BlueAngel,

I don't think you've understood the terms of the challenge. 100% guarantee of profit means that you should look at the worst case scenario, in terms of variance, in the 1000 spins (no house edge, with one chip added per 100 spins - 10 chips bonus in all).

Flat betting won't cut it, but some kind of progression might. I have a few ideas for this, but in the meantime here are my results for flat betting on singles, splits, streets, quads, sixlines, dozens, and ECs (bonus chips added).

I've assumed a negative variance of -3 standard deviations over the 1000 spins and calculated the returns and losses for each of the bets. Even though -3 SD covers 99.7% of scenarios, it can get worse than that, so in a sense I'm being a little generous here.

The formula for variance is:

W = NP ± Z × sqrt(NPQ)

N = number of bets (1000 in this case)

W = number of wins

Z = z-score (in this case -3)

P = probability of a win

Q = probability of a loss

Having found the number of wins for each group of numbers, you can then multiply by the payouts to get the return. I wrote a little program to do all this and here are the results:

BET RETURN LOSSES

single 442.000 -558

split 604.000 -396

street 694.000 -306

quad 739.000 -261

sixline 796.000 -204

dozen 874.000 -126

even 914.000 -86