Raise to protect AK on ragged flop? cruching the numbers...

[maverickai]

I'm doing some EV calculations, to see if raising on a ragged flop with AK is worth it to protect my big overs, compared with just calling.

3 players:
UTG is lagg, and will always c-bet. His range on stove is 66+,A6s+,K9s+,Q9s+,J9s+,T9s,98s,ATo+,KTo+,QTo+,JTo
MP is HERO
CO's range on stove similar to UTG.

I will formulate my EV calculations as calling to showdown to simplify things.

I hold AKs in MP, and the preflop is capped, 3 multiway.
Preflop Pot size: 6BB

Flop comes ragged: 5 [img]/images/graemlins/heart.gif[/img] 7 [img]/images/graemlins/diamond.gif[/img] 9 [img]/images/graemlins/spade.gif[/img]
UTG leads, so the question is should we raise or call? Which has better EV?

The equity for 3 players going to show down, and 2 players going to showdown are as follows:

HERO 57%
UTG 43%

HERO 36%
UTG 32%
CO 32%

1st scenario, I raise to protect, and CO folds. Thus my equity increased from 36% to 57%.
EV = ((0.57*(6+1+1+1))+(0.42*(-1-1-1))) = 3.87BB

2nd scenario, I raise to protect, but CO and UTG calls. Equity remains the same as 36%
EV =((0.36*(6+2+2+2))+(0.64*(-1-1-1)))= 2.40BB

3rd scenario , I just call, and CO calls along.
EV = ((0.36*(6+1+2+2))+(0.64*(-0.5-1-1)))= 2.36BB

Ok, EV jumped from 2.40 to 3.87 if I protect my hand successfully, but remains about the same of ~2.40 if I had raised and CO called. raising is definitely the correct move...basically raising to 'buy' equity is very vital, cos the equity would increase by 21%, and 21/36 is a 58% increase!

Hope you guys dun mind me doing math here. Just need to work these out to convince the quantitative part of the theory of protecting overcards.