The few times I’ve been gambling, I’ve invested a few bucks in a roll of coins, and budgeted that to last the time I planned to spend before gorging on the $4.99 buffet. $10 of quarters gives you a lot of sensory overload, with the lights, bells, sirens, and coins spilling into the loose metal cup. My lastgambling escapade was over ten years ago. I travel to Atlantic City every year for a conference, and haven’t felt the need to gamble since the time in Tahoe where I lost, let’s see, $20 between my wife and me.

Maybe we gambling because what we care is not about the expected value, since we receive more “utility” to high gain than to middle or low gain. So, we indeed are rational people, even if we gamble. In other words, even knowing statistics, I can gamble and being a rational man.
That’s what we’ve learned a long time ago with St. Petersburg Paradox, isn’t it?

Sounds to me like its Doctrow who needs to learn how statistics works. Data mining or any other diagnostic procedure allow us to calculate a posterior probability of an event which may be much higher than the prior probability, suggesting whether or not we should investigate further–we may have a much SMALLER haystack.

As one statistician said about our detractors: “There are liars, outliers, and out-and-out liars.” And lots of folks who should have taken TWO semesters of statistics, and passed with better than a C.

let’s adress 3 paradoxes he mentions: a guy going to Vegas thinking he can win big, a parent who panicks at the slightest menace to their child, and the paradox of a false positive where a test that work 99% of the time to detect a condition that happens once on a million cases actually gives misleading results 9999 times on 10000.

guy goes to vegas:
mathematically, if one plays indefinitely they will lose an infinite amount of money. but this can’t happen as one’s lifespan and resources are limited. on the other hand if one wins big, which has admittedly very small chances of happening, they could get more money than they ever could earn in a lifetime. and until they actually spend their betting money, they enjoy the hope of winning which has a non-null value.
In other words: you spend a limited amount of money, which you accept to lose, and you get a chance to win an unrelatedly high amount of money. Is that such a bad deal? If one had an infinite amount of time and money at their disposal, then gambling could only yield negative results, but such is not the case.

For the panicking parent, the same reasoning apply in the opposite direction. Losing a child has an infinite cost, even though it has a low chance of occuring (unfortunately higher than winning at the lottery but still), while taking all possible precautions has a non-null cost. while such precautions could seem excessive and unjustified, they make sense in the face of the unbearable possiblity of letting your child be harmed. Again if one felt comfortable with the idea of putting a price tag on a child’s life, there could be a treshold where it would be rational to stop. That’s the difference between the real world and a hypothetic model.

finally the example he gave is not too convincing. it is inaccurate to say that this test gives erroneous results 9999 times out of 10000; because it also gives correct results for 990000 people…

I’m a mathematician that gambles now and again. and loses more often than not. but that’s ok

It does make you reconsider the use of visualization as a “this is how it is and will be” tool of analysis and prediction. But then again, it’s pretty difficult to account for those rare events.