Devil Hypothetical

Quite awhile back, I used a hypothetical where God stopped time and showed you the hands of all the other players. It's about time the Devil got his chance. This is potentially trivial for a lot of you.

You're playing deep-stack (stacks of 200+ BB) no-limit hold 'em, and you're in late position. The only action before you is a loose player who limped, and you raise it up to 4xBB with the black aces. Both blinds fold, and the limper calls.

The flop comes 8♥6♠2♥. The limper checks, you bet the pot and he calls. The turn is the deuce of clubs. The limper checks, and now the Devil stops time and whispers this in your ear:

"He has one of two hands: It's either Q♥10♥ or A♥6♣. They're both as likely. He will fold either hand if you bet anything more than a quarter of the pot, but will call with both hands if it's that or less."

This player will never bluff and never checkraise.

How much do you bet? What are your options, and what's your expected value for the different scenarios?

OK,

Your options are:

Check and let him get a free card to either make his hand or improve his hand to a better losing hand.

Raise by more than a quarter pot and take down the pot here and now.

Bet a quarter and let him draw, or bet less than the quarter and let him draw.

I vote for betting a quarter each time. In each scenario he is less than 25% to make his hand, so you gain extra equity for each dollar you get him to commit to the pot above his justified odds. Also, his implieds are zero. As it stands there are 28.5BB in the pot. You are ahead and are favourite to win from here.

If the pot is 28.5BB then betting a quarter is 7.125BB. He then calls 7.125BB for a final pot of 42.75BB

EV Situation 1 Qh 10h
(42.75BB x 0.8125) - (42.75 x 0.1875)
+26.71BB

EV Situation 2 Ah 6c
(42.75BB x 0.9580) - (42.75BB x 0.042)
+39.15BB

The payout could also change because if he catches a card that improves his own he cold pay us more, while we obviously wont pay him anything more if he makes his hand.

Another question, would you combine the two scenarios, giving him 11 outs, in order to gauge EV or would you do each one individually? If you combine them then the quarter bet is still correct and the EV is
(42.75 x 0.7756) - (42.75 x 0.2244)
+23.57BB

If we were looking purely at a single decision on the flop, I would definately bet higher than the quarter pot.

If the same rules apply to the flop, turn and river, then I would bet exactly a quarter on the flop, exactly a quarter on the turn, and exactly a quater on the river. However....

If a 6 or a heart comes on the turn I would check. If he doesnt bet the turn I would bet exactly a quarter.

As long as an unbetted non-heart 6 on the turn, isnt followed by a 3rd heart, I would bet the river

And as long as an un-betted heart on the turn wasnt followed by a 6 on the river, I would bet the river.

I think you may have misread it, Welly: Your decision is for the turn. The turn was dealt the deuce of clubs.

Oh that just makes it way too easy

I like to complicate things..lol



Just bet a quarter then.

Id fold. The devil is a liar! He has the 2

Even without doing all the exact calculations, my poker intuition tells me the EV+ play here is to chase him out with a standard 3/4 pot sized value bet. Why?

Because he's got much better implied odds against me than I have against him.

The one and only case which is good for our implied odds is when the remaining ace of diamonds falls on the river while he holds A♥ 6♣.

All other scenarios that improve his had have us burried, therefore slowplaying is a bad option. Raise healthily and dont be greedy.



ps. I'm quite new to poker so if I'm wrong dont hesitate to prove it.

He doesnt have any implied odds.

"He never bluffs and he never check raises". We know a check means he has nothing, and a bet means he has something. We also know the scare cards to make us check.

i personally bet him out for 1 good reason all you are going to win from the remaining pot is the quater because he will fold worse hands on the river and bet better ones i take the pot while im guarenteed it and play on for the other quater pot which you left behind

i'd bet as much as I could get him to not fold. he's in real bad shape with the A6, hopefully the case ace comes out on the river and you get to stack his aces up?