Re:Gambler’s Fallacy and the Regression to the Mean
by alan-crowe on Saturday January 08, 2022 @10:49AM
(#29852744)
I find it interesting that saying "a black spin is needed to push the ratio back towards 50/50" feels like a sensible thing to say. What role do context and framing play?
Consider the first one hundred spins breaking 60 red, 40 black. That is a little odd, but not outrageously so. The ratio is 60/40 = 1.5
Suppose that the next one hundred spins break 50/50. There are no surplus blacks to push the ratio towards 50/50. So what is your intuition? It seems clear enough that the totals are 110 red, 90 black, for a ratio 110/90 = 1.22...
Having imagined the next hundred spins vividly, we are comfortable saying "Unless the surplus reds keep coming, the ratio is going to drift back towards 50/50 all by itself.". There is a striking clash between different "things we might say" seeming sensible, depending on the vividness and detail with which we imagine the situation.
Consider the first one hundred spins breaking 60 red, 40 black. That is a little odd, but not outrageously so. The ratio is 60/40 = 1.5
Suppose that the next one hundred spins break 50/50. There are no surplus blacks to push the ratio towards 50/50. So what is your intuition? It seems clear enough that the totals are 110 red, 90 black, for a ratio 110/90 = 1.22...
Having imagined the next hundred spins vividly, we are comfortable saying "Unless the surplus reds keep coming, the ratio is going to drift back towards 50/50 all by itself.". There is a striking clash between different "things we might say" seeming sensible, depending on the vividness and detail with which we imagine the situation.