Great Expectations

Bozzer

Been lurking for a bit - decided to post one.

There was a thread on here a few of days ago about calculating the EV of playing some draw heads up in nlhe.

This will probably bore most of you but I thought the following hand is a useful exercise for such calculations:

NL Hold'em
the flop is As 8h 9h

you are on the button with Js Th

SB (who you are 100% certain has top set) leads at the $200 pot with a $150 bet (making a total of $350 in the pot and $150 for you to call).....it is folded to you....if you call the $150 you will have $575 left (and you are 100% certain he will bet you all-in on the turn no matter what the card is).

Do you make this call?
Give your first instinct answer and the math one if you wish .
I’ll post my answers if necessary.

ArmaniJeanss

Clear Fold, you have 8 outs to a straight, no flush outs except runner-runner and you also have to hope the board doesnt pair to give a house to Mr TopSet.
Did you maybe make a mistake in your typing the hands ???

Regards,
AJs

roryc

Maybe he had Jh.

Would make it more interesting....

ianmc38

roryc wrote:

Maybe he had Jh.

Would make it more interesting....

Yes well otherwise it's a definite fold. Pot odds are alot shorter than 1 in 8.

Bozzer

I mentioned that you were certain opponent would would push turn regardless, so the odds you are being offered are 925/150 > 6:1. You are 5.625/1 to hit on the turn, so you are getting odds ignoring his redraws.

But how much do the redraws affect the decision....

padser

V good. Nice reasoning. two problems.
1) if the board pairs ((7 outs on the turn, 8 on the river i think)
2) your never going to be in situation of knowing he has top pair and will push on the turn regardless

NickyOD

Bozzer wrote:

I mentioned that you were certain opponent would would push turn regardless, so the odds you are being offered are 925/150 > 6:1. You are 5.625/1 to hit on the turn, so you are getting odds ignoring his redraws.

But how much do the redraws affect the decision....

You need to hit one of 8 cards on the turn AND one of 34 cards on the river since he can make a house or quads.

(8/45)*(34/44) = .129

So since this happens only 13% of the time then its a fold. If you had another $200 and he still had you covered then you can call.

However you are never going to have the implied odds to make this since you are never going to know what your oponent has or what he will do on the turn with 100% certainty.

NickyOD

...

Bozzer

I was looking at it as more of a hypothetical situation.

If opponent is known as a real rock and preflop action went – a few limpers, you raise on button, he re-raises from SB and gets 3 callers.
(Imagine he only re-raises with QQ-AA.)

Then when the flop comes A high and he leads into 3 ppl you can probably put him on AA.
Then just assume he never folds top set.

I just thought the interesting part was how much the redraws made this a clear fold.
I think you actually need a grand behind to call the flop here Nicky.

Anyway here's my math which I think is right....

There are three outcomes when you call the flop bet.

(1) fold turn -150
(2) call turn and win +925
(3) call turn and lose -725

When opponent doesn't have the Ah:

when I fold turn:
37/45 * -150 = -5550/45

when I call turn:
8/45 * [((34 * 925) + (10 * -725)) / 44] = 4400/45

so:
(4400 - 5550) / 45 = -$25.56 EV


If he does have the Ah:

when I fold turn:
37/45 * -150 = -5550/45

(calling a non-heart turn)
6/45 * [((34 * 925) + (10 * -725)) / 44] = 3300/45
+
(calling a 7h turn)
1/45 * [((28 * 925) + (16 * -725)) / 44] = 325/45
+
(calling a Qh turn)
1/45 * [((27 * 925) + (17 * -725)) / 44] = 287.5/45
= 3912.5

so:
(3912.5 - 5550) / 45 = -$36.39 EV

and finally, it's 2/3 likely that he has the Ah, so:
2(-36.39) - 25.56) / 3 = -$32.78 Total EV

So obviously calling the flop bet is a clear -EV play like you all said

Hitman Actual

I think your odds of hitting the straight are incorrect: I make it 4.625/1 (37 cards miss you, 8 cards hit you).

As Padser points out, if he hits the house on the turn you're obviously going to fold. This happens 15.5% of the time. The other 84.5% of the time, you only win when:

a) You hit the turn (17.7%) and he then misses the river (15.9%). Happens 2.8% of the time.
b) You miss the turn (82.3%) and then hit the river (18.18%). Gives 15%.

So once he misses the turn, you win 17.8% and lose 82.2% of the time.

I think you can then work out the EV like this:

EV = -0.155(150) + 0.845(0.178*925 - 0.822*525)
EV = -290.15 = Negative EV.

It's a while since I got a maths question right on this forum, so feel free to point out the errors!

Bozzer

You're right about the odds of hitting straight on turn, they should be 4.625/1.

Your calculations are wrong because we are only calling when a Q or 7 comes, which is 17.8% of time.

(0.822)(-150) + (0.178)(+925)(Prob we will win) + (0.178)(-725)(Prob we will lose)

I calculated these probabilities above.

Hitman Actual

Bozzer wrote:

Your calculations are wrong because we are only calling when a Q or 7 comes, which is 17.8% of time.

Sorry, I thought you were going to call the all-in whether you hit the turn or not.