[Leviathan]

hello david
i think i'll be the first one to post a complete mathematical solution.
I hope it's your solution too but, even if it's not, please take the time to read my entire post. It took me much time to come to it and i'd like your opinion on why it works/doesn't work.
A pb here is that people are afraid to have to enumerate all possible flops/boards/possible plays by vilain when he merely calls. The way i evaluate the different possibilities (fold/call/small raise/big raise) won't face this issue as you will see.
0. Pre calculations
Hand__times
AKs 2
AA 6
KK 1
QQ 6
JJ 3 (because vilain will make this play with only HALF JJ)
goofy 2
goofy has to be 10% of the total, hence 2. total=20 hands

1.Hero folds
EV=0 (we consider our 100$ are already lost, the fold decision doesn't cost us more)

2.Hero 3bets big
Something like 100=>500=>1500 (pot reraise)

__2.1Vilain 4bets big (here it means all in): should hero call?
_____2.1.Hero folds ro Vilain's all in reraise
EV=-1.400
_____2.1.1Hero calls all in

Hand_____EV Hero Hand__Hero's share__Net win__________Prob win
_____Times_____Size pot_____Cost call_______Prob Hand
-------------------------------------------------------------------
AKs__1,6__0.66__7035__4643__3400___1243_____22,2%_ _276
AA __4,8__0,18__7035__1266__3400___-2134____66,7%__-1422
KK___0,8__0,50__7035__3518__3400___117,5____11,1%_ _13

Explanations:
=>AKs 1,6 times among 1,6+4,8+0,8=7,2 possible hands, so probability of this hand=1,6/7,2=22,2%.
=>Prob win=net win x probability of this hand IN THIS SCENARIO (=among hands vilain will shove with)

EV=276-1422+13=-1133$
So, in case vilain shoves, Hero MUST CALL ALL IN.
Vilain will shove 7,2 times out of 20 (36%)
So the EV of 2.1 will contribute for 36% (-408$) for the total EV of the hand, if played under 2. scenario (hero 3 bets big).

__2.2 Vilain folds (ship it kid!)

Hand_____EV Hero Hand__Hero's share__Net win__________Prob win
_____Times_____Size pot_____Cost call_______Prob Hand
-------------------------------------------------------------------
QQ___6____1_____635___635___0______635_____54,5%__ 346
JJ ___3____1_____635___635___0______635_____27,3%__17 3
goo___2___1_____635___635___0______635_____18,2%__ 115

EV=346+173+115=635$
Vilain will chicken out 11 times out of 20 (55%)
Contribution of 2.2 for 2.= 0.55x635=349$

__2.3 Vilain calls
Here is the "secret" to avoid enumerating boards: i suppose that hero and vilain have equavalent skills and noone will create EV (in the long run) after the flop. So, the EV of Hero's hand just depends of it's preflop EV and of the size of the pot just before the flop is dealt.
3 things tell me that this hypothesis can't be exactly true:
i/Vilain has a positionnale advantage (advantage Vilain)
ii/Hero has info on the hands Vilain can hold (advantage Hero)
iii/some of vilain's possible holdings work better when all in preflop. Like AKs: most of the tme vilain will miss the flop and will have to fold to hero's bet. Hero's advantage.
So, my hypothesis equals to saying that i and [ii + iii] perfectly neutalize each other. We will see later that it won't always be true.
Hand_____EV Hero Hand__Hero's share__Net win__________Prob win
_____Times_____Size pot_____Cost call_______Prob Hand
-------------------------------------------------------------------
AKs__0,4__0.66__3035__2003__1400___603______22,2%_ _134
AA __1,2__0,18__3035__546___1400___-854_____66,7%__-569
KK___0,2__0,50__3035__1518__1400___117,5____11,1%_ _13


EV=134-569+13=-422$
Vilain calls 1,8 times out of 20 (9%)
Contribution of 2.3 for 2.= 0.09x(-422)=-39$

Final EV of 2. (Hero 3bets big)= -408 + 349 - 38 = -97$
First conclusion: between fold and raise big, hero should fold (loss=0$ after the firts raise, or -100$ after cards are dealt).

Strategy 3 (raise small) in next post