Maybe the last chance ESPN has to get its facts right

I don't know if ESPN will continue with its "Poker Facts" feature with the next broadcasts, which are to be a final table preview, then the final table itself. If so, fine, I get more chances to see how they do. If not, then last night's show was their last chance to shine. Let's see how they did. (For previous posts in this series, start here and work backwards through the links provided.)




The first fact, shown above, requires the assumption that "an Ace" is meant literally--i.e., you do not have two aces.

Now we have to determine the probability that none of the other eight players at the table was dealt one of the other three aces. Each of them has two cards (because, as usual, we're presumably dealing with Texas hold'em here), for a total of 16 cards. The probability that the first player's first card is not an ace is 47/50, because there are 50 unknown cards and 47 of them are not aces. The probability that this player's second card is not an ace, given that his first card was not an ace, is 46/49, because there are now 49 cards left, of which 46 are not aces. We continue the same logic for all 16 cards, and end up with this expression for the joint probability that none of those 16 cards is an ace:

47/50 x 46/49 x 45/48 x ... x 32/35

Fortunately, the arithmetic is simplified by the fact that many of the numbers appear in both the numerator of one term and the denominator of another, and thus cancel out. But when you do the multiplication, you end up with 0.3053, or 30.53%. Note that this is exactly the inverse of ESPN's claim; i.e., 100% - 69.47% = 30.53%.

The problem, though, is that ESPN did the calculation correctly, but then used the wrong part of the result! 69.47% is the probability that there is at least one other ace held by another player. 30.53% is the probability of there not being another ace among those 16 hidden cards.

This makes sense if you think about it for a second. We're talking about 16 cards out of 50, or a hair under one-third of the deck in opponents' hands. There are three aces. It stands to reason that on average there will be one other ace out there, so you would expect the probability of another player holding an ace to be over significantly over 50%.

ESPN's blunder here was made worse by the voiceover, which said, "At a nine-handed table, if you hold an ace pre-flop, there is a 70% chance you're the only one who has one, so use it wisely."






The second poker "fact" of the night was the one shown above. This one is actually really difficult for me to check. It's not hard to find a list of Main Event champions and where they were calling home at the time that they won. But finding where they all were born is not easy. I don't know of any available resource that has that information all in one place.

Nevertheless, I think ESPN is correct. To the best of my ability to check things quickly, here's the list of non-American-born winners and their homelands:

Johnny Chan (1987, 1988)--China
Mansour Matloubi (1990)--Iran
Hamid Dastmalchi (1992)--Iran
Scotty Nguyen (1998)--Vietnam
Noel Furlong (1999)--Ireland
Carlos Mortensen (2001)--Spain
Joe Hachem (2005)--Australia
Jerry Yang (2007)--Laos

The caveat is that it's certainly possible that one of the apparently American winners was actually born somewhere else, while living most of his life in the states. But I'm going to assume that that is not the case, and give ESPN credit for this one.

This week's score: 1 for 2.