Sunday, November 22, 2009

An interesting Spot and E.C. practice

In order to continue to improve at poker I am going to need to analyze the game on a deeper level, and one way to do that is to work out equity calculations. Comparing your pot odds, and likelihood of winning the hand against your opponents likely range of holdings and then making the correct decision in tricky spots separates the great players from the average. This hand is particularly interesting in that there are many possibilities that our villain could hold and our equity may not be immediately apparent.

In the early middle stage of a multi-table tourney we open raise with 89s, the button and big blind both call. We flop middle pair and an open ended straight draw. The big blind check raises all in and we have a tough decision to make.

Full Tilt Poker $38,000 Guarantee No Limit Hold'em Tournament - t20/t40 Blinds - 9 players - View hand 383965

The Official Hand History Converter

CO: t3755 M = 62.58

BTN: t2293 M = 38.22

SB: t4653 M = 77.55

BB: t2198 M = 36.63

UTG: t3833 M = 63.88

UTG+1: t2790 M = 46.50

UTG+2: t4355 M = 72.58

Hero (MP1): t2673 M = 44.55

MP2: t3450 M = 57.50

Pre Flop: (t60) Hero is MP1 with 9 of hearts 8 of hearts

3 folds, Hero raises to t120, 2 folds, BTN calls t120, 1 fold, BB calls t80

Flop: (t380) 8 of spades 7 of hearts T of spades (3 players)

BB checks, Hero bets t240, BTN calls t240, BB raises to t2078 all in, Hero requests TIME

Should we call or not? The answer might surprise you. Here are the steps we need to take to make the correct decision:

1) Figure Pot odds
2) Figure our equity vs. villains range of holdings
3) Convert equity percent to a decimal
4) Compare equity to pot odds

Pot odds: 1.6 to 1
This part is straight forward and exact. After our villain shoves, there is 2938 in the pot and it costs 1838 to call. Pots odds are 1.6 to 1 (2938/1838 = 1.59)

Equity vs. villains range:
This is a little trickier to figure and is not an exact science. First you need to determine the possible hands that you are up against then estimate the likelihood of each holding and finally compare the winning chances of your hand against his entire range of possible holdings.

In this particular hand this is the range of hands and % likelihood that I have assigned to our villain. The use of a poker calculator like Poker Stove is the easiest way to determine your equity vs. various villains holdings.

Villains Hand Our equity
Flush Draw ~50%
Top Pair, Top Kicker 47%
2 Pair 30% - 50%, average 40%
Set 28%
Top Pair, open ended 27%
Bluff 85%

Now we need to assign a likelihood to each holding. This is just our best guess.
Villains Hand Likelihood
Flush Draw 25%
Top Pair, Top Kicker 20%
2 Pair 20%
Set 15%
Top Pair, open ended 10%
Bluff 10%

(Equity X Likelihood)
Flush Draw (50 X .25) + TPTK (47 X .20) + 2 pair (40 X .20) + Set (28 X .15) + TP Open Ended (27 X .10) + Bluff (85 X .10) = (12.5 + 9.4 + 8 + 4.2 + 2.7 + 8.5) = 45.3

So we can now say that our equity against his range of holdings is 45%!

Now we need to convert that percentage to a decimal for the purposes of comparing it to the odds the pot is laying us to determine whether or not we should call.

45% = (100 - 45 or rather 55 to 45) = 55/45 = 1.222

Since the pot odds of 1.6 are greater than 1.2 we have a definite call!

As an aside even if our villain had more chips and the call was twice as much, 3676 chips to call instead of 1838, (and assuming that we had enough chips to make the call) it would still be correct to do so as our pot odds would be 1.3 to 1, which is larger than the 1.2 required!

In the actual hand I went into the tank and made the call. Our villain showed 9T for top pair with an open ended straight draw and had us crushed. We lost the hand and busted out of the tournament but we can rest easily knowing that we made the correct decision, and that folding would have been a weak play.


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