r/learnmath•
lilmorrris

Question about probability (blackjack)

Hello,

My friends and I are playing on a Minecraft server that has the possibility to play blackjack. My friend insists that if he bets the minimum amount a number of times (lets say 3) and loses them all, and then bets all of his money, he somehow has a bigger chance to win, because he previously lost a number of bets. This obviously sounds like textbook gambler's fallacy, but he insists that the "weight" of the bets change the probability and gambler's fallacy doesn't apply here and with each loss his chance to win increases exponentially.

Let's assume the server plugin for blackjack is identical in function to a normal real-life blackjack game, and card-counting is not possible. Let's also assume the blackjack odds of winning are 42% for the player, 49% for the dealer, and the rest of the time it's a tie (9%).

Let's assume a chain of 4 bets. It's my understanding that before the bets, his chance of losing all 4 are 0.49^4 = 0.057 which is 5.7%. Now, let's say he played 3 bets of 10 $ each and lost them all. He now thinks that he is way more likely to win his next bet because he lost 3 previous ones, and bets 100 000 $.

Is this true? I have a hard time believing his odds have changed from the original ones (42% to win, 49% to lose and 9% to tie). Probability doesn't have memory, right? Does something change because of the bet sizes?

Thanks in advance!

Posted Jan 4, 2025, 8:39 PM UTC

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