Marty has a little flight of fancy about introducing Fibonacci straights into poker. Link (thanks, Marc!)
A Fibonacci straight is a hand of 5 cards forming a subsequence of the Fibonacci sequence. So, in poker there would be three such straights: A, A, 2, 3, 5; A, 2, 3, 5, 8; 2, 3, 5, 8, K. The latter two can occur in flush form too.
Based on my quick calculations, the 5-card odds of getting dealt a non-flush fibonacci straight are 925:1, and the odds of getting dealt a fibonacci straight flush are 324,869:1.
That makes a fib-straight more rare than a full house, and a fib-straight flush more rare than a straight flush. However, if I was going to play with these (which I'm not), I'd probably make a fib-straight the same class as a normal straight, and a fib-straight flush be the same class as a normal straight flush, ranked on high straight card -- so A2358 gets beaten by 45678, 2358K gets beaten by 9TJQK, and AA235 is the lowest straight. That would make straights and straight flushes both slightly more common, but enough to disturb the "natural" poker rankings.
You may notice that it's "harder" to make AA235 than any other straight - there are 768 of those, versus 1020 of the others. So that's an argument for making it the highest straight. But I would favor leaving it on the bottom because that preserves card order, and in practice AA235 would be "easier" to make than many other straights because AA and Ax are much more common hold'em starting hands than, say, 97.
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