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#15 11-21-2005, 04:50 AM

At first I thought this flop raise stunk big time... I need some help with the maths, if anyone can help me out, but I'll give it a go.

The only reason you would make this raise is for the free card.
With the GS draw to the nuts and the BDFD we assign roughly 20% equity (for ease) to Hero's holding.

EV of raising = (.2*14.5sb) - 2 = .9
EV of calling = (.2*10.5sb) - 1 = 1.1

So calling is .2sb or .1BB better. But that doesn't factor the free card.
If you don't make your hand on the turn, Hero's equity drops to about 11%. So, if you get your free card, the Villians grant you your 11% equity for free.
ie. (.11*7.25BB) = .79BB

So, Hero only needs to be 13% sure of getting the free card to make this raise correct.
ie. EV(calling)-EV(raising)/free card EV = .1/.79 = .13 = 13%

BUT... this makes a few assumptions.
1. that everyone calls your raise on the flop.
2. That you're not 3bet on the flop.
3. you wouldn't have got the free card anyway.
4. BB would not have fired again on the turn when you made your hand.

This last one is the most important.
11% of the time, Hero will make his (nut str8)hand on the turn. Giving him ~95% equity of bets going in.
If BB would have fired again on the turn, had Hero not raised, Hero has cost himself 95% of between 2 and 16BB. If we assign a reasonable figure of 6BB -
.95*6BB = 5.7BB

Hero costs himself 5.7BB 11% of the time = .627BB.

If you factor this into the flop call EV calculation.

EV(calling)-EV(raising)/free card = (.1+.627)-.79 = .92

You now have to be 92%sure that you will get the free card.

There is definitely a greater than 8% chance that villians will improve on the turn and deny you the free card.

 Overall making this play -EV.

If you factor in the amount of times that you get 3bet on the flop AND don't get your free card it's a pretty easy call.

Seeing as you raised......TAKE THE FREE CARD.

I found this play very interesting and it definitely doesn't stink as much as I first thought. Something I wouldn't have thought of doing, but against the right opponents, it may be a good way to mix up your play.