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I agree - they state the following: “You’d never lose the million. If you got to [$500,000 in losses], you would stop and take your 20 percent discount. You’d

I agree - they state the following: “You’d never lose the million. If you got to [$500,000 in losses], you would stop and take your 20 percent discount. You’d owe them only $400,000.” ... So when Johnson got far enough ahead in his winning sprees, he reasoned that he might as well keep playing. I don't quite see how this makes any sense - if you get far ahead in a winning spree, the value of your discounted loss diminishes significantly... doesn't it? For instance, if you won $2 million, the discount is now $100k on a $2.5 million loss, which is only 4% (much smaller than the initial 20% discount of $100k on a $500k loss)

acak 15y ago
He went in with $1M, odds of 50/50 and a 20% discount once the losses are over $0.5M. Lets assume for simplicity that all hands he plays are equal ($0.1M according to the article) Because the discount kicks in at $0.5M of losses, he should plan to lose bets for $0.5M first. This is a setup. Now he needs play to win the bets for remaining $0.5M he has. Because the odds are 50/50, after a few rounds of playing with the $0.5M he has, he's going to have lost half the hands, and won half of them. While he gets 2x for his wins, he gives up only 0.8x for his losses. Net = 2x - 0.8x = 1.2x. He just had to rinse and repeat with the $0.5M he was left with. Though I'm sure he brought in a lot more money once the $0.5M loss kicked in the discount. Just note that this explanation is a simplification. 50/50 odds (technically 49.75/50.25 according to Johnson) have to be accompanied by an even performance on double-downs and splits.