I've always wondered how many heads/tails you'd get in a row if you could just keep flipping coins forever. The other day I was bored so I put together a stupid matlab script to try it out (leaving out the "forever" bit).
It's obvious that in theory you could get a never ending series of heads or tails, but in practice that is infinitely unlikely to happen, so I just wanted to get a feel for a "reasonable" figure in terms of how many repetitions one should expect to experience if one actually started tossing coins (or betting money on red/black at the roulette) for a very long time.
Out of 100 million series of coin tosses (where a series is defined by an uninterrupted streak of heads or tails) the longest streak of identical outcomes was 26 (I wanted to try with a billion series but was taking too long).
That means that if you go to a casino to make money doubling bets on red/black (the so-called Martingale strategy) and you are particularly unlucky you might have to flush out 20*(2^25) = 671,088,630 $ (a single bet is usually at least 20 $) on your last bet to actually make a profit (plus all the money you spent to get there).
If you play smart though, and you wait for 5 reds/blacks in a row before you start betting against that, then you can get away with a last bet of only 20*(2^20) = 20,971,520 $ (that's 20 millions!).