[maverickai]

Question 1
Total hands he can hold:
AA
1 possible hand
1 spades hand

KK
6 possible hands
3 spades hands

QQ
6 possible hands
3 spades hands

JJ
6 possible hands
3 spades hands

AK
8 possible hands
4 spades hands

Therefore odds is (1+3+3+3+4)/(1+6+6+6+8)
= 51.8% he has a spade.
I will round up to 52%

Question 2
Let's assume villian bets out on turn and river, and HERO calls.

Total EV of calling down = ((0.48*15)+(0.52*-2))
= 6.16BB

EV of turn and river call down bets = ((0.48*2)+(0.52*-2))
= -0.08BB

Pot's too big to ignore. Calling is still +EV, so reasonable to call down.

Question 3

Assuming villian will call when he holds no flush, and he will raise if he has a flush.
EV of HERO's turn bet/fold = ((0.48*1)+(0.52*-1))
= -0.04BB

EV of HERO's turn check/call = ((0.48*1)+(0.52*-1))
= -0.04BB

Same EV for both decision. I'd go for check/call, you get to see the river, and you don't forfeit the huge pot.

Question 4

So that adds hands like:
TT
6 possible hands
3 spades hands

AQs
2 possible hands
1 spades hands

The odds he's holding onto spades becomes = (1+3+3+3+4+3+1)/(1+6+6+6+8+6+2)
= 51.4%

Well... not much difference if he's range is widened.

So teacher, is my math correct??? [img]/images/graemlins/confused.gif[/img]