After five shuffles the deck is still far from random, but then there is a fairly abrupt convergence to random. Here we see, distance to random, plotted against, number of shuffles. In a remarkable 1992 paper by Bayer & Diaconis, with a really cool name: Trailing the Dovetail Shuffle to Its Lair, it is shown that seven riffle shuffles are necessary and sufficient to get a deck close to random: One popular method of shuffling cards is the riffle shuffle. Note there are possible orders that a deck can be in so when a deck is random the probability that a deck is in a specific order is The cards is equally possible then the deck is considered random.
If one is handed a deck of cards, face down, and if each possible order of Here let me introduce a mathematical realisation of random: These can all be given a precise mathematical realisation (see the introduction here for more). Here we used three terms: deck, shuffle, mixed up. What we are interested in is what happens after all this, before another hand is dealt?Ī shuffle is required to mix up the deck. There after follows a round of betting, the reveal of three more cards (the flop), more betting, another card (the turn), another round of betting, another card (the river), and another round of betting: ‘ Texas‘ is a poker game where a number of players sit around a table. I wasn’t sure if it was true but it appears that it is.
