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Many casual players believe that, all other factors being equal, the odds of winning at a single-deck game are the same as in shoe games. They figure that, although more decks are used, the same relative number of cards is still involved; therefore, even for a card-counter, there is no advantage to playing in one game over the other. In fact, this is not the case.
Aside from nonmathematical considerations (e.g., single-deck games are easier to count successfully), Thorp proved that the player’s overall advantage diminishes as the number of decks used in the game increases. Following proper BS, the player has a 0.13% advantage over the casino in a single-deck game, but if 5,000 decks were to be used, then the player would be at a theoretical disadvantage of 0.58% without tracking the cards. This makes sense because the fewer cards that are used in a game, the more directly the removal of any finite number of them affects the distribution or “composition” of the remaining cards.
Consider two imaginary decks, one consisting of only twenty cards, and the other made up of two thousand cards. Each deck is composed of half T’s and half non-T’s. Right after the shuffle, your chances of drawing a T are an even fifty-fifty, or 50%, from each of these two hypothetical decks. Now suppose that nine of the T’s are removed from each deck. Your odds of drawing a T as your very next card would be only slightly over 9% from the small deck (1 out of 11 = 9.1%), but still almost 50% from the large one (991 out of 1,991 = 49.8%). The more cards initially involved, the less the remaining pool is influenced by the removal of specific cards during play. This is one reason your BS play should change slightly if you move from a multiple-deck to a single-deck game (see chapter 7 for details). Therefore, since card-counting is a bit less reliable in shoe games, BS reflects the need to play somewhat differently in them as opposed to single-deck games.
Another reason to choose a single- or double-deck game as opposed to a six-deck shoe, whenever the rules are similar, is that you are less likely to get blackjacks in games that employ more cards. It sounds incredible, but compare the following two examples mathematically: (1) In the single-deck game there are 190 (20 X 19 + 2) possible two-card combinations involving the four Aces and sixteen T’s, 64 (4 X 16) of which produce blackjack; 64 chances out of 190 equals about 34%. (2) In the six-deck shoe, although the ratio of T’s to Aces remains 4 to 1, there are 7,140 (120 X 119 + 2) possible two-card combinations involving the twenty-four Aces and ninety-six T’s, a total of 2,304 (96 x 24) producing blackjack; 2,304 chances out of 7,140 equals just over 32%.
No wonder most casinos are moving toward offering only six-deck shoe games. Out of every hundred hands composed of Aces and T’s that are dealt from a shoe, the expectation of blackjack appearing is nearly two fewer than it is from a hundred similar single-deck hands. Of course, the dealers will also draw the same reduced number of blackjacks in the shoe games, but they can avoid paying the players 3 to 2 on an average of almost one fewer blackjack per shoe, depending upon the number of decks used and how many players are at the table. (The math here allows for considerable discrepancies, but the reader can certainly get the general idea.)
One additional reason that your potential gains decrease in multiple-deck games concerns Modified Basic Strategy (MBS) play, which is detailed in chapter 7. The TC (True Count) tends to stay within narrower limits as the number of decks increases. For example, using only one deck, the TC = 0 only 18% of the time, while for a six-deck shoe the TC = 0 almost 30% of the time. This means that you usually have to wait longer in shoe games for an opportunity to use MBS play at all. Similarly, the TC ranges between 5 and + 5 only about 82% of the time in single decks, but it stays within this same limit over 95% of the time in shoe games. This is not good for the counting player, who depends upon the fluctuation of the TC in order to win his larger wagers. The counter’s edge increases when he can use MBS plays to full advantage a job that requires more patience in shoe games.
Although it is slightly more difficult to beat shoe games as opposed to single decks, there are some advantages to playing the shoes. Shoe rules are often better than in hand-held games, dealer cheating is much more difficult to manage from shoes, and because there are so many more multiple-deck games offered, the player has a much greater choice of tables.
The more decks involved, the more the TC tends to stay within narrow limits. A single deck subsequently allows more variance in the TC than multiple decks. As the TC increases in magnitude, however this discrepancy is reduced, e.g., the TC will stay between 10 and +10 virtually 100% of the time, whether you are playing a single- or multiple-deck game. This means that it is unlikely that you will ever encounter a TC beyond 10 or +10 in any game.
When the TC stays within the -3 and +3 range (i.e., 86.6% of the time in a six-deck shoe game), your MBS playing gain is only 1.7%, but when the TC ranges from 6 to +6, for example, your gain climbs to 1.9%. Your MBS advantage varies directly with the magnitude of the TC, whether positive or negative. Therefore, you are more often able to apply MBS with greater success and frequency while playing in single-deck games, as opposed to the more common shoes. It should be evident from this data that double-deck and four-deck games are somewhat preferable to six- and eight-deck shoes with similar rules, for the same reasons.