Also, why if you keep failing, you should keep trying. It doesn't work so well on slots in the long run, but too many people give up without giving themselves enough chances to succeed.
At first glance, pressing the button seems like a great opportunity. Each press has a 50% chance to double your wealth and a 50% chance to halve it (EV = 1.25x). Mathematically, this implies infinite presses should lead to infinite wealth. It becomes an infinite random walk where every positive outcome occurs with certainty. Awesome. In theory.
However, a game can offer a seemingly generous 25% average return on each press, yet most participants can still lose money because of the nature of multiplicative betting. The mean (average) wealth can explode to extremely large amounts with the median (the wealth of the typical participant) and the majority of players losing money.
In this game, wealth compounds multiplicatively, not additively. The average outcome is wildly profitable. The typical outcome is stagnation or loss. The majority of players go to zero, on a series of highly EV trades. The problem is in how much you bet each time. Position sizing transforms this risky gamble into a sustainable strategy. Let's say you do 50% instead of 100%. It instantly becomes a great strategy.
In any high-volatility, positive-EV scenario, the path to long-term profitability for the majority is careful position sizing. Survival is a prerequisite for realizing your edge. “Just survive” is not simply feel-good advice but actually useful.