The big question is, what is the tradeoff? Let us look at a very simple scenario: tossing a biased coin with probabilities of 60% chance of landing on heads and 40% landing on tails. Thorp: The root idea of the Kelly criterion is that there is a tradeoff between risk and return. How can you use the Kelly criterion in the stock market given a large array of potential outcomes and holding periods? Pysh: With respect to probabilities, there are similarities between gambling and investing. I probably could have reached those approximate solutions by hand.

However, as I learned more about the game, I realized that you could make approximations that would still result in decent solutions. Thorp: At the time, I thought I had to make exact calculations. Pysh: Do you think you could have solved the mathematics without the computer? I spent almost a year teaching myself how to program and running subroutines that I would later piece together into a program that would evaluate how the missing cards affected the game of blackjack. There I had access to a high-speed computer. I started with hand calculations, which did not get me very far, and then I went to teach at MIT. I developed many card counting systems and spent the next year executing these systems. Therefore, players want small cards to come out of the deck. On the contrary, when the deck is filled with small cards, it shifts the edge in favor of the casino. When the deck is filled with big cards, it becomes in favor of the player.

I repeated this process with all ranks of the deck. This was good news because if I put back in four aces, I knew the exact opposite would happen and the cards would now be in my favor. To calculate these probabilities, I first had a computer take out four aces from a full deck, and I discovered that the deck shifted in favor of the casino by quite a lot. Preston Pysh: I am curious to know how you came up with the idea to beat the odds of blackjack when everyone else believed that it could never be done.Įdward Thorp: By solving equations, it is possible to calculate the precise probabilities of losing, given any collection of cards for any number of decks. Below is an edited summary of his interview with The Investor’s Podcast where Thorp discusses probabilities and his storied investing career. As Thorp transitioned out of gambling, he then achieved the unthinkable with 20% annual returns over 30 years trading options. He revolutionized gambling as he proved how to beat blackjack with card-counting and invented the first wearable computer. Edward Thorp is the bestselling author of Beat the Dealer.

Edward thorp on gambling and trading