3 ms·
What about just after the unfair coin sequence toggling every even position? HTHHTHHTTHHH HHHTTTHHTTHT Should be fair. Though there is order now when the coi
by MrQuincle 6y ago
What about just after the unfair coin sequence toggling every even position?
HTHHTHHTTHHH
HHHTTTHHTTHT
Should be fair. Though there is order now when the coin was unfair.
- Someone 6y agoFair, but only over time, and not truly random. Only over time: this doesn’t help if you need _one_ fair flip. Not random: for any 2 flips in sequence, you want a probability of ¼ to get two heads. This gets you either 70% × 30% or 30% × 70%, both of which are 0.21. That’s only 84% of the expected 0.25. In general, longer sequences of heads or tails are too rare with this method (e.g. for four flips: 70% × 30% × 70% × 30% is 0.0441; only 70.56% of the expected 0.0625. The probability of 6 consecutive heads or tails is less than 60% of what it should be, etc.)
- MrQuincle 6y agoGood point about it not being random over sequences. Would be fun to find a method that would obey more constraints and requires fewer flips than TH, HT from the other comment.
- Someone 6y agoAs https://news.ycombinator.com/item?id=25531532 https://news.ycombinator.com/item?id=25531532 said look up arithmetic coding (https://en.wikipedia.org/wiki/Arithmetic_coding https://en.wikipedia.org/wiki/Arithmetic_coding) It’s not 100% the same, but understanding it should enable you to use the same idea for this problem.
- EvgeniyZh 6y agoEach individual flip is still unfair