Re: Okay, I\'ll go first!
[ QUOTE ]
Actually, all other things being equal, if you flip heads 50 times in succession, there's a significant possibility that the coin is somehow weighted -- albeit perhaps in ways you can't easily detect. I'd be expecting a greater than 50% of heads over the next N (very large) tosses.
Cris
[/ QUOTE ]
Why require N to be very large? You have a pretty freaking good bet on the 51st flip alone.
Once you accept there's a nonzero chance that the coin is unfair, then: either it IS unfair, or you've just witnessed a one in 562-trillion odds event: like winning a one in 24-million lottery twice in a row. I think you can inch your estimation of the likelihood of another heads a tad up from 50%.
Seriously, forget about the math. If you knew you weren't being set up or hustled somehow and saw a coin flipped the same way fifty times in a row, wouldn't you be willing to give some pretty freaking long odds that it's going the same way next time too? I should hope so! There are a lot of potential gambling fallacies swirling around this subject matter, but predicting the future based on the past is only a fallacy when the events are actually random. In "real life" you're supposed to be somewhat results oriented -- otherwise known as the scientific method.
|