Remember when a computer was just a $2,000 deck of cards? I had a flashback to Windows 3.1 days the other evening. I was clicking around, bored, and decided to open up a game of Solitaire.
There’s something that has always intrigued me about the computer version of this game. Specifically, how does the computer treat cards which have not yet been revealed? There are two possible scenarios: 1) the computer randomly assigns a particular location to every single card at the beginning of the game (randomness upfront), or 2) the computer randomly assigns a card from the remaining pool of unrevealed cards at the click of the mouse (randomness during gameplay). The first scenario, of course, is similar to what we expect when we play solitaire the old-fashioned way (assuming the deck is well-shuffled), and how I assume sol.exe operates.
To illustrate the second scenario, consider a computer solitaire game in which we have revealed all cards except two, let’s say, the queen and king of clubs. In this scenario, the computer has not assigned a location for either card yet – it just randomly selects from the remaining pool of unrevealed cards, in this case, the queen and king of clubs, until one of the cards is revealed by a mouse click.
Interestingly, from the player’s perspective, the two scenarios are indistinguishable. The probability of the remaining two cards being either a queen or a king is 0.5: whether predetermined upfront or randomly selected at the mouseclick makes no difference. And of course, after revealing, say, the queen, the probability of the remaining card being the king is 1.
Now, what fascinates me is that, even if we turn off the computer and use real cards to play a game of solitaire, the two scenarios are still indistinguishable. Intuitively, of course, we opt for the first scenario: randomness is introduced by shuffling and the position of each card is determined and fixed at the beginning of the game. But of course, we don’t really know until we’ve checked, and once we flipped the card, we’ve taken a peek at whether the cat made it.
Further reading: The Quantum World, J.C. Polkinghorne
