# Fibonacci poker

Leonardo Fibonacci was an amazing mathematician. His greatest achievement was introducing the western world to decimal number system. I’m not sure if I should be grateful for this. There is no doubt that decimal is better than the Roman numeral system it replaced, but the choice of 10 as the base is not optimal except for counting on your fingers. Fibonacci himself seemed to prefer base 60, but I don’t think that would be a good default either. Hackers would prefer 8 or 16. For everyday use, 12 would be much better than 10.

Fibonacci, though, is not famous for decimal numbers: he just popularised them; they had been used in India and Arabia long before he found them. He is famous for a eponymous sequence of numbers.

The Fibonacci sequence starts with 0 and 1. Subsequent values are obtained by adding the previous two values, so the first 10 values are 0, 1, 1, 2, 3, 5, 8, 13, 21, and 34. Patterns from the Fibonacci sequence occur in nature, and the related /golden section/ is interesting too.

I was watching to Karen, Marc, and Tony play poker this afternoon. Tony mentioned a Fibonacci straight, probably in an effort to fleece Marc out of his money. I think it’s a great idea, and we should include it in all poker games. To do that, we need to know what it is and where it lives on the poker ladder.

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.

I haven’t had a chance to calculate all the odds yet, but a Fibonacci straight is higher than a normal straight.

## 1 comment

1. Phil says:

Three combos, but one involves a pair of aces… …with two combos you would have 2048 possible hands, with three (distinct cards) it adds up to 3072. The pair of aces makes it somewhere in between, and I’m too lazy to calculate the exact value. In any case, it puts the Fibonacci straight higher than a full house, but lower than four of a kind.

The Fibonacci straight flush should beat any straight flush, although the “high” Fibonacci straight flush (2-3-5-8-K of the same suite, aka Royal Fibonacci) has the same odds as the Royal Flush. Whether it beats it or not then becomes a matter of taste… …if you go only by the rule that a Fibonacci straight is stronger than a regular straight, then the Royal Fibonacci wins.

But since the odds are identical, you may decide that a Royal Flush “always is the strongest hand”, and has acquired rights to the title.

Anyways, the odds of ever having to enforce that rule are rather slim :).