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Unformatted text preview: 3.1. PERMUTATIONS 87 king,” just as in frustration solitaire. If the dealer goes through the 13 cards without a match he pays the players an amount equal to their stake, and the deal passes to someone else. If there is a match the dealer collects the players’ stakes; the players put up new stakes, and the dealer continues through the deck, calling out, “Ace, two, three, ....” If the dealer runs out of cards he reshuffles and continues the count where he left off. He continues until there is a run of 13 without a match and then a new dealer is chosen. The question at this point is how much money can the dealer expect to win from each player. De Montmort found that if each player puts up a stake of 1, say, then the dealer will win approximately .801 from each player. Peter Doyle calculated the exact amount that the dealer can expect to win. The answer is: 26516072156010218582227607912734182784642120482136091446715371962089931 52311343541724554334912870541440299239251607694113500080775917818512013 82176876653563173852874555859367254632009477403727395572807459384342747 87664965076063990538261189388143513547366316017004945507201764278828306 60117107953633142734382477922709835281753299035988581413688367655833113 24476153310720627474169719301806649152698704084383914217907906954976036...
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- Spring '09