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?

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    $\begingroup$ "I realize that it will vary from casino to casino" pretty much captures it. It's hard for me to imagine what an interesting answer to the fully general question would be. $\endgroup$ – Ben Millwood Jan 11 '16 at 14:32
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    $\begingroup$ But: this is not a completely crazy idea, and you might be able to make money doing it. But probably not very much. $\endgroup$ – Ben Millwood Jan 11 '16 at 14:32
  • $\begingroup$ Well, I think that it just seems so much like "free money" and "to good to be true", that I am just looking for someone to agree that it is feasible. Btw, roulette averages 40 spins an hour, which ought to smooth out the probability bumps. I am at work at the moment, so can't look at casinos, but I can post this evening. let's say I find on that says "if you bet 500 of your won money, we ill give you an addition 500 which can only be bet, not cashed in (although any winnings from that can be cashed in)", then it seems to me that I will win 1,000 * (36/38) on average, for my 500 investment. $\endgroup$ – Mawg Jan 11 '16 at 14:57
  • $\begingroup$ It looks like I will have to "suck it and see". I would like to say that I will report here about back how it goes, but if I lose my shirt I will likely be too embarrassed to admit it; and if it works I won't need a shirt and will be too busy signing up to more casinos via satellite link from my new tropical island ;-) $\endgroup$ – Mawg Jan 13 '16 at 9:22
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    $\begingroup$ It certainly used to work 10 years ago. Online casinos offered an automated blackjack player that you could program with a perfect strategy (easily available online) and let it play itself overnight. Any such perfect strategy has negative expectation but padded with the bonus becomes profitable overall. Really easy money and this is exactly the reason that it shouldn't work today. But really the best place to ask are gambling forums but be aware that most ppl will be biased if they make money by commissions when they introduce you to online casinos $\endgroup$ – K_P Feb 14 '16 at 10:32

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