The Gambler’s Fallacy applies in both directions: if an event has happened more frequently in the past than expected, then the Fallacy states that it is less likely to occur in future as well. So for example, rolling a 6-sided die three times and getting two sixes in such a world should also decrease the probability of getting another six on the next roll by some unspecified amount.

That is, it’s a world in which steps in every random walk are biased toward the mean.

However, that does run into some difficulties. Suppose that person A is flipping coins and keeping track of the numbers of heads and tails. The count is 89 tails to 111 heads so far. Person B comes in watches for 100 more flips. They see 56 more tails and 44 heads, so that A’s count is now at 145 tails to 155 heads. Gambler’s Verity applied to A means that tails should still be more likely. Gambler’s Verity applied to B means that heads should be more likely. Which effect is stronger?

Now consider person C who isn’t told the outcomes of each flip, just whether the flip moved the counts more toward equal or further away. Gambler’s Verity for those who see each flip means that “toward equal” flips are more common than “more unequal” flips. But applied to C’s observations, Gambler’s Verity acts to cancel out any bias even more rapidly than independent chance would. So if you’re aware of Gambler’s Verity and try to study it, then it cancels itself out!

So if you’re aware of Gambler’s Verity and try to study it, then it cancels itself out!

This is fantastic!

I’m not sure the best way conflicting expectations could resolve. It could be a flat vote or have magnitude proportional to the amount of observations...Or even based on relative emotional investment! What could possibly go wrong?

The Gambler’s Fallacy applies in both directions: if an event has happened more frequently in the past than expected, then the Fallacy states that it is less likely to occur in future as well. So for example, rolling a 6-sided die three times and getting two sixes in such a world should also

decreasethe probability of getting another six on the next roll by some unspecified amount.That is, it’s a world in which steps in every random walk are biased toward the mean.

However, that does run into some difficulties. Suppose that person A is flipping coins and keeping track of the numbers of heads and tails. The count is 89 tails to 111 heads so far. Person B comes in watches for 100 more flips. They see 56 more tails and 44 heads, so that A’s count is now at 145 tails to 155 heads. Gambler’s Verity applied to A means that tails should still be more likely. Gambler’s Verity applied to B means that heads should be more likely. Which effect is stronger?

Now consider person C who isn’t told the outcomes of each flip, just whether the flip moved the counts more toward equal or further away. Gambler’s Verity for those who see each flip means that “toward equal” flips are more common than “more unequal” flips. But applied to C’s observations, Gambler’s Verity acts to cancel out any bias even more rapidly than independent chance would. So if you’re aware of Gambler’s Verity and try to study it, then it cancels itself out!

This is fantastic!

I’m not sure the best way conflicting expectations could resolve. It could be a flat vote or have magnitude proportional to the amount of observations...Or even based on relative emotional investment! What could possibly go wrong?