Analysis of an Overcall

In his most recent blog entry, Matt Matros poses a question to his readers. I will pose the question as given on his site, then my response.

Full Tilt Poker Game #654277261: WSOP Main Event Qualifier (4011295), Table 4 - 20/40 - No Limit Hold'em - 21:18:22 ET - 2006/05/21
Seat 1: MVMadman (1,840)
Seat 2: pennohawk (3,875)
Seat 3: jacksup (3,315)
Seat 4: twopairdad (1,290)
Seat 5: DavidH (1,685)
Seat 6: bert2245 (3,710)
Seat 7: Steve Zolotow (1,865)
Seat 8: All In At 420 (275)
All In At 420 posts the small blind of 20
MVMadman posts the big blind of 40
The button is in seat #7
*** HOLE CARDS ***
Dealt to jacksup [Th As]
pennohawk folds
jacksup raises to 90
twopairdad folds
DavidH folds
bert2245 calls 90
Steve Zolotow calls 90
All In At 420 folds
MVMadman folds
*** FLOP *** [2s 9c 9s]
jacksup checks
bert2245 bets 40
Steve Zolotow calls 40
jacksup calls 40
*** TURN *** [2s 9c 9s] [Ks]
jacksup checks
bert2245 checks
Steve Zolotow checks
*** RIVER *** [2s 9c 9s Ks] [5s]
jacksup checks
bert2245 checks
Steve Zolotow bets 450
jacksup calls 450
bert2245 calls 450
*** SHOW DOWN ***
Steve Zolotow shows [Jd Ad] (a pair of Nines)
jacksup shows [Th As] (a flush, Ace high)
bert2245 mucks
jacksup wins the pot (1,800) with a flush, Ace high
*** SUMMARY ***
Total pot 1,800 | Rake 0
Board: [2s 9c 9s Ks 5s]
Seat 1: MVMadman (big blind) folded before the Flop
Seat 2: pennohawk didn't bet (folded)
Seat 3: jacksup showed [Th As] and won (1,800) with a flush, Ace high
Seat 4: twopairdad didn't bet (folded)
Seat 5: DavidH didn't bet (folded)
Seat 6: bert2245 mucked [2h 4h] - two pair, Nines and Twos
Seat 7: Steve Zolotow (button) showed [Jd Ad] and lost with a pair of Nines

Before I give any analysis, I'm going to take a poll. What was the EV, to the nearest unit, of bert2245's overcall on the river?


Obviously this call is horrible. Even against two completely random hands, bert2245 only has the best hand about 10% of the time. His EV in this case is (.1015 * 1350) - 450 = -313.

But jacksup and SteveZ don't have random hands. bert's EV against their actual hands is (x * 1350) - 450, where x is the percentage of times he has both players beat. Let's argue this from two different logical extremes.

1) The problem here is that jacksup can't be bluffing. It's difficult to imagine a scenario where jacksup can't beat a pair of deuces -- he would have had to call with A-high or worse with another player still to act behind him. SteveZ is reputed to be a solid player, so it will be incredibly rare to see jacksup calling here without being able to beat a pair of 2s. And even when he does, SteveZ has to happen to be bluffing at the same time!

I will estimate that the likelihood of both of these events happening added to the likelihood that one or both of jacksup and SteveZ misclicked with worse hands at 1/4 of 1% (which I think is incredibly generous). So bert should expect to win (0.0025 * 1350) = 3.38 by calling 450, making his EV around -447. This is the worst case for bert.

2) One could also argue that the probability that SteveZ is bluffing is particularly high because he's likely to only bet either a K-high flush or better or A-high and worse on this type of board, making this probability something like 75/25 in favor of him bluffing. A bet this large makes it look even more like a bluff. Knowing this, jacksup might call with ANYTHING that beats a bluff, down to hands like A-high. This means that jacksup is calling with any A, K, 9, 5, 2, pair, or spade in his hand, which accounts for about 81% of his possible holdings.

bert's equity against jacksup's range is still only 12.12%. According to these numbers, bert will win the pot about 9% of the time when he calls, making his EV (.09 * 1350) - 450 = -328. This is the absolute best case for bert.


One could reasonably argue both of these extremes or anything in between. Such arguments would likely depend on other factors, like if both jacksup and bert both know that SteveZ is steaming or something. In the absense of other such factors, I think the reality is that it is incredibly unlikely that jacksup will call here with things that can't beat a pair of 2's, even given that SteveZ is probably bluffing here quite often. All things considered, I'd say bert has the best hand something like 0.5% of the time, making his EV (0.005 * 1350) - 450 = -443.


By the way, this hand is from a $1000 buy-in tournament. Wow.