Negative expected value, ball has no memory (independent rolls), table limits... almost everything about the odds has already been said.

But this is /biz/, so let's talk about risk/reward and sunk costs of Martingale which nobody has touched upon yet (short of the image in >>22875207).

>Round 1

Bet 1, Total Exposure 1, Max Profit 1

>R 2

B 2, TE 3, MP 1

>R 3

B 4, TE 7, MP 1

>R 4

B 8, TE 15, MP 1

>R 5

B 16, TE 31, MP 1

You notice something? Your bets grow, your total exposure grows, but your max profit always stays the same - a measly 1x your initial bet. With Martingale every consecutive bet becomes more and more unreasonable. You're throwing good money after bad because of sunk costs. By round 10 you're pushing in an additional 512 for a total investment of 1023 in the hopes of ending up with an over-all profit of 1. Now take a step-back in think if you would put 512 of your hard-earned money on a 50/50 bet that could result either in total loss or in a gain of 1. This is the position Martingale forces you in.

Best case, that means if Martingale works out and you hit your color before you go broke or hit the table limit, you've risked a shitton of your money for a miniscule profit. That's not a sound investment strategy, even if the odds were stacked in your favor (which they aren't).