> “I know that the fact that the roulette wheel has come up red 10 times in a row tells me NOTHING about spin #11. On the other hand, I know that over time, there will be just as many black spins as red spins, so at least intuitively, a black spin seems at least a little more likely to come up next in order to push that ratio back towards 50/50. Are these two principles actually in tension with each other? If not, how do we resolve the apparent tension? If yes, isn’t it the case that there must be “some” validity to the gambler’s ‘fallacy’?”
To this my answer would be: if you are doing millions and millions of spins then you should see roughly 50/50 but that just means over a few million spins it will balance out -- and even then it's not usable for predictions because it's not exact. Also, in a similar long sequence you would expect that in 2046 spins you see 10 of a single color in a row. That's not such an outrageously big number...
To this my answer would be: if you are doing millions and millions of spins then you should see roughly 50/50 but that just means over a few million spins it will balance out -- and even then it's not usable for predictions because it's not exact. Also, in a similar long sequence you would expect that in 2046 spins you see 10 of a single color in a row. That's not such an outrageously big number...