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In the novel Spaceland by Rudy Rucker, the protagonist Joe Cube is grafted with an eyestalk that sticks vout into the fourth dimension. This lets him see under and inside three-dimensional objects the way we could see inside the bodies of Flatlanders. His wife encourages him to take advantage of his new ability by going to Las Vegas to cheat at Blackjack.

Thanks to his “subtle vision”, Joe never has to bust, as he can see what the top card in the deck is, and stand if it would put him over 21.

However, it's still not possible to win every hand. For example, on his first hand:

  • The dealer has 18 (a hole card of 10, and an 8 showing)
  • Joe has 16 (a 6 and a Jack)
  • The card on top of the deck is a 7.

If Joe stood on his 16, it would lose to the dealer's 18, but if he hit, he'd bust. Lose-lose. (He decided to draw the card because he figured it might look suspicious if he never busted.)

But, it's clear that the extra information would give Joe an advantage over a normal player. The question is, exactly how much greater would his expected outcome be, with the same bet, versus a player with optimal strategy but normal vision?

For the same of simplicity, assume that the dealer shuffles together an infinite number of standard 52-card decks, and ignore “split”, “double down”, and “insurance” bets (unless you want to calculate them). The house must hit on 16 and stand on 17, regardless of whether hard or soft.

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