Tactile Simulation of a 2006 WSOP Final Table Hand

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Although it's been a few weeks since Harvey hit, and over a week since Irma hit, I recently caught wind that one of the hosts of a podcast that I listen to (@NateMeyvis of the Thinking Poker Podcast) has been offering free copies of his ebook on tournament poker strategy if you send him a copy of your receipt for a >$5 donation to a Houston and/or Irma-related charity.

Lish and I have been thinking that Houston and Florida are both probably going to need money for some time to come still, so I figured I would help spread the word despite it having been a bit since the disasters. Nate has asked for receipts to be sent to the following email address: backing at fastmail dot fm; if you've donated, send a copy of your receipt there to get a copy of his book in return.

Now, onto the post!

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Let's go back to the beginning for a minute: the very first page of the textbook we've been using opens with the following...

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"It's hand 229 of day 7 of the 2006 World Series of Poker (WSOP) Main Event, the biggest poker tournament ever played, and after the elimination of 8770 entrants it is now down to the final three players. The winner gets a cash prize of $12 million, second place is just over $6.1 million, and third place gets about $4.1 million. Jamie Gold is the chip leader with 60 million in chips, Paul Wasicka has 18 million, and Michael Binger has 11 million. The blinds are 200,000 and 400,000, with 50,000 in antes.

Gold calls with 4♠ 3♣
Wasicka calls with 8♠ 7♠

Binger raises with A♥ 10♥
Gold and Wasicka call.

The flop is 10♣ 6♠ 5♠

Wasicka checks, perhaps expecting to raise, but by the time it gets back to him, Binger has bet 3.5 million and Gold has raised all-in. What would you do, if you were Paul Wasicka in this situation?"
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I absolutely love that this is how our book begins. And, if a picture is worth a thousand words, then a video must be worth even more than that... so here is the ESPN footage of this hand, which of course also shows what ultimately ends up happening in the hand (the link should cue it up to the right spot automatically, but in case it doesn't, this hand starts at 31:43 in the video).

• Fun Fact 1: I was one of the 8770 entrants who were eliminated prior to this (I went out on Day 2)
• Fun Fact 2: In my recollection, this final table was the first time that footage of any major tournament was ever shown live (and if it wasn't the first, it was definitely the early days of it). Poker viewing got popular in the Chris Moneymaker year of 2003 and ESPN did a great job of covering it, but it was always, and still often is, shown in 1-hour, made-for-TV packaged episodes that were/are shown months after it actually happened. Live footage is still not the most widely-consumed form of poker viewing, although it is has been very slowly heading that way for some time. ESPN and PokerGO teaming up to bring live coverage of the 2017 WSOP throughout the entire summer was a step in the right direction.
• Fun Fact 3: I had my eyes glued on this particular live-stream because I had placed a bet on one of the players at the final table to win the whole thing (I placed $150, getting 10:1 odds, on Doug Kim who ended up busting in 7th). I remember watching this as I was trying to pack up my entire life to move from Baltimore to Seattle to start my Ph.D. at UW, and being unable to get much packing done that night.

The beauty of this example is that it has so much going on in it, especially for those, like many of my students, who came into the class with little or no poker background. Our author has done a great job of revisiting this example numerous times throughout the first few chapters to illustrate various concepts that we have been learning, and I think having that constancy is a nice pedagogical tool.

We have thus been following that path, starting from watching the footage of the hand back in the first week of class. Then, across the past few weeks, we have been answering small questions about the hand as we develop our tools, such as:

• What is the probability that Wasicka makes a straight flush on the turn?


• What is the probability that Wasicka makes a straight flush on the turn or the river?


• What is the probability that Wasicka makes a flush on the turn?


• What is the probability that Wasicka makes a flush on the turn or the river?

(See comments section below for the answers)

One of the big questions, of course, is what Wasicka's overall probability of winning the hand is, knowing everything that we know at the time of the flop. ESPN tells us in the footage that it's 54%, but how did they come up with that number?

Well, it turns out that there are a ton of cases to consider, which makes the calculation a huge pain. Our author does it on pages 35-36 of our textbook, but it's not something that I would ever put my students through on a quiz or exam.

I did, however, make them explain (in Question 1 of this assignment) why it's not simply that Wasicka wins if he makes a straight or a flush. Basically, the answer is that Binger or Gold could still win with a bigger hand. For example, if the turn is the 10♠, then Wasicka has made his flush, but Binger could still win with a full house if the river is any remaining Ace.

But the real thing I wanted my students to walk away with last week is that, if a probability calculation is cumbersome, we can approximate it via simulation.

To this end, in class this past Friday, we did an activity in which we did exactly that:

• I put my students into groups of 3 (or 4 as needed)
• In each group, the students pretended to be Wasicka, Gold and Binger
• They extracted the hole cards from the deck for each player, and the flop of
  10♣ 6♠ 5♠
• Then they dealt the turn and river cards, and determined who won.
• I asked them to pull back the turn and river, shuffle the deck, and repeat for a total of 20 times.

In statistics education, we call this a tactile simulation (as opposed to a computer simulation) since we are doing it with physical objects that we have to touch in order to randomize and allocate.

A couple action shots:

Bobby is Paul Wasicka
Zach G. is Jamie Gold
Zach D. is Michael Binger

Looks like a winner for Jamie Gold over here.

At the end of class, I tallied up the results across all groups. Not every group got 20 replicates, but we were close enough to get an idea. Here's what we got:

And here's a snapshot of the ESPN footage showing the true percentages:

So, we were pretty close on Gold, but a little bit off on Wasicka and Binger.

The final point that I made was that, while tactile simulation is good for illustrating what is happening, in practice it is better to get estimates via computer simulation. That is, it took us about 20 minutes to get this many replicates across the entire class, and they were quick to recognize that if we got more replicates, we would get more accurate estimates of the true probabilities -- but that it would take a long time to get an amount that we are happy with.

To this end, we are also learning how to code up simulations of exactly this type in R. And with R, we can get, say, a million replicates for a situation like this in a matter of seconds.

You can check out the full worksheet for the activity here.


Next up: we have our 2nd poker night next week, to which I have also invited our ASA club and a couple other statistics instructors to help out!