[baobabKoodaa]

> I'm not sure why that's called out. If you've just had 6 heads in a row the next 4 "should" be tails, so it's not an add thing to bet on tails is it?

I realize you're probably joking, but since this argument is intuitively appealing to many people, I will answer as if it was serious: if you have a weighted coin that is 60% likely to land on heads, that means it's 60% likely to land on heads on any given toss. On the first toss. On the second toss. Any given toss. Even after you have tossed it 6 times and seen 6 heads in a row, the coin is still 60% likely to land on heads. The coin has no "memory". Previous results have no effect on future results.

[vgeek]

I quickly searched but couldn't find the exact study, but I've read that by adding the past numbers digital signage to roulette tables, casinos experience a significant (I'm thinking it was like 100%+) increase in wagers when people believe that a color is "due" simply from not understanding independent vs dependent events. Humans love to look for patterns, even when there isn't any real _meaning_ behind them.

[dehrmann]

There's a corollary to the gambler's fallacy that says is P(heads) is 60% and you get 6 heads in a row, the people running the experiment probably lied to you.

[intuitionist]

If they said P(heads) is 60% and you get 4 tails in a row, you also might think the people running the experiment lied to you, especially if it happens near the beginning. But there’s a 13% chance in any sequence of four tosses.

[lupire]

but that means you should bet into the bias, not against it.

[dehrmann]

True; my point was that the person falling for the gambler's fallacy was wrong, but in a sense, so were all the people explaining the gambler's fallacy.

[6gvONxR4sf7o]

Moreover, the important feature of coin flips isn’t randomness, it’s independence (from previous coin flips and from everything else). Independence is in fact a useful mental model for randomness.