Trousers wrote:
How about BBBBBBBBBBBBBBBBBBBBBBBBBB?
Quote:
The most famous example of the gambler’s fallacy occurred in a game of roulette at the Monte Carlo Casino on August 18, 1913,[5] when the ball fell in black 26 times in a row. This was an extremely uncommon occurrence, although no more nor less common than any of the other 67,108,863 sequences of 26 red or black. Gamblers lost millions of francs betting against black, reasoning incorrectly that the streak was causing an "imbalance" in the randomness of the wheel, and that it had to be followed by a long streak of red.[1]
Ouch! Nasty if you were betting/doubling up on red from the start of that little sequence.
Like I've said though from the start, I realise what happened to me is entirely possible, merely very, very unlikely within the comparatively tiny number of spins played. Odds of 5700:1 (per spin or sequence of losing spins) are very, very long odds indeed, contrary to what has been suggested, or at least alluded to here. To my mind there are but two possibilities: either I was unlucky (
very unlucky), which is entirely possible of course - or the game wasn't entirely random at all times.
Lets put this into some context. Now, we're going to look at the mean expected
profit, at 10p per spin (probably the average seed stake amount I went for, ranging from 5p to 25p in actual fact), before a losing sequence of 12 consecutive spins could reasonably be anticipated, according to simple laws of probability.
According to my thumbnail calc (probabilities ain't my thing), the odds against
losing after 12 consecutive spins (upon which unlike my earlier example, we must now include the zero as a losing spin also), are approximately 3000:1 against. So, it'll take fully 3000 spins (or sequence of losing spins) before, on average, this is "due" to occur. In simplistic terms, even on a 10p stake, you would therefore have expected my profit to have well exceeded £7 before the 12 consecutive losers occurred? I'm not clever enough to work it out, but it should be a pretty rare event statistically to even have three reds or three blacks in a row, and roughly half the time you should be winning on the very first spin, so let's say this works out as approximately ~2000 wins before catastrophic failure - which is a profit of ~£200 on 10p/stake. Not £7...
edit: Actually, thinking about it, I've over complicated things incorrectly here. The actual expected profit is £300, not ~£200, since a PART sequence of losing spins interrupted by a winning opposite colour counts as ONE "spin" in this example. So, it's simply £0.10 x 3000 = £300 for a probability of 1.0. On that basis, a measly £7 profit before it *actually* occurred is fairly nasty.