Re: Play a Hand With the Masters #3 Flop B
Alright I finally got a hold of Pokerstove and have been playing with some numbers. Here's what I found:
I had to take some liberty in making assumptions for our opponents range of hands...sorry if you disagree.
PREFLOP--Opponents range of hand:Preflop: Any pocket pair, any suited connectors (45 and above--throws away 23s etc), any one-gap suited connectors (46 and above), AJ+.
FLOP: 7[img]/images/graemlins/diamond.gif[/img] 5[img]/images/graemlins/heart.gif[/img] 9[img]/images/graemlins/heart.gif[/img]
FLOP--POT EQUITY (no betting):
Hero's Equity= 75% of the pot or $127.50
Villian's Equity= 25% of the pot or $42.50
The pot has $170
We could discuss the implications of this, but it gets much more interesting if we limit the range of our opponents hand after the flop betting.
Action: BB checks. Hero bets t140. BB raises to t300. The pot has $610
FLOP--Opponents range of hand--post action (Caveat...I did not take into account that he could be on a total bluff. Sorry...I'll redo the numbers later if I have time):
Any pocket pair 55+ (55,66,77, etc),
Any flush draw
Any straight draw
Any made straight (68)
Any pair with a gut draw (56s,67s,78s,89s,9Ts...not hearts)
Any 9Js (not hearts).
FLOP POT EQUITY--Opponents Limited Range:
Hero's Equity= 65% of the pot
Villian's Equity= 35% of the pot
Then I figured the pot equity for the Hero and Villian based upon different Turn cards:
POT EQUITY--Based on various turn cards and Villian's limited range of hands as stated above:
Turn: 2[img]/images/graemlins/spade.gif[/img]
Hero's Equity= 77%
Villian's Equity= 23%
Turn: T[img]/images/graemlins/spade.gif[/img]
Hero's Equity= 65%
Villian's Equity= 35%
Turn: J[img]/images/graemlins/spade.gif[/img]
Hero's Equity= 60%
Villian's Equity= 40%
Turn: 2[img]/images/graemlins/heart.gif[/img]
Hero's Equity= 66%
Villian's Equity= 34%
Turn: J[img]/images/graemlins/heart.gif[/img]
Hero's Equity= 50%
Villian's Equity= 50%
Turn: 6[img]/images/graemlins/spade.gif[/img]
Hero's Equity= 50%
Villian's Equity= 50%
Below Hero has less equity:
Turn: 8[img]/images/graemlins/spade.gif[/img]
Hero's Equity= 42%
Villian's Equity= 58%
Turn: 6[img]/images/graemlins/heart.gif[/img]
Hero's Equity= 42%
Villian's Equity= 58%
Turn: 8[img]/images/graemlins/heart.gif[/img]
Hero's Equity= 35%
Villian's Equity= 65%
Turn: 9[img]/images/graemlins/spade.gif[/img]
Hero's Equity= 38%
Villian's Equity= 42%
Thoughts: It was more or less what I expected, but I thought that it was interesting that the 9[img]/images/graemlins/spade.gif[/img] reduced the Hero's equity almost as much as an 8[img]/images/graemlins/heart.gif[/img]. I guess being counterfeited has a large influence.
Implications: So I grouped every possible card that could come on the turn into a set based upon how significantly it effected Hero's pot equity.
GROUP A: Turn: 5[img]/images/graemlins/diamond.gif[/img][img]/images/graemlins/club.gif[/img] 7[img]/images/graemlins/diamond.gif[/img][img]/images/graemlins/club.gif[/img] for a total of 4 cards.
Hero's Equity= 95%
GROUP B: Turn: A[img]/images/graemlins/club.gif[/img][img]/images/graemlins/spade.gif[/img][img]/images/graemlins/diamond.gif[/img]Q[img]/images/graemlins/club.gif[/img][img]/images/graemlins/spade.gif[/img][img]/images/graemlins/diamond.gif[/img]K[img]/images/graemlins/club.gif[/img][img]/images/graemlins/spade.gif[/img][img]/images/graemlins/diamond.gif[/img]2[img]/images/graemlins/club.gif[/img][img]/images/graemlins/spade.gif[/img][img]/images/graemlins/diamond.gif[/img]4[img]/images/graemlins/club.gif[/img][img]/images/graemlins/spade.gif[/img][img]/images/graemlins/diamond.gif[/img](in other words no heart) for a total of 15 different turn cards:
Hero's Equity= 75% of the pot.
GROUP C: Turn: J[img]/images/graemlins/club.gif[/img][img]/images/graemlins/spade.gif[/img][img]/images/graemlins/diamond.gif[/img] T[img]/images/graemlins/club.gif[/img][img]/images/graemlins/spade.gif[/img][img]/images/graemlins/diamond.gif[/img] 3[img]/images/graemlins/club.gif[/img][img]/images/graemlins/spade.gif[/img][img]/images/graemlins/diamond.gif[/img](in other words no hearts) or 2[img]/images/graemlins/heart.gif[/img] 4[img]/images/graemlins/heart.gif[/img] Q[img]/images/graemlins/heart.gif[/img] K[img]/images/graemlins/heart.gif[/img] A[img]/images/graemlins/heart.gif[/img] for a total of 15 different turn cards.
Hero's Equity= 59%-68% of the pot.
GROUP D: Turn: 6[img]/images/graemlins/club.gif[/img][img]/images/graemlins/spade.gif[/img][img]/images/graemlins/diamond.gif[/img] T[img]/images/graemlins/heart.gif[/img] J[img]/images/graemlins/heart.gif[/img] for a total of 5 cards.
Hero's Equity= 50-56% of the pot.
GROUP E: Turn: 9 [img]/images/graemlins/spade.gif[/img] [img]/images/graemlins/diamond.gif[/img] [img]/images/graemlins/club.gif[/img] 8 [img]/images/graemlins/club.gif[/img] [img]/images/graemlins/heart.gif[/img] [img]/images/graemlins/diamond.gif[/img] [img]/images/graemlins/spade.gif[/img] 6 [img]/images/graemlins/heart.gif[/img] for a total of 8 cards.
Hero's Equity= 35-42% of the pot.
SO WHAT ALL THIS MEANS IS:
Note that the above groupings account for all 47 unseen turn cards.
The pot has $610.00
On the turn:
Group A: Hero's Pot Equity 8% of the time will be $580 (95% of the pot)
Group B: Hero's Pot Equity 32% of the time will be $458 (75% of the pot)
Group C: Hero's Pot Equity 32% of the time will be $397 (65% of the pot)
Group D: Hero's Pot Equity 11% of the time will be $317 (52% of the pot)
Group E: Hero's Pot Equity 17% of the time will be $232 (38% of the pot)
TURN POT EQUITY:
The weighted sum of the Hero's Pot Equity on the Turn based upon the opponents range of hands is:
Pot Equity = (.08x580)+(.32x458)+(.32x397)+(.11x317)+(.17x232)
= ( 46.4 )+( 146.56 )+( 127.04 )+( 34.87 )+( 39.44 )
= $394.31
TURN POT EQUITY= $394.31 or 65% of the pot
Note that this is the exact same number that Poker Stove gave for our pot equity at the top of this post.
So how can you and I use this?
Dicuss what you'd do differently if a card from Group A vs Group B vs Group C vs Group D vs Group E came on the turn. And you can discuss it in terms of how it effects the Hero's pot equity!!
Or discuss why my range of hands for the Villian sucked and why I suck and why this post was a big waste of time. If people HATE that I didn't include any hands that would be a total bluff, I will redo the numbers with the villian bluffing 10% of the time which Harrington suggests is typical. Or if someone wants to start a post about what the Villian's range is, and there is some consensus then I'd be happy to use it.
And if you thought this post was useful and interesting, just wait until you start plugging in numbers for various river cards...check out my following post.
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