Casino Game

There are a well known group of Casino games. Craps, Roulette, Blackjack and so on. But new, playable Casino games don't come up that often.

I have the blue-print of a Casino game that relies on factorization for its entertainment value. Alpertron's ECM is a well known number sieve, and will serve to illustrate my example..

The ratio and proportions of my numbers are not fixed. Rather, it would be necessary to test them with real equipment, to see how feasible a set of numbers would be. 

Here is the example:

First, choose 100 true random Base 10 digits, and concatenate for a random 100 digit number. 10 casts of ten-sided dice would do, since ten sided dice can be fair, if order is not dictated.

The player places a wager. 

The ECM does a highly deterministic probable prime test.

If the number is prime, the player wins outright.

If it factors in the first n seconds (5 mins) the player loses.

If it doesn't factor within the next o seconds (5 mins) then the player wins. Few numbers will take (n + o) seconds to factor - most factor quickly.

If it factors within a final p seconds, the player finally loses.

At the end of n+o+p seconds, if the number still doesn't factor, the player wins

This computation could be done on some normal PC, with performance features necessary to make the game fun.

Meanwhile, a distributed factorization, using the same algorithm is performed in a back room on a network of high performance computers behind the counter, so that the player can be provided with the factors upon request. 

When designing odds, available improvements are to offer higher Jackpots at each threshold, and/or adding to the wager.

A thorough knowledge of the distribution of primes, and experimentation with various hardware, would be necessary to make it practical, but it might be fun!

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