3. Uneven payout

Now let’s change the rules of the game a bit.

• When heads, John gives Paul $1.20.

• When tails, Paul still gives John $1 (feel free to change the numbers in the yellow fields).

  The new rule changes the game fundamentally: although each run will still be different, the results will tend to trend. And the trend in this case is a trend not by random chance but the result of a mathematical necessity.

  In the second game, Paul has an edge. Paul will, most likely, make money. Yes, with fluctuations, but, over the long run, mostly consistently.

Warning: if you keep pressing F5 enough times, you will also bump into disappointing results. That is because the effect of luck, aka random chance, is never zero. Even though we have an edge, some of the runs may still turn out to be disappointing. This mathematical fact has profound implications to trading.