Friday, August 10, 2012

An example of range variance in poker.


BB is a 50/31 fish with 57% bet.  He loves these little min donk bets.

MP is a 27/20 donk with 14% 3 bet pre, 24% 4 bet, 16% flop raise, 25% flop check raise.  He's aggro as fuck.  He folds to 3 bets pre 57%, which isn't a lot.  He raises any draw on the flop.  We'll be seeing him more later in this blog post, stay tuned!

Merge - $0.04 NL (6 max) - Holdem - 6 players
Hand converted by PokerTracker 3: http://www.pokertracker.com

UTG: $6.14
MP: $8.66
CO: $3.71
Hero (BTN): $4.00
SB: $5.24
BB: $1.61

SB posts SB $0.02, BB posts BB $0.04

Pre Flop: ($0.06) Hero has Ah Kh

fold, MP raises to $0.14, fold, Hero calls $0.14, fold, BB calls $0.10
I elect to flat him here for balance and deception.  I had just 3 bet him with AA in a hand you'll see next, and I didn't feel like calling a shove with AK since he shoves at least JJ+ if not TT+ as well as AK+ (but not AQ, he flats with that hand).  So against that range I don't feel like I'm in the best shape, and I'd rather keep his worse aces in.  He's also so aggressive that if I miss with AK in a 3 bet pot I'll have lost a lot more and he's likely to attack every single pot in existence.  and if I hit, I get payed off huge for sure.  This might have been a mistake but I don't think a huge one.

Flop: ($0.44, 3 players) 5s Jh Qs
BB bets $0.04, MP raises to $0.43, Hero raises to $3.86 and is all-in, fold, MP calls $3.43
BB donk min bets, which means absolutely zilch.  MP raises, which also means very little.  He raises every single draw, so every flush draw in his range, every gutshot, every open ender, every Q.  Against a Q, I have 40% equity, and against his range total I felt like I was a favorite, including fold equity.  He wouldn't likely call me with his draws, only probably a Q or better, so a lot folds.

Turn: ($8.20, 2 players) 2d

River: ($8.20, 2 players) Ac

MP shows Qd Jd (Two Pair, Queens and Jacks) (Pre 37%, Flop 78%, Turn 91%)
Hero shows Ah Kh (One Pair, Aces) (Pre 63%, Flop 22%, Turn 9%)
MP wins $7.79

Here's the math:

Text results appended to pokerstove.txt

 101,970  games     0.005 secs    20,394,000  games/sec

Board: Qs Jh 5s
Dead:  

equity  win  tie        pots won  pots tied
Hand 0:  43.269%   38.89%  04.37%           39661       4460.50   { AhKh }
Hand 1:  56.731%   52.36%  04.37%           53388       4460.50   { JJ+, 55, AQs+, AsJs, ATs, As9s, As8s, As7s, As6s, As5s, As4s, As3s, KQs, KsJs, KTs, Q9s+, JsTs, T9s, AQo+, ATo, KQo, KTo, QTo+ }


This includes only those suited combos with a flush draw, so not all KJs, only KJ of spades.  For gutshots and OESD's it includes all suits, since he raises any draw at all.  These hands were all in his preflop raise range.  This range is 12.1% of hands.  When I shove, I expect to only get called by AA, KK, AQ, KQ, QQ, JJ, QJ.  With blockers factored in, that's 4.4%, or approx 1 out of 2.75 of his hands call me while the rest fold out.  Around 2/3 of his range folds to my raise.  Against his calling range, I have 24.8% equity.

Text results appended to pokerstove.txt

  43,560  games     0.002 secs    21,780,000  games/sec

Board: Qs Jh 5s
Dead:  

equity  win  tie        pots won  pots tied
Hand 0:  24.821%   24.49%  00.34%           10666        146.00   { AhKh }
Hand 1:  75.179%   74.84%  00.34%           32602        146.00   { AcAd, AcAs, AdAs, KcKd, KcKs, KdKs, QQ-JJ, 55, AcQc, AdQd, AsQs, AsJs, AsTs, KsQs, KsJs, QJs, JsTs, AQo, KQo, QJo }

I think you can see this is a clearly +ev move.  So, I ran into the premium part of his range.


Same villain.  Copy+Paste:  MP is a 27/20 donk with 14% 3 bet pre, 24% 4 bet, 16% flop raise, 25% flop check raise.  He's aggro as fuck.  He folds to 3 bets pre 57%, which isn't a lot.  He raises any draw on the flop.  This hand was maybe 5 minutes prior to the above.

Merge - $0.04 NL (6 max) - Holdem - 5 players
Hand converted by PokerTracker 3: http://www.pokertracker.com

BB: $4.34
UTG: $4.00
CO: $3.18
Hero (BTN): $5.14
SB: $4.28

SB posts SB $0.02, BB posts BB $0.04

Pre Flop: ($0.06) Hero has As Ac

UTG raises to $0.14, fold, Hero raises to $0.28, fold, fold, UTG calls $0.14
He's so aggressive pre, I am begging him to 4 bet or shove me here.  Unfortunately he just calls.

Flop: ($0.62, 2 players) Jc Jd Kd
UTG checks, Hero bets $0.41, UTG raises to $1.37, Hero calls $0.96
He's raising any K, any J, and any draw here.  Since he flatted my 3 bet, his continuing range after a 3-bet is 11.4%, but some of that range 4 bets, so in reality his flatting range is something like 8.6%.  ATs+, ATo+, KTs+, KQo+, QTs+, 77+ according to pokerstove.  We can probably adjust a few things to make it more realistic like taking out 77-88, ATo and A9s and adding in KJo and QJo, but this seems pretty reasonable.

Villain raises every draw and every top pair+.  Which is 7.1% of hands, or 0.84% of the hands in his range.  So he's raising me here over 4/5 times.  I'm a 50% favorite against this range according to pokerstove, we'll see the math a little later.  However, I figured if I ship it, he lays down all his draws and only calls me with a J, maybe a K, but he might even lay down a K.  This is still probably the most +ev way to play it, but I know he's aggressive and he's going to barrel basically every turn card.

Turn: ($3.36, 2 players) Ts
UTG bets $1.68, Hero calls $1.68
Given my knowledge about his range, I have to call this.  I'm getting 3:1 and I know he barrels 100% of his range here basically.  According to pokerstove I have 37% equity against his range here, which is certainly +ev.

River: ($6.72, 2 players) Kc
UTG checks, Hero checks
If he had a K, it got there.  My equity on the river against his range is 5%.  This seems like a clear check-back.  Although, if he had a K, he'd bet this river, so I have a chance to steal it by shoving, since he probably thinks I have a full house.  At the time this didn't really occur to me - I just thought he was probably done bluffing and he folds all worse always, so why bet? 

UTG shows Ad Qs (Straight, Ace High) (Pre 7%, Flop 19%, Turn 90%)
Hero shows As Ac (Two Pair, Aces and Kings) (Pre 93%, Flop 81%, Turn 10%)
UTG wins $6.39
... yeah.



  42,570  games     0.001 secs    42,570,000  games/sec

Board: Jc Kd Jd
Dead:  

equity  win  tie        pots won  pots tied
Hand 0:  52.221%   52.01%  00.21%           22139         91.50   { AcAs }
Hand 1:  47.779%   47.56%  00.21%           20248         91.50   { AQs-ATs, KTs+, QJs, AQo-AJo, KJo+, QJo }

   1,848  games     0.001 secs     1,848,000  games/sec

Board: Jc Kd Jd Ts
Dead:  

equity  win  tie        pots won  pots tied
Hand 0:  36.986%   35.71%  01.27%             660         23.50   { AcAs }
Hand 1:  63.014%   61.74%  01.27%            1141         23.50   { AQs-ATs, KTs+, QJs, AQo-AJo, KJo+, QJo }


---

 35  games     0.001 secs    35,000  games/sec

Board: Jc Kd Jd Ts Kc
Dead:  

equity  win  tie        pots won  pots tied
Hand 0:  05.714%   05.71%  00.00%               2          0.00   { AcAs }
Hand 1:  94.286%   94.29%  00.00%              33          0.00   { AQs-ATs, KTs+, QJs, AQo-AJo, KJo+, QJo }


No doubt both hands were +ev, although they might not be the most +ev lines to take.


And we'll end with a bit of variance:

Merge - $0.04 NL (6 max) - Holdem - 6 players
Hand converted by PokerTracker 3: http://www.pokertracker.com

BTN: $4.30
SB: $5.59
BB: $1.29
Hero (UTG): $4.24
MP: $4.10
CO: $4.00

SB posts SB $0.02, BB posts BB $0.04

Pre Flop: ($0.06) Hero has Ks Ad

Hero raises to $0.14, MP calls $0.14, fold, BTN calls $0.14, fold, BB raises to $0.32, Hero raises to $1.38, fold, fold, BB calls $0.97 and is all-in

Flop: ($2.88, 2 players) 4s Qd 4d

Turn: ($2.88, 2 players) 3s

River: ($2.88, 2 players) Qs

BB shows Qh Qc (Four of a Kind, Queens) (Pre 57%, Flop 99%, Turn 100%)
Hero shows Ks Ad (Two Pair, Queens and Fours) (Pre 43%, Flop 1%, Turn 0%)
BB wins $2.74


And a little positive variance early on:

Merge - $0.04 NL (6 max) - Holdem - 6 players
Hand converted by PokerTracker 3: http://www.pokertracker.com

CO: $4.16
BTN: $5.57
SB: $2.74
Hero (BB): $4.00
UTG: $4.00
MP: $4.00

SB posts SB $0.02, Hero posts BB $0.04

Pre Flop: ($0.06) Hero has Jc Kh

fold, fold, fold, BTN raises to $0.08, SB calls $0.06, Hero calls $0.04

Flop: ($0.24, 3 players) Ad Ts 2c
SB checks, Hero bets $0.12, BTN calls $0.12, SB calls $0.12

Turn: ($0.60, 3 players) Qc
SB checks, Hero bets $0.36, BTN calls $0.36, SB calls $0.36

River: ($1.68, 3 players) 5d
SB checks, Hero bets $0.99, BTN calls $0.99, fold

Hero shows Jc Kh (Straight, Ace High) (Pre 26%, Flop 17%, Turn 97%)
BTN shows Kd As (One Pair, Aces) (Pre 74%, Flop 83%, Turn 3%)
Hero wins $3.48



Got AA once and lost.  Got AKs once and lost.  Got AKo twice, won once.  Got KQo twice, got 3 bet both times from MP (same guy) and had to fold.  Those were his only 3 bets.  Not the best session, haha

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