Nate Silver is Right(Sort of) and a Hand

In the last few days before the election, Nate Silver and his statistical analysis(http://fivethirtyeight.blogs.nytimes.com/) gave Obama approximately a 90% chance to win.  He was disparaged by many in the media, especially on the conservative side who disagreed with his analysis and who “knew” better.  People like Joe Scarborough called him a “joke” and said he should not be allowed to write until after the election was over.  All this hate over mathematical models?  I am reminded of those baseball players, managers and general managers who did not believe what sabermetrics and the idea of “Moneyball” was telling them until it started working.  To many, Silver is now vindicated because what he predicted came to be true.

To me, Silver is the same person that he always was.  I respect him immensely and love that he has brought this type of analysis to the mainstream.  However, in this case, he made a prediction about the election(with confidence intervals mind you) and he happened to be right.  His sample size for this election is 1, and even he would agree that you need a much larger sample to determine if his modeling is right(I believe it is).  If Romney had won, Silver would have been considered a fool, despite the fact that his models suggested that it would happen about 10% of the time.

A hand I won yesterday gave me similar feelings to the ones I have about Nate Silver.

A bad player($2500) who is playing every hand and never folding preflop or on the flop limps, a good player($2500) who I have played with before raises to $45 and I call($4000) next to act with 33.  A tight player calls behind me and the limper calls.

The pot is $180 and the flop comes Jc4s3c.  The bad player checks and the good player bets $140.  I elect to call for a few reasons.  Firstly, I think there is a lot of money to be had by letting the bad player call the flop(with few outs) which he will do a lot of the time.  If he elects to raise as a bluff, semibluff or with a Jack, I can find myself winning a really big pot having great equity.  I can also trap the good player in there(since he can’t fold to the bad player’s raise) and potentially win a massive pot.  Secondly, I think if I raise the flop, it’s going to be tough to stack the good player when I have represented a good hand and play fairly tight.  Thirdly, noone ever calls with a set there on a drawy board, so he won’t expect me to have one.  The bad player calls as well.

The pot is $600 and the turn comes the 5h.    Both players check to me and I have to decide how much to bet(betting is obviously) the correct play here.  For what its worth, the 5 is a pretty good card because the bad player will call with any pair+straight draw for just about any amount.  It is possible that he hit a gutshot(because he never folds the flop with it) but it is less of a concern.  I bet $425, which is a healthy bet(2/3 pot) and one designed to allow the bad player to call and potentially make a huge mistake on the river(either making a hand that is no good, or picking a bad time to bluff).  Unfortunately, he folds and surprisingly the good player calls.

I am surprised that he called because I thought he would have bet every hand he wanted to continue with, since he wouldn’t want it to risk getting checked around.  In fact, I hadn’t considered him calling, since once he checked, I assumed he was giving up.

The pot is $1450, there is $1900 left and the river is the 8h.  That is a great card since all the draws missed, and I am an overwhelming favorite to have the best hand, since the good player always raises the turn with a better hand than mine.  He checks and I think about how much to bet.  I think that if I bet somewhere in the “normal” value betting range, like $700 he is likely to realize its a value bet and not call too weakly.  I considered betting like $1100, but I think that looks relatively strong as well and while he might call weakly, I think it gets called less often than $700.  I thought for a bit and realized that if he called $1100, he would probably call $1900 with about the same frequency and that it looked a little more like a bluff.   If I had to put percentages on it, the times that he could call(excluding the times he missed a draw and was folding to any bet) were 80% to call $700, 50% to call $1100 and 35% to call $1900.  So the expected values(according to the model I gave and used in real time) are $560, $550 and $665.  In any event, he thought for a very long time and eventually called, I showed my set and won a nice pot.

I was very glad to be called and to have won a such a nice pot.  However, I immediately realized how lucky I was, since my model had him folding 2/3 of the time!  I calculated what I thought was the right play, but over a very small sample size, any slight tweak in the percentage of times he calls can change the model significantly.  Plus, I was in the pursuit of an extra $105 with a $1900 bet, with a sample size of 1!

Just like Nate Silver, you take in all the information you can, make the best model and predict using it.  Whether you are right or wrong over a small sample size is irrelevant to whether or not you did a good job modeling in the first place, despite what everyone thinks.  You just keep on doing a good job and let the numbers fall where they may.

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