[DcifrThs]

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She could make this play with a nine a jack, a draw or a big hand like a set. Like pipedream said, I figured if I did three bet, there was a good possiblity of getting 4 bet, and I was not folding my hand under any circumstances.

So if she does have me beat and I three bet, she will four bet me, and I will have to call her four bet, and a river bet. So If I'm wrong, I lose 5 bets total between the turn and the river. If she has a draw, and I just call the turn, she will bet into me again on the river so I get three bets total. But if she has a draw and I raise her, I still only get three bets because she obviously won't pay off on the end. Finally, she could have a made hand that is inferior to mine, in which case she will call my three bet and another bet on the river. So I get 4 bets when she holds a worse made hand.

It got me thinking about some of those checkraise situations where you are up agaist someone who is very possibly on a draw, but could also hold a big hand. Sometimes I think it's better not to three bet without a very big hand in these spots, because if it is a draw, they are probably going to bet the river anyway a lot of time, so you get the same amount of bets. But when you are behind, you can end up losing as many as five bets if you are reraised and then bet into on the river.

So supose a third of the time she has a draw, a third of the time she a hand she can call my three bet with and pay off the river with, and a third of the time she had a hand that has me beaten and it costs me five bets to showdown. I'm not a math guy, so whats the right play?

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Well since you asked i'll give that math answer a wirl. its one of those situations where that is EXACTLY what you would want to do against good/tricky and other tricky players and is well thought out. BUT we may not be dealing with one of those because its a MANIAC.

anyway i did the EV/time played calculations and ended up with +$0.33 per time we reraise the turn and maniac caps and we call maniacs river bet/bluff. so we know that its at least a positive ev play. but is it the play with the most positive ev? if we just call it costs two fewer bets on the turn but we win two bets fewer bets those 2/3's of the time where we'd get them on the turn. i did the calculations w/ identical assumptions and found out that it is +$0.22 per time played because we don't win those 7 total bets when we reraise he caps the 2/3's of time with worse hand) when we call turn c-r and call when bet into on the river.

In addiation, the initial assumptions were 1/3 hand worse, 1/3 hand better, 1/3 draw which wouldn't pay off but would bet if we called. but maniac will r-r with ANY draw and will have worse hands and draws MUCH more than 2/3 of the time in this situation...probably more like 5/6 of the time or higher if its a real maniac, kq would give the maniac a draw, any qt, any aj, even a9 (a little unlikely since h'ed most likely bet and 3 bet flop with top pair top kicker), but other hands include any bigcard+jack or even overcards with some people. so i think maniac would cap and bet out river a total of many more times with worse hands/draws when we take into account the likelihood of each hand he'd do it with.

As a result, you're looking at an even higher EV for the reraise turn vs. call turn & river (probably more than $0.50 maybe even $1.00 b/c of the two bet difference a lot of the times the maniac has worse hands which are so much more likely).

Other variations like call turn raise river or reraise reraise reraise again (pretty unlikely...i wouldn't wanna spend that much on this hand) but i think they won't be much higher than the reraise & maniac caps and we call river as per above analysis.

And i think the reason the less aggressive approach is better vs. a good player is b/c those times won't be 1/3 1/3 1/3...it is much more likely the better player has much better hands in this situation and won't be raraising w/ cockeyed draws giving us 2 extra turn bets and 1 extra river bet so the times we are reraised on turn we'll be looking at a winner much more often than with the maniac.

what does everybody think? and can someone check my math (i did it in spreadsheet form on excel) questions? comments?

-Barron

So there's my shot at an introductory "math answer" for you