America The Casino : Part 2 - Deception of Random Trends

[rose-colored-coolaid]

Flip a fair coin a trillion times, and it will almost certainly come up heads 50% of the time (within some quantity of noise). Flip it until infinity, and it will definitely approach an even split.

But the real world doesn't work that way. Instead, flip the coin 10 times. Now what's the chance of exactly 5 heads? for binomial distributions, which will give the answer. You have about a 1/4 chance of 5 heads, and 1/5 of 4 heads or 6 heads. In fact, there's a 0.1% chance of 10 heads. If this were gambling, one out of 1000 people would be 'undefeated' after 10 flips. Clearly, in small sample sizes even a fair process can look uneven.

Let's bring this back to the casino example. Remember average bets return 5%. Let every person at the casino play 10 games, gambling the same dollar amount each round. In such a case, 62% would come out ahead (5 or more wins out of 10), and 21% would come out only slightly behind (4 wins paying 110% -vs- 6 loses paying out 0) losing around 6% of their original money. Its clear how people would be split up into winners or losers.

But allow gamblers to adjust their bets and the difference between winners and losers multiplies. Those who win early can now bet more each round. Their wins increase in value. And they have a good reason to increase their bets, because each round usually pays out 5% gains. But they also can 'diversify' their bets, by playing more games at lower amounts. This reduces the likelihood of doubling their money, but also reduces likelihood of losing everything.

Thus, we see how early streaks might pigeon hole all the gamblers. Such streaks create or enforce the psychology of winners/losers I suggested in part 1.