Protecting against flushes

[bizaff]

Ok, here we go.

Hero should win about 63% of the time from the flop.

EV of pushing on the flop = 75 * .627 - 25 * .373 = 37.7

Assuming you check on the flop and take a look at the turn, the following outcomes are possible:

Card (# possible / % chance \ Hero win % @ Villain win % | EV of hero pushing now)

2 of clubs (1 / 0.022 \ 0.068 @ 0.932 | -18.18)
Other club (8 / 0.178 \ 0.000 @ 1.000 | -25)
Other Q/J (6 / 0.133 \ 0.727 @ 0.273 | 47.73)
A spades (1 / 0.022 \ 0.818 @ 0.182 | 56.82)
Any K (3 / 0.067 \ 0.750 @ 0.250 | 50)
Any other (26 / 0.578 \ 0.795 @ 0.205 | 54.55)

We know 2 things: we're not going to push if we're behind without odds to draw (we'll assume villain will push and not let us draw free if he hits his flush) and villain will not draw without pot odds. This means any negative EV is reduced to zero, and any EV over 50, villain won't pay off and will fold, in which case we win the 50 in the pot for an EV of 50. After limiting EVs (0 < EV < 50) and multiplying each EV by the chance to get that particular outcome FROM THE FLOP, we sum them together to get 39.70. (47.73 * 0.133 + 50 * (0.022 + 0.067 + 0.578))

It's fairly close, but if the villain will play as specified, check the flop and push a safe turn.

[Macquarie]

Hey,
it's getting pretty heated.

Two conclusions I think.

EV of a line through a hand is defined as expected profit from this decision forward relative to folding. Folding has 0EV. A line that starts with a check can have a negative EV if we make bad decisions afterwards; saying the check itself has -EV is meaningless without stating what your line is for the rest of the hand.

Folding the flop has 0EV by definition. If we decide to check the flop and fold any turn, that line has 0EV. If we check the flop and push a non-club turn, that line is +EV. If we decide to check the flop and fold any non-club and push any club turn, that line is -EV.

Whenever we talk about the EV of a decision we are actually also assuming how we will play out the rest of the hand and are really talking about the EV of a complete line to the end of the hand. Whenever we talk about the EV of calling a turn bet on a draw, we are assuming that we will not put in more money if we miss, and make a guess that villain will put in $x when we hit. In this case we are estimating how the hand will play out after the turn decision in order to make the EV calculation.

Other conclusion is, checking the flop and giving the villain "infinite odds" to draw to his hand is a better play than the push that gives villain better than correct odds. But this applies only in this case where we cannot protect with two cards to come on the flop, but can protect with one card to come on the turn.

[Ghazban]

You should also come to the conclusion that the flush draw would maximize his EV by pushing the flop even if he knows he's up against two aces. Your original phrasing of the scenario was somewhat paradoxical as the flush draw player would not check that flop (even if he knew he was against aces), particularly if he understood pot odds as you stated he did. The whole issue of what the AA should do is mostly irrelevant as the AK should never have checked in the first place.

[CamelZoo]

interesting ev calculations, but in the real world in this case who wouldn't push AA on this flop with pot = 2x their stack? anything else and you're letting villain off way too easy... this is more a lesson of stack size vs. flush protection.

[Macquarie]

[ QUOTE ]
interesting ev calculations, but in the real world in this case who wouldn't push AA on this flop with pot = 2x their stack? anything else and you're letting villain off way too easy... this is more a lesson of stack size vs. flush protection.

[/ QUOTE ]

So you're saying "Interesting EV calculation, but in the real world I'm gonna push anyway."

Just so you know, EV calculations do apply to the real world too [img]/images/graemlins/grin.gif[/img]

[midget23]

bet 10.25 on the flop and 14.75 on a non flush making turn

[FlyingStart]

It's not best for AKs to get allin on flop.. The best for AKs is to check both flop and turn. The reason why he should not check here is because we will bet the turn. Given that, AKs should move allin

[fathertime]

You give him odds to call on the flop with any bet, if and only if he gets to see BOTH cards.

You give him infinite odds on the flop if you check.

And so you must bet the flop--about 2/3rds and then bet any non club turn an amount that gives him bad odds to call. Pushing the turn is only good imho if you think he will call it. Otherwise bet an amount on the turn that you think he will call but that gives him the wrong odds to do so.

His call on the turn will only be correct if he calculates that the implied odds are there and that you will pay him off. That is you have enough in your stack to make his call correct if he hits his hand AND knows that you will pay him off.

[midget23]

[ QUOTE ]

His call on the turn will only be correct if he calculates that the implied odds are there and that you will pay him off. That is you have enough in your stack to make his call correct if he hits his hand AND knows that you will pay him off.

[/ QUOTE ]

its impossible for us to pay him off...he showed us his cards

[midget23]

actually i like pushing the flop. He knows that we know he is holding 2 overcards and a flush draw. There probably isnt a reason he doesnt think his A and K is good as well at this point so he probably assumes he is behind but still favored to win the hand with 15 outs.