The interesting thing about betting on the next coin toss is that – while the coin technically always has an exactly 50% chance of coming up either side – what came before is not entirely irrelevant. The number of times the coin has been tossed, and the appearance of a streaks and its size, can inform how to place your bet, because the chance of a streak of length X at some point in the process is affected by the number of total flips. The more times you flip, the larger the chance of a streak of a given length, that length increasing the more you flip. That is, if you flip enough times, you create a significant chance of the coin coming up the same side a certain number of times in a row. Probability is weird.
I didn't know that at the time I experienced this part of the story, or I would have known that 99 times the same with only one flip left rendered it effectively impossible for the streak to continue to 100. Actually, 99 out of 99 already has a 0% chance. This would have made me suspicious of the question, which I dismissed as Idriel playing metaphysical games of no practical concern (oh foolish me). A streak of at least 5 heads has a 0.8% chance in 100 flips. 10 goes down to 0.044%. By the time you get to a streak of at least 25 heads, the chances are nearing zero, so close that a bet against it is an almost sure thing. At 54 the chance becomes indistinguishable from zero and so can be treated as impossible.
If you're curious about this (as opposed to bored or going WTF is he on about?) you can check out a calculator here:
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By the way, I tried to find out how many flips you'd need to have a non-zero chance of a streak of 99, and the response was "Wow, that's a lot of flips! Our calculator can't do that without breaking your computer. Why don't we try something smaller?" I was only trying 10,000! But even 1,000 flips won't give you a non-zero chance of 54 heads in a row. (They're probably joking about breaking the computer, and no doubt calculating up to much higher numbers is possible, but the higher you go the longer it takes and they decided that was a reasonable place to stop).
At the college party, Idriel hints that Orion is missing something when the problem is presented again – most likely that the coin toss was being manipulated, or rather that the circumstances represented by the metaphor of the coin toss were being manipulated. I originally guessed heads, and because she was asking again now realised it must be important so changed to tails, and her response was something like "You're beginning to understand."
