A Blackjack Paradox
Now that you have your mathematical thinking cap on, root out the fallacy in logic from the following argument:
At the end of each shoe, when the shuffle card comes out, if the count is very positive it means that a lot of little cards have been used, and therefore the players have been at an overall disadvantage, possibly throughout the entire shoe. But, if the count is very negative at the end of the shoe, it means that more than a normal number of T’s and Aces have appeared (which tend to use up fewer cards per hand); therefore, the dealer can squeeze in another round or two before the shuffle while the players are still at a disadvantage! Therefore, in shoe games casinos must always have the odds in their favor.
No answer is being provided for the above paradox; you are fully capable of solving this one on your own.
Throughout this blog I have made a conscious effort to avoid personal anecdotes. Many blackjack publications are absolutely crammed with such items, which, although mildly entertaining, prove absolutely nothing and are basically worthless to the reader. Alter all, personal testimonies can be paraded out to “substantiate” anything under the sun. While writing the above paragraph, however, I was reminded of a shoe game that I experienced years ago in the casino on Paradise Island, Bahamas. I believe the incident is worth relating.
While strolling behind various tables one afternoon, I happened to notice one particularly bad shoe. It started out negative and got progressively worse as it neared the end. The TC was 14 when the shuffle card finally came out, and I almost said something to the dealer as he proceeded to deal another round to the almost full table. As I fully expected, he drew a pat hand, and the players lost all of their doubles and splits. None, however, apparently even noticed the shuffle card just lying there beside the discard tray; at least no one commented about this obvious “oversight.” When the dealer finally picked it up to start the shuffle, he shot me a sheepish glance. Although I had said nothing out loud, maybe he had picked up on my negative “vibes” somehow, since I was certainly disgusted and amazed at such unabashed audacity. This may have been just an innocent mistake. Alternatively, he may well have been a dealer who could count, and who was instructed to make a little extra money for the house by dealing additional hands whenever the shuffle card came out while the count was very negative.
Earlier in this chapter, the chance of ten heads or ten tails appearing consecutively was said to be just over 500 to 1. The odds of such strings happening are calculated as follows: The probability of two similar consecutive results is dead even, or one out of two attempts. To determine the odds for three-in-a-row, it is necessary to multiply by 2, i.e., one out of four flips. It is seen that for heads or tails to appear x number of times in a row, the probability can be represented by 2x_I. Therefore, the odds of ten in a row occurring is once every 29 trials, i.e., once every 512 flips. The chance of a roulette record-board filling up with only reds or blacks (and ruining a Martingale, as mentioned earlier in the dealer’s story) is considerably less than once every 2′5 spins of the wheel, because of the 5.26% appearance of the greens.
