Protecting against flushes

[kongo_totte]

Ok, I tried to do some math about the so far given examples.

Push flop:
We will win $75 62.73% of the time and loose $25 37.27% of the time, EV= $37.73/hand.

Check and push a non-club turn:
We will win $50 80% of the time and will never loose any money, EV= $40

Bet $10 on flop and $15 on non club river:
We will win $75 62.73% of the time and loose $10 20% of the time and loose $25 16.4% of the time,EV= $40.95/hand.

The time he misses the turn and hits the river, you will lose $25. This will happen 16.4% (0.8*0.205) of the time.

If my math is correct, the results are quite interesting. Of course this should mean there is an exact amount that is more optimal on the flop. Can someone smart figure out a formula to get that number?

EDIT: In this post I disregarded what effect a turn ace or king will have on the calculations. And I am way too tired to make the calculations with that taken into the picture right now.

[ajmargarine]

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Answer: check behind, push any non-club turn.

-cj

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Actually, if a non-club Q or J come on the turn, it gives villian 3 extra outs to hit an inside straight in addition to the flush. These 3 outs make a big difference whether or not to bet the turn in this hypothetical. Villian now has 12 outs and is 2.83 to 1 to make his hand. As the best Hero can do is bet $25, Villian is getting 3:1 on this call and it would be +EV for him long term to do so.

If a K came on the turn, it would give villian two extra outs to hit a hand (trip K's) that beat Hero giving him 11 outs total. Now he is 3.18:1 to make his hand and so Hero should bet the $25.

It's an interesting hypothetical that could actually teach EV to someone?!? Intuitively, the bet $10 now and then $15 on the turn, doesn't seem like to me like it should be a higher EV than the check behind. Might have to run some math on that to see for sure.

[Macquarie]

Nice post.

You're absolutely right. Ignoring for now the complications if an A, Q, or J fall (i didn't mean to include that complication) and just considering a 1/5 flush draw.

Actually there is an optimal amount to bet on the flop. Just looking at your

[ QUOTE ]
62.7% win 75, 20% lose flop bet, 16.4% lose 25

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I gues that we want to bet as little as possible on the flop [minimise our 20% loss], but enough so that the villain will just call our river bet [if we bet less than this on the flop, villain will fold to our river bet and the equation breaks down because now we don't ever win $75].

So the flop bet that gives villain just 4:1 odds for calling the river push is $5, making a pot of $60 for the $20 turn push.

EV is almost $43, compared to flop push EV of $35 and flop check EV of $40. Your numbers are slightly out since they don't quite add to 100%, but the gist is correct I think.

Pretty complicated...

[ajmargarine]

[ QUOTE ]

So the flop bet that gives villain just 4:1 odds for calling the river push is $5, making a pot of $60 for the $20 turn push.

EV is almost $43, compared to flop push EV of $35 and flop check EV of $40.

[/ QUOTE ]

This can't be right. Where's my calculator?

[DoomSlice]

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Is it a general rule that checking has a higher EV than betting an amount that gives viallin odds to call?

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Most certainly not, since checking is giving him infinite odds.

The only situation where it arises is when you don't have enough money to allow him to make a mistake on the flop, but you do have enough to have him make a mistake (or a very close decision) on the turn.

[DoomSlice]

Just cause villain has odds to call doesn't mean you shouldn't push the turn. Giving him a free shot at it is a lot worse than giving him 3:1 odds.

[ajmargarine]

[ QUOTE ]
Just cause villain has odds to call doesn't mean you shouldn't push the turn. Giving him a free shot at it is a lot worse than giving him 3:1 odds.

[/ QUOTE ]

I think we are talking here about maximizing EV. And it's been shown that checking behind is higher EV for Hero than pushing on the flop.

[Macquarie]

Doomslice is right about the turn play, as he stated - on the turn it is always better to bet than to check against a draw that is <50% probablilty of completing.

The possibility of it being best to give a draw a cheap card only arises on the flop when we have to consider the possibility of gaining an even greater EV by holding back until the turn.

[Macquarie]

Post deleted by Macquarie

[xcrack999]

Very nice post, Macquarie. I think your example is very similar to the situation in TOP (but TOP's situation is for limit hold'em) that says if you bet on the flop with a good but not invulnerable hand and your opponent raises, and you think your opponent is raising on the come (raising with a draw), it is better to just call his raise and bet out on a non-draw-completing turn. I don't know if what I said is 100% correct, but I remember I read something like that in TOP. Maybe someone who still has his TOP can check it.