need some basic EV help

[SimaoMacaco]

I need some maths help please.. here is my problem

On the turn I bet $7 that was called to make a pot of $23.95, I am 92% fav at this point.

I am all in on the river regardless and he somehow sucks out to the nuts.. He bets 43.78 which i call. This seems +EV maybe not optimal but not -EV. I am trying to calculate exactly how +EV it is.. so i can see if my session was good/bad/sucked out.

I think i can calculate it thus..

assume

HWR = his win rate
then HWR = (1/(1-0.92))

-(HWR*$7) = -87.5

to win the river bet of $43.78+pot-turnbet

not sure if this is right.. bright maths peeps please help!

[Tom1975]

I don't know where to start. There's not a single thing about your post that I understand.

[SimaoMacaco]

Okay.. let me explain better

*Pot = 9.75
*My bet = 7
*Villain calls 7
*My probability of winning = 0.92

*At this point the river card is left to come and if it gives villain a better hand he pushes 47 more and i call the 47 - villain does not push the river if he does not gain the winning hand

Q. is this +EV

Now.. i think..

I put 7 into a pot of 16.75 with a prob of winning at 0.92

So villain wins 16.75 + 47 = 63.75 per 11.5 hands played
11.5 hands = (1/[1-0.92])

So it costs villain 7 * 11.5 = $80.5 to win $63.75, clearly a bad play

Therefore I win 7*11.5 + the pot at 23.75 = $104.25 over 12.5 hands

So.... my EV per hand = ( (104.25 villains long term loses) - (7 my bet on turn) - (47 river call) ) / 12.5 = $4.02

Now.. hopefully its clearer but is my maths right? is there an easier way to calc this.

PS how do you avoid the suck out on the river too =D

[Tom1975]

Ok, I understand this better now.

On the turn, the villian's play is -EV. Here's how I calculate this:

.08*63.75 - .92*7= -1.34

92% of the time he misses and loses 7 dollar. Eight percent of the he hits and wins the 9.25 in the pot plus your 7 dollar bet plus your remaining 47 on the river. This assumes you'll always call his push.

[SimaoMacaco]

Phew.. i think i got it..

but how do i calc my EV?

is it...

0.92*16.75 - .08*53 = 11.17

[SimaoMacaco]

Can someone validate my rather simple maths please.

[img]/images/graemlins/laugh.gif[/img]

[AaronBrown]

You have to be careful to define what you are computing your EV with respect to.

If you bet the $7, he calls and call any push then 92% of the time you win $16.75 and 8% of the time you lose $54. 0.92*$16.75 - 0.08*54 = +$11.09.

That is your +EV compared to conceding the hand without betting $7. But that's not relevant for your decision. You would never do that.

One other option is to bet enough to make him fold now. Then you get +$9.75, which is not as good as $11.09. Or, you could check, and still call a push. Then you make $9.75 92% of the time and lose $54 8% of the time for an EV of +$4.65. So the $7 bet is better than either a very large bet or a check. But if you could bet more and still get him to call that would be even better for you.

You should also consider folding to some pushes. If you always fold, he figures that out and always pushes, and you always lose. But with $23.75 in the pot and a stack of $47, you only have to call one-third of the time to make it not worth his while to bluff. So why throw away the extra money by calling all the time? Your job is to protect your pots, not keep him honest. Leave that to his parole officer.

[SimaoMacaco]

Thanks Aaron, I have been looking at the maths recently in a bid to improve my game. I appreciate you long response. I was looking at the worst case. I ran some further calculations with a 50% fold on the river and a 1/2 value bet bet called sometime too. It seems to me that the Math simplifies the game, and makes me feel much happier about the variance.

It was interesting to consider some cases of betting more, and him folding. His call of 7 is so bad in the long run that its hard to squeeze any extra value.

Some simple calculations convince me that betting for value is clearly the big winner in poker. Unfortunately you get suck outs.....