Confession: this question was put on hold as off-topic at "personal finance". I probably ought to have asked here straight off, but didn't think it was "mathy" enough. Just some straight arithmetic plus maybe a teensy soupcon of probability.
I realize that it will vary from casino to casino, but many on-line casinos offer quite generous sign-up bonuses. They also have some requirements, to prevent you cashing the bonus out immediately (you have to agree to play a certain amount).
It seems to me that if I play roulette and consistently bet either red or black which pay 1:1 if you win, not placing it all at once, but over say 20, 50 or 100 spins, then by the time that I have met the requirements for play, I will have broken even and effectively "laundered" my sign-up bonus such that I can now cash out everything (what remains of my initial buy in plus the sign-up bonus).
Broken even - minus, of course, the house take for 0 and 00 (Europe only has a single 0 - no 00). My math may be wrong, but that looks like I will, on average, retain 36/38 of what I gamble on those 50:50 shots.
If the sign up bonus is more generous than that, surely I will make a profit (on average) and the more casinos I sign up to, the more probability will smooth out the odds and the larger my profit.
What is wrong with my logic?
And is there a bet which offers more, with no knowledge of the rules or strategy of the game? (o.k, maybe with very simple rules such as where to hit/stick at baccarat)
[Update] I checked 3 casinos so far (from dozens) and they each have a requiement like this
The Wagering Requirements for any bonus are as follows - you must wager at least twenty times (x20) your allocated funds plus your bonus amount, unless explicitly stated otherwise in the relevant supplemental Terms and Conditions.
For example, if you allocate £100 and receive a bonus worth £100, you will be required to wager (£100 + £100) x 20 = £4000.
So, now I am off to find an online roulette simulator, to figure out if I can make a profit or not.
Unless you can figure it ot for me ...
[Update 2] Given the rules stated above, then even on European, single zero, wheel, I will lose, on average, one spin in 37.
If I wager that in 100 spins of £40, I will lose £4,000/37 = £108.018, which is more than my sign up bonus. So, even if I break even one number of red/black results, my £100 gets me, on average £100 + £100 - £108.10, or a loss of £8.10.
Of course, I could place fewer bets. Say 4 spins of £100. that would my chances of hitting zero, but increase the likelihood of my bets on red losing to a short term red/black imbalance.
Would anyone care to find the sweet spot?