Here is a Fibonacci-based betting strategy that I have been developing. It is the simplest and the safest of my strategies for beating a standard house at craps. It seems effective but I wonder whether its reliability can be decided more precisely
The basic game of craps is to match your point on the dice before you "seven-out". The probability that you will seven-out (and fail to match your point) depends on the point, but on average is .66.
Let us define a loss as sevening-out six times in a row. The probability that you will lose is .08. The probability of a win is then .92. And the probability of winning 5 times in a row is .65 and of winning 8 times in a row is .51. The strategy outlined below yields a 25% profit with roughly 5 to 8 wins. So it is likely on this betting algorithm to come out ahead by 25%.
Here's the strategy.
Begin with $400. Remember to quit when you have earned $100 (or go bankrupt, which is about 6 losses in a row).
Bet only Fibonacci numbers (in order) on the "pass line"
1, 2, 3, 5, 8, 13 ...
So, always begin with $1 on the pass line. If you fail to match your point, then bet $2 on the passline. If you fail to match your next point, then bet $3, and so on, traversing the Fibonacci series. If at any stage you do match your point, then begin the sequence again.
Most importantly, always take 10x odds behind the line. Completely ignore wins and losses on the come out roll, since the gains and losses there will be negligible (i.e., the game play that matters begins only after the point is established and 10X odds are placed behind the line ). The game is over when you're up $100 (and walk with $500 total) or you go bankrupt (and walk with $0 total).
Give the method a try here. Click on "options" to set your virtual bankroll and to set the game to 10X odds.
What is the precise reliability of the strategy described above? If the problem is undecidable (as I expect it is), then might one nonetheless be able to design a computer program that would run the strategy a sufficient number of times for statistical probability?