Wednesday, September 13, 2006

WSOP Final Table Hand No. 229: Split Decision

Call or Fold?Okay, one more. All in all, ESPN’s pay-per-view was well done, I’d say. I can’t imagine sitting through the whole thing live, but watching it this way -- in easier-to-digest segments, after the fact -- has been a treat. In fact, as this here post exceeds all reasonable guidelines for length, let me suggest you approach it similarly. Don’t feel obligated to read all at once . . . take it in small chunks, if needed. The discussion comes in three parts: (1) a description of the action; (2) an attempt to assess one of the player’s decisions using game theory; (3) a last reflection.

I. The Action

This is the last hand to feature three players. Jamie Gold has 63,425,000 in chips. Paul Wasicka has 13,325,000. Michael Binger has 12,650,000. The blinds are still 200,000/400,000 (with the 50,000 ante). We watch the action from the bird’s-eye view of the overhead camera. Not following Jesus’s advice for playing the button while three-handed (described in the previous post), Gold limps from the button from over on the right-hand side of the table. On the left, Wasicka calls from the small blind. Binger -- in the middle -- puts in a raise of 1.5 million. Gold pauses and calls Binger’s raise. We are shown a lengthy close-up of Wasicka riffling his chips as he decides what to do. We hear Wasicka speaking. “You can’t have a hand every single time, Jamie . . . Jeez.” About twenty seconds go by, and Wasicka makes the call. The pot is 4,650,000.

“And here’s the flop,” calls out the tournament announcer -- 6sTc5s. Wasicka very deliberately taps the felt with an extended finger. Phil Gordon points out how “it wasn’t an instant check . . . he did study it.” Binger reaches forward and pushes in a healthy 3,500,000 chip bet. Close to half of Binger’s chips are now in the pot, so he’s likely committed to go all the way here. Before he can even bring his hands back to his sides, Gold waves back-handedly and says “I’m all-in.”

Wasicka immediately groans and stands up from the table, obviously less than thrilled with Gold’s move. “This is sick,” he says through gritted teeth. Gold loudly cries out “This is it, guys!” “This is sick,” repeats Wasicka. “We all got a hand, let’s do it,” says Gold. “Let’s go all three . . . let’s get it over with, right now.”

Wasicka is fit to be tied. “Are you kidding me?” he says to no one in particular, sitting down and reexamining his cards. He stands again and asks Binger how much he has bet. Gold interrupts saying it doesn’t matter because he’s all-in, but Wasicka objects and Gold backs off. A moment passes and Wasicka again voices his displeasure. “This is disgusting,” he says. Gold nods as if in agreement. His nod evolves into a goose-like bobbing action, then he stands upright and claps his hands. Wasicka folds and Binger instantly calls.

Binger has AhTh for top-pair, top-kicker. Gold has 4c3s for an open-ended straight draw. Gold claps his hands, then shakes Binger’s hand and wishes him good luck. Gordon announces Gold has eight outs, but soon we learn that he actually only has seven. “Paul, You didn’t have the best hand, did you?” Gold calls across the table. “I had the seven-eight of spades,” answers Wasicka. He has folded an open-ended straight flush draw. “Wow,” says Gordon. “I don’t know how you can fold that hand.”

The pot is 26,800,000. “Gimme a spade, at least,” asks Gold. The turn comes -- the 7c. Even better. Gold is hugging Johnny Chan. And Binger is drawing dead.

Binger is smiling and very gracious. He tells a friend he’s curious to see what the river card is, and whether it would have helped Wasicka beat him (if Gold had stayed out of the pot). He walks over to Wasicka and they shake hands. “It’s been a pleasure, man,” says Wasicka. “I’m curious if I would’ve beaten your hand,” says Binger. He’s thinking about what would’ve happened if he had gone all-in first. Would Gold have folded? (Probably not.) If Gold had folded, would Wasicka have called him? “I probably would’ve,” says Wasicka. “One of us has to take [chips], you know.” The now-meaningless river card comes -- Qs. Wasicka would’ve made his flush.

Wasicka wanders around the table with a half-smirk, half-grin on his face as Harrah’s officials set the stage for heads-up play. Within seven hands, Gold will take the rest of the chips (between scoops of blueberries).

II. Wasicka’s decision

Gold’s all-in was bold. It is probably safe to say it altered the outcome of the hand. It arguably sealed his victory for the tournament as well. If Wasicka had made the call with his straight-flush draw, he would’ve won the hand and had around 38 million chips -- not too far from half of the chips in play. Let's forget about that spade on the river for a moment. Should he have called?

If we are talking strictly pot odds, the answer is yes. He need to put 12 million in to win a pot of nearly 27 million -- that’s 3.25-to-1. With a whopping 15 outs for the turn and the river, he’s looking at better than 2-to-1 to hit a winner. If this were a cash game, calling would be a no-brainer.

But this ain’t no cash game. If he calls and wins, terrific. However, if he calls and Gold still wins the hand, the tournament ends right there with Wasicka finishing in second place (since he began the hand with more chips than Binger). If Wasicka calls and Binger wins the hand, he will either be left with 675,000 chips (if his hand beats Gold’s), or will be out right there in third place (if Gold’s hand beats his) -- either way, he’s very likely destined to finish third. So calling could end well or disastrously. But folding also is something of a risk. Folding means either assuring himself at least second place or becoming the short stack by a fairly large margin (he’d be about 15 million behind Binger).

Put yourself in Wasicka’s position. What would you do?

How about this. Let’s say everyone was allowed to turn their cards face up after Gold went all-in. Now put yourself in Wasicka’s position. Let’s say you were even allowed to use CardPlayer's Texas Hold ’em Calculator. You know you’re 53.82% to win the hand. You know Binger is 29.01% to win. You know Gold is 17.17% to win. What would you do?

Here’s where we might actually use some of that game theory stuff we keep hearing people like Chris "Jesus" Ferguson answering questions about but most of us never really pay much heed. (If numbers ain’t yr bag, save yourself some grief and skip now to section III.)

Let’s say you make the call. Over half the time you end up heads-up with nearly half the chips. Let’s also say if that were to occur, you’d have a 50-50 chance of winning the whole ball of wax. About a third of the time you will either finish in third right here or within the next hand or so. Another 1/6 of the time you’ll finish in second place right here. So by calling . . .

-- 27% of the time you win $12 million (after winning a heads-up battle)
-- 43% of the time you win $6 million (after losing a heads-up battle or after busting out right here in second)
-- 30% of the time you win $4 million (after busting out right here or soon afterwards in third)

Let’s say you fold. Once you’ve folded, Binger is about 65% to win and Gold 35%. (I can’t be precise here, but that’s about where it stands given Gold has seven available outs plus the backdoor flush draw.) Let’s also say that if Binger wins the hand, 2/3 of the time you’ll end up playing for awhile and getting bounced out in third place. (I say that because he’d have a bit over twice your chips.) And if Gold wins (as happened), let’s make you a 6-to-1 dog to overcome the huge chip lead and somehow win. (I say that because Gold has over 6 times Wasicka’s chips when heads-up begins.) In other words, by folding . . .

-- 5% of the time you win $12 million (after winning a heads-up battle)
-- 52% of the time you win $6 million (after outlasting Binger and making it to second or after watching Binger lose here and then eventually losing a heads-up battle)
-- 43% of the time you win $4 million (eventually busting out in third)

Which is the better decision? Isn’t it obvious? (Ha ha.)

Knowing what we know, calling is going to be the more profitable play here. Let’s say we play out this scenario 200 times and we call 100 times and fold 100 times. The 100 times we call, here’s how we do:

Win $12 million 27 times = $324 million.
Win $6 million 43 times = $258 million.
Win $4 million 30 times = $120 million.
TOTAL = $702 million or an average of $7.02 million each time.

The 100 times we fold, here’s how we do:

Win $12 million 5 times = $60 million.
Win $6 million 52 times = $312 million.
Win $4 million 43 times = $172 million.
TOTAL = $544 million or an average of $5.44 million each time.

Thus, between the two choices, calling is clearly going to be more profitable than folding. So says game theory, anyway . . . .

III. Final thoughts

To be fair to Wasicka, this here experiment assumes full knowledge of everyone’s cards and all of the relevant percentages. Not precisely what happened in real life, to be sure. However, I think it is safe to say Wasicka pretty much knew where he stood when he made the decision. He knew how many chips everyone had. And he knew that all 15 of his outs were probably good. (He could’ve feared a higher spade draw, but I’d be willing to bet that possibility really didn't affect his thinking too greatly when he made his decision to fold.) [EDIT (added 9/18/06): Listening to Wasicka on CardPlayer's The Circuit this week, I discovered that, in fact, he was worried Gold was on a higher flush draw here! So I'd have lost that bet.] So even without knowing that the spade came on the river, Gordon was probably right when he suggested calling was the play to make here.

While it's doubtful Wasicka had all of this worked out to the nearest hundredth of a percentage point, he still knew (I'd argue) that he probably should call. And that he probably wasn’t going to. That’s why he is repeating how “sick” and “disgusting” the situation is. We’ve all been there (though never for these stakes). We know know know what is right, but we just can’t act on that knowledge and the pull the trigger.

In the final hand of the tournament, Wasicka did pull the trigger and make the call of an all-in. Only this time Gold had him beat. As I mentioned before, I’m gonna leave that hand to others to decipher. Watch it here, if you want. Meanwhile, for anyone who’s made it all the way through this monster of a post, it’s been a pleasure . . . .

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2 Comments:

Anonymous Yorkshire Pudding said...

All I can say is he must have liked the look of second place money more than third. I don't know how he could fold a possible 15 outs whilst playing 3 handed. Maybe that's why I donk around playing NL10 and NL25 and $5 MTT's whilst these guys are playing for ridiculous money?

9/14/2006 6:56 AM  
Blogger Short-Stacked Shamus said...

Of course, folding didn't guarantee Wasicka second . . . in fact, when Gold lucked out here so did Wasicka, b/c otherwise he'd have been in sore shape relative to Binger.

(I've added an edit in the post today after hearing Wasicka on The Circuit this week -- turns out I was dead wrong when I guessed he wasn't fretting over the higher flush draw.)

9/18/2006 4:24 PM  

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