![]() ![]() The idea is that if you riffle-shuffle the pack several times, you perform a pseudorandom sequence of cuts each time you divide the pack before each riffle, mixed together with a pseudorandomly variable sequence of pseudorandom interleaving operations involving an N-from-the-left-then-M-from-the-right process. ![]() Other techniques result in (or feel as though they should result in) to better mixing, for example the riffle shuffle, where you split the pack roughly in half, hold one half in each hand, and “flip” the two halves together, interleaving them in a pseudorandom way that alternates between taking a few cards from one side, then a few cards from the other. ![]() Levels of complexityĬlearly, there are some shuffling techniques that don’t mix the cards up much at all, such as simply cutting the pack into two parts and moving the bottom part to the top. Schneier’s blog posts links to a fascinating piece by the BBC that describes how a mathematician/magician called Persi Diaconis of Stanford University, together with Jason Fulman and Susan Holmes, conducted a formal investigation into this very issue earlier this century, in a paper entitled simply: ANALYSIS OF CASINO SHELF SHUFFLING MACHINES. Shuffle for too long, and play will be too slow, so that players will get bored and wander off, something that casinos desperately try to avoid. Shuffle for too short a time, and the casino might actually make things easier for card counters, if there’s a known bias in the distribution of the cards right from the start. There’s obviously a limit to how quickly it can perform pack splits, card swaps and interleaving operations before the speed of the mechanism starts to damage the cards, which means that there’s a limit to how much randomness (or, more precisely, pseudorandomness) the machine can introduce before it’s time to play the next hand. Ace to King of Hearts, Ace to King of Clubs, King to Ace of Diamonds, King to Ace of Spades), how much partial ordering is left after the machine has done its work?Ĭould you “guess” the next card out of the shoe better than chance suggests?Ī fully electronic randomiser is limited in its complexity mainly by the speed of the CPU that it uses, which is typically measured in hundreds of millions or billions of arithmetical operations a second.īut an electromechanical card shuffler literally has to move the cards around in real life. Notably, with six new packs of cards, which arrive in a predictable order (e.g. That immediately raises the question posed by Schneier: just how well-shuffled are the cards when they emerge from the machine? To save time and to remove suspicion from the dealer, a pseudorandom electromechanical machine shuffles the cards right on the table, in front of all the players. Shuffle the entire shoe of 312 cards (six packs) before every hand.This means that each hand dealt out skews the remaining distribution of cards less than if a single pack were used. Deal hands from a shoe loaded with six packs (decks) of 52 cards.To reduce the counterbalance of probabilities that card counters enjoy (those who haven’t been caught yet, at least), the casinos typically: You might not end up in court, but you will almost certainly get escorted off the premises, and never let back in again. If you can balance the probabilities in your head in real time, then you may be able modify your bets accordingly and come out ahead in the long run.ĭon’t actually try this, at least in Nevada: the casino is likely to catch you out pretty quickly, because your pattern of play will diverge notably from the most informed winning choices available if you aren’t counting cards. Ace and one of 10-J-Q-K) and winning at once, and an above-average chance of going bust before reaching the stopping point of 17 and above. That term is used to refer to players who have trained their memories to the point that they can keep close track of the cards played so far in a hand, which gives them a theoretical advantage over the house when predicting whether to stand or hit as play progresses.Ĭard counters can acquire an advantage even if all they do is keep track of the ratio of 10-cards (Ten, Jack, Queen and King) to non-10s left in the dealer’s shoe.įor example, if the dealer is sitting with an Ace, but an above-average number of 10-value cards have already been used up, then the dealer has a below-average chance of making a blackjack (21 points with two cards, i.e. If you’ve ever been to a casino, at least one in Nevada, you’ll know that the blackjack tables don’t take chances with customers known in the trade as card counters. Cryptoguru Bruce Schneier (where crypto means cryptography, not the other thing!) just published an intriguing note on his blog entitled On the Randomness of Automatic Card Shufflers.
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