> I just tossed the koin a few times. Here's the sequence it's landed in so far:
> T H T T T T T
> How likely do you think it is to land heads on the next toss? You might look at that sequence and be tempted to think a heads is "due", i.e. that it's more than 50% likely to land heads on the next toss.
> That's irrational. Right?
> Wrong. Given your evidence about koins, you should be more than 50% confident that the next toss will land heads; thinking otherwise would be a mistake.
Given the evidence I have about koins (the sequence) I would actually make the assumption that it's most likely for the next toss to be T. And that koins is not a fair coin.
In a more gambler relevant context, if a roulette ball ends on red 10 times in a row. It's more likely to end on red on the 11th time as well, the implication being that the roulette is not fair.
> T H T T T T T
> How likely do you think it is to land heads on the next toss? You might look at that sequence and be tempted to think a heads is "due", i.e. that it's more than 50% likely to land heads on the next toss.
> That's irrational. Right?
> Wrong. Given your evidence about koins, you should be more than 50% confident that the next toss will land heads; thinking otherwise would be a mistake.
Given the evidence I have about koins (the sequence) I would actually make the assumption that it's most likely for the next toss to be T. And that koins is not a fair coin.
In a more gambler relevant context, if a roulette ball ends on red 10 times in a row. It's more likely to end on red on the 11th time as well, the implication being that the roulette is not fair.