draw, one card, odds are about 1:4 against.
lets say the pot is 10 and he bets 5, giving you 3:1 pot odds. You should get 4-3* the bet he made on the river to break even.

In this case you lose 4 times the $5=$20
you win 1 times 15$+ the $5 on the river = 20$
Is this correct and all? you take the "big number" from drawing odds and minus the "big number" from pot odds..

I also thought, that can you get your estimated value of a hand by multiplying the pot odds with drawing odds somehow?

Thanks a million, and please tell me every other calculatable things that you suggest getting familiar with!