A Man for All Markets: From Las Vegas to Wall Street, How I Beat the Dealer and the Market

by Edward O. Thorp

The IBM 704 had done a thousand man-years of hand calculations in just ten minutes of computer time. I looked at these results with great excitement, for they would very likely either prove I was right or dash my hopes. The result was a player disadvantage of 2.72 percent with all the Aces gone—2.51 percent worse than the overall 0.21 percent casino edge. Although this was a huge shift in favor of the casino, it was actually great news. It proved conclusively what I believed in that Eureka moment back in the UCLA library when I thought I could beat the game, namely, that as cards were played there would be huge shifts in the edge, back and forth, between the casino and the players. The math also showed me that if removing a specific group of cards from the deck shifted the odds in one direction, adding an equal number of the same cards instead would move the odds the other way about the same amount. This meant that with an Ace-rich deck rather than an Ace-poor deck, the player should have a big advantage. For instance, with twice the usual proportion of Aces, which happens when all four Aces remain among the last twenty-six cards (half the deck), the player ought to gain roughly 2.51 percent over his initial 0.21 percent disadvantage, for a net edge of about 2.30 percent.

It's worth remembering that 2.5% constitutes a "large edge." You still have to play correctly for a long time to take advantage.