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In his second edition otBeat the Dealer, Thorp presented a “point-count” system, which formed the basis of all subsequent counting systems and it provided the model for innumerable variations that have since evolved. Although Harvey Dubner’s quite similar system appeared slightly before this publication, it primarily entailed modifications or simplifications of Thorp’s original presentations and research.
Thorp was the first to note the relative values of each and every card (not just the 5s) to the player, as shown on the chart page 80 in chapter 4. With the help of Braun’s more sophisticated computer programs, he determined that the player’s advantage was greatest when more small-ranking or “low” cards (i.e., 2s, 3s, 4s, 5s, and 6s) were used up during play, leaving a surplus of 10-value cards (and Aces), the “high” cards, remaining to be dealt. It followed logically that the dealer had the odds with her after more high cards came out during the game.
This should begin to make sense for the reader as well: Players will win more money when there is a higher-than-normal concentration of T’s and Aces available to appear. To be absolutely clear on this point, consider the hypothetical extreme, where only T’s and Aces are left in the shoe. If such an opportunity presented itself, would you want to play under these circumstances? Stop and consider the situation for a minute, since it ably demonstrates the tremendous value to the player of Ace- and T-rich decks.
To determine what theoretical advantage would exist in such a scenario, examine each of the six possible hands that you could receive from a pool of only Aces and T’s:
1. T,T versus A is a no-lose hand for you. Taking insurance, you only win even money if the dealer has a blackjack, but you win big if the dealer doesn’t, since you would split the T’s to the limit and necessarily win all of the splits. (In a shoe game there is the remote possibility that the dealer could end up with 11 Aces in a row and then draw a T to win with 21, but the odds of that happening are very low.)
2. When you have blackjack versus the dealer’s Ace, by taking even money you would always get a sure win. If you decided to hold out for your 3-to-2 payoff, the worst that could happen would be a push.
3. Take advantage of the insurance proposition with A,A versus A and you will generally at least break even. If the dealer has the blackjack, you lose nothing. For those times that the dealer does not have a blackjack, splitting your Aces wins back more than the lost insurance, i.e., half of your original wager, since only rarely will two more Aces appear on both of your splits. The dealer is almost certain to bust, since the only way she could end up with a pat hand would be by drawing six more straight Aces obviously an impossibility in a single-deck game, and highly unlikely in a shoe with the normal ratio of T’s and Aces remaining to be dealt.
4. T,T versus the dealer’s T represents several potential 21 wins for you when they are split to the max, if the dealer doesn’t flip over an Ace. Pushing with 20s is the worst thing that can happen otherwise. When the dealer does get a blackjack, you lose only your one original wager, so on the whole this situation would make you money.
5. Your blackjack versus T wins you the 3-to-2 profits more often than not. When the dealer also has the natural, the resulting push doesn’t cost you anything.
6. A,A versus T is your worst possible hand within this hypothetical situation. Splitting would usually provide very good moneymaking potential, since the dealer will not have an Ace in the hole more than 20% of the time. Your probable 21s will beat her 20 in most cases, but drawing an Ace on at least one of your splits is always a possibility, in which case you would only break even on the hand overall. As a whole, you would end up winning many more of these hands than you would lose, since the only way you could lose, other than the dealer’s having a blackjack, is if you happen to draw two more Aces on your split.
Hopefully, you can see the huge advantage over the casino that you would enjoy if the only cards left in the game were Aces and T’s. The wisdom of betting more in such a situation should be obvious. The extreme importance of the availability of 10-valued cards and Aces to the player should be growing much clearer.
Although it is not as evident as in the above ideal playing situation, the player also enjoys favorable odds when only slightly more T’s and Aces as opposed to 2s through 6s are left in the shoe. Understanding why this condition represents bigger potential gains for the player is essential, no matter which counting system you may eventually choose to use. Similarly, when there are more low cards available to appear next, the knowledgeable card-caser enjoys an advantage over the non-counters as well, because he will then bet less and play more conservatively if he decides to play at all with such a poor count.
Consider the following reasons why knowing that there is either an excess of high cards or an excess of low cards available could help the player make better playing decisions:
1. More blackjacks than normal will occur when the shoe is Ace-T rich. The subsequent 3-to-2 payoff is a big plus for the player.
2. After doubling, which the player will do more frequendy if the composition of the remaining cards favors T’s and Aces, the player’s final totals will tend to be higher, resulting in more wins.
3. When more T’s than usual are available, the dealer will break more frequently (being forced to hit her stiffs, and therefore ending up over 21 even more often). This provides the player with more than his usual winnings. (Unlike the dealer, the player has the option to stand on stiff hands in this situation, which represents a definite strategy gain.)
4. Knowing that a surplus of high cards exists is a powerful tool when determining the correct play. A player can alter BS accordingly, sometimes avoiding going over 21 by standing even when BS says to hit (e.g., 16 versus T, or 12 versus 3).
5. With an abundance of T’s and Aces in the deck, splitting will generate more doubling situations, which could prove favorable, and better totals for the player when doubling is not advisable.
6. With a significantly higher than normal density of T’s available, the knowledgeable player is able to take full advantage of the profitable insurance wagers.
7. The surrender option offers the player an even bigger advantage when large quantities of T’s are imminent.
8. When a surplus of low cards remains, the counter knows not to double weak beginning totals, especially certain soft hands against the dealers stiff up-cards, since the dealer is more apt to draw a pat hand. Against the player’s potentially even weaker doubled-down total, this would be all the more disastrous.
9. Knowing enough to bet only the minimum (or not to play at all) when a superabundance of little cards are left in the shoe will save the player many otherwise wasted chips.
10. Knowing that a surplus of low cards exists is also a big advantage when deciding whether to hit or stand on certain totals. A player can more readily take a card on weak stiff hands without undue risk, even against the dealer’s stiff up-cards. More often than not the hit (too dangerous to try normally according to BS) will result in pat hands.
Thorp’s original point-count system still remains relevant, attractive, and practical even today because of its innovative methodology. Its combined simplicity and playing efficiency are impossible to beat. Basically, the system involves counting each card as it is seen: the low cards (2s, 3s, 4s, 5s, and 6s) as +1 each, and the high cards (10-value cards and Aces) as -1 each. The 7s, 8s, and 9s are nearly neutral to the player anyway, so they are ignored. Thus, keeping track of the various cards as they are used up normally in a game, the counting player can easily tell whether the remaining pool of cards contains an excess of high or low cards or if it is completely neutral.
For example, suppose that you saw the following ten cards appear during the first round of play immediately after a shuffle in a single-deck game, and you wanted to determine whether the remaining cards favored the player or the dealer:
2, 5, 7, A, 3, 9, T, 4, 6, 3
As you saw the 2 you would think to yourself, ” + 1.” When the 5 appeared, you would mentally add another +1 and think, “The total is now + 2.” The 7 is neutral, so, ignoring it, you skip on to the A and think “-1,” which brings the count total back down to +1 again. Similarly, the 3 takes the count up another point, the 9 is neutral, and the T pulls the count back down one point. You now have the count back at +1 once more. Adding in the 4, 6, and 3, the count climbs to + 4 after this whole sequence of cards has been seen. This means that the odds of the player winning the next hand would be greater, since diere are four more high cards (Aces and T’s) than low ones (2s through 6s) now available to be dealt.
By keeping in mind just one number at a time in this manner, you will always know whether you or the dealer has the upper hand. Any positive point-count means that the odds favor you, while any negative point-count reflects an advantage for the house.
Generally speaking, it is advisable to play more aggressively when the count is positive and more conservatively when it is negative. In other words, when there are more high cards waiting to be dealt, you should stand, double, and split a bit more often than you would when abiding by normal BS. Conversely, when more low cards are ready to appear, you would tend to double and split less often but hit more frequently.