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In other words, by playing a system the gambler ''can'' affect the ''distribution'' of outcomes, but not the average outcome. A gambler who bets red or black on a single spin of a fair roulette wheel has half a chance of winning and half a chance of losing. By following a martingale, the gambler can convert this into a high chance of winning a small amount, '''but this is balanced''' by a small but nevertheless very real chance of losing a very large amount.
In other words, by playing a system the gambler ''can'' affect the ''distribution'' of outcomes, but not the average outcome. A gambler who bets red or black on a single spin of a fair roulette wheel has half a chance of winning and half a chance of losing. By following a martingale, the gambler can convert this into a high chance of winning a small amount, '''but this is balanced''' by a small but nevertheless very real chance of losing a very large amount.
The martingale lends itself to a cruel self-deception. It is in the nature of the martingale that there is always a real possibility of huge loss. However, when it occurs, the gambler is likely to feel that he would have won if only he had been able to raise the money for one more bet, and therefore the loss is not the fault of the system. It would have worked, the gambler thinks, had he not had the impossibly bad luck of encountering eight, or nine, or ten "black" spins in a row.