When I go to the casino I tend to play the penny slot machines. I will...

When I go to the casino I tend to play the penny slot machines. I will bet a penny per line until I've lost several rounds in a row. Then I feel like I must be about due for a win and increase my bet until I do win.

See if you can explain why this is faulty reasoning.

Solutions

Expert Solution

Penny slot machine

When you place a bet on the penny slot machine, you have a small probability of winning.

Each subsequent bet on the penny slot machine does not change this probability.

For example, let us assume this probability is 1%.

When you play for the first time, the probability of you winning is 1%,

When you play for the second time, the probability of you winning remains unchanged at 1%.

Every subsequent play is independent of any previous play i.e. losing/winning on the first try does not influence the probability of losing/winning in any subsequent try. (This is a Markov chain exhibiting memoryless property)

Feeling that you are due for a win after multiple losses is a flawed argument since your probability in each play of winning and losing remains constant. You would not have a higher chance of winning just because you lost in multiple previous plays.

If satisfied, please do upvote! Let me know in the comments if anything is unclear. I will reply ASAP

orchestra answered 1 year ago

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