Meat And Potatoes Real Life Good Question

[Leviathan]

1/there aren't 3 goofy hands but 2 obviously
2/if you 3 bet big, vilain pushes and you call , you will lose much more than 50$
all calculations have been done

[shawny boy]

but the villin is only calling 40% of the time and even then you win 33% of the time. check my calculations above, I think they are correct.

[riverboatking]

[ QUOTE ]
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

[/ QUOTE ]

wow great. now just do that in the one or two minutes you have to make a decision at a poker table and you'll be well on your way to poker stardom.

[creedofhubris]

RBK: Don't knock the man's efforts; if you do enough of these calcs you don't need to do them at the table.

[riverboatking]

[ QUOTE ]
RBK: Don't knock the man's efforts; if you do enough of these calcs you don't need to do them at the table.

[/ QUOTE ]

i think that trying to assign conditional probabilities and %ages to good players is a pretty futile excersize.
good players don't play the same hand the same way all the time, so to have any kind of preconcived formula in order to determine how to play a hand is a very nieve way to approach the game.

i mean i could be completely wrong on this, but i know from a personal standpoint i'll play big pairs or any two cards any number of ways depending on my opponents, game conditions, and numerous other factors and i don't think my opponents could possibly predict my range of actions based on some equations they've worked out prior to the game.
period.

[KaneKungFu123]

RBK, agreed.

[CaseAceJ]

All this math is crazy. What ever happened to playing the player. I play live NL Holdem for over a year now and do well. I know Sklanskys a math guy but Phil Ivey would crack up if he read these posts. It is impossible to say what % of the time someone holds a certain hand. You are just guessing. If you can't fold KK preflop (most can't) you will not be able to play this game for long. NL of course. The swings are so much bigger then limit, and it's so much easier to get your money in a better spot.

[yvesaint]

[ QUOTE ]
The swings are so much bigger then limit, and it's so much easier to get your money in a better spot.

[/ QUOTE ]

man these two sentences are so contradictory its not even funny

[LuvDemNutz]

[ QUOTE ]
i think this is a good question and leads to why position is so important in nl with any hand that you have. I have yet to hear an answer from anyone on this site. Personally I do not take math into the equation here as much as i should and because of it my play probably is not the positive ev that others might have. I smooth call with kk in this spot and then depending on what is on the flop i check 80 percent of the time to see how his betting pattern is comparable to other times I have played against him when he has had aa shown down in those situations.

[/ QUOTE ]

I like this line the best.

[swedeD]

[ QUOTE ]

i think that trying to assign conditional probabilities and %ages to good players is a pretty futile excersize.
good players don't play the same hand the same way all the time, so to have any kind of preconcived formula in order to determine how to play a hand is a very nieve way to approach the game.

i mean i could be completely wrong on this, but i know from a personal standpoint i'll play big pairs or any two cards any number of ways depending on my opponents, game conditions, and numerous other factors and i don't think my opponents could possibly predict my range of actions based on some equations they've worked out prior to the game.
period.

[/ QUOTE ]

If the purpose of this exercises was to determine a perfect formula on how to play in every sitution, I totally agree with you. This exercises can be really helpful though to found leaks and fundamental misunderstandings about the mathematical side of the game. If we try to consider all numerous factors in every hand that are discussed, most discussions would be pointless because only one or a few would know or "feel" this factors. Needless to say, adjustment always have to be done, and thats the beauty of the game.

I'm really thankful to all posters that are making these kind of efforts and putting in a lot of work on their posts (I'm to lazy for that). Thanks!!!