Extraordinary Claims

“Extraordinary claims require extraordinary evidence!” When Carl Sagan popularized this expression, he was referring to claims made about the paranormal or the miraculous. In reality, the more unusual or unexpected a claim is, the more we should demand that there be accurate and verifiable proof. Recently, some scientists claim to have uncovered situations in which matter moved or could move faster than the speed of light (Einstein claimed that the speed of light was ‘God’s speed limit’). Immediately, the scientific community demanded definitive proof, which has not yet been provided.

One hears many extraordinary claims about poker and poker players. It is very easy to be confused by statistical variance and expectation. If someone said to you that he was very good at predicting whether the next card dealt would be red or black, you’d ask him to prove it. Suppose you deal one card and he calls its color correctly. Would you be impressed? Of course not. How about if he got seven right out of ten? Or 70 out of 100? Or 700 out of 1,000? As the sample size gets bigger, the percentage difference between his actual result and his expected result will get smaller. If the result is random, it will approach 50 percent. By the time you have a million trials, the result is very likely to be between 49 and 51 percent. The real result will be within one percent of the expected result, but one percent of a million is 10,000. So, an actual result that is 8,000 above average wouldn’t really be unusual. Anyone who claims to be good at picking colors is making an extraordinary claim, and they better come up with some very convincing proof if they expect to make anyone believe them.

Yet, poker players frequently claim to be really good at poker. I have a friend from New York City who took a two week vacation in Vegas. He told me he was convinced he could average $120 per hour playing $2-$5 no-limit hold’em. His proof was that he had played about 100 hours during this time and won $12,220. What do you think? I’d guess that his real average win would be a lot smaller if the sample had been bigger. Anyone claiming to win more than 20 big blinds per hour is making an extraordinary claim. Perhaps a really great player, who carefully waited for the weakest small games, might approach this figure. In my friend’s case, he was fooled by randomness.

There is a phenomena psychologists call “The Fundamental Attribution Error.” Basically, we attribute our successes internally (to our skills or efforts) and attribute our failures to bad luck or other external causes. With other people, we do the reverse. If I trip, it was because the sidewalk was cracked. If you trip, it is because you’re clumsy. Thus, we attribute winnings to our skill and advantage over our opponents. And when we lose?

Reasons for losses are another area of extraordinary claims. My favorite is the player who claims that his opponents are so bad he can’t beat them. He can go on a losing streak at $1-$3 no-limit hold’em, which he knows is caused by how badly his opponents play, and immediately move to a $5-$10 game expecting to win. Let me assure you that $1-$2 and $1-$3 games have a lot of bad players. That makes them much easier to beat than higher-stakes no-limit games. Clearly, playing badly can’t be a winning strategy, or it wouldn’t be playing badly. In general, if you can’t beat smaller games, you won’t be able to beat bigger games. Occasionally. an exception occurs when several very rich, weak players are playing in a high-stakes game. This might allow someone who breaks even or loses small at a lower stake to be a winner here.

Other extraordinary claims of bad luck relate to a run of cards. I sometimes kid around and say, “I haven’t won a pot since dinosaurs ruled the earth.” Other people seem to seriously believe their complaints. A typical example: “The last ten times I’ve had aces, I’ve lost.” Obviously, the chance of losing with aces depends on the number of opponents and what their hands are. To see how unlikely it is that this claim is true, let’s assume aces win 80 percent of the time. Losing ten times in a row, would occur about once every ten million times you have aces! Even losing three times in a row happens less than one percent of the time. In case you are interested, the results chart for aces three times is as follows:

3 wins, 0 losses 51%
2 wins, 1 loss 39%
1 win, 2 losses 9%
0 wins, 3 losses 1%

I could continue with examples of extraordinary claims of great skill or bad luck. My advice is not to pay much attention to them. The person making these claims won’t be able to provide extraordinary evidence or even moderately credible evidence. Even when the claim is historically true, like my friend’s win rate for 100 hours of play, don’t assume it represents the real expectation. The more extraordinary it sounds, the more likely it is to be either false or a statistical aberration. ♠

Steve ‘Zee’ Zolotow, aka The Bald Eagle, is a successful gamesplayer. He has been a full-time gambler for over 35 years. With two WSOP bracelets and a few million in tournament cashes, he is easing into retirement. He currently devotes most of his time to poker. He can be found at some major tournaments and playing in cash games in Vegas. When escaping from poker, he hangs out in his bars on Avenue A in New York City -The Library near Houston and Doc Holliday’s on 9th St. are his favorites.