Drawing Bad Cards
Written June 4, 2008 by Jack Jones
Winning gamblers often credit lady luck or some higher being who is responsible for miracles, but what’s happening even more often is they attribute their success to their gambling prowess. Losers on the other hand look to blame others, even when these people have absolutely nothing to do with their winning or losing.
There isn’t a game that this is more apparent than in blackjack. If someone isn’t following basic strategy while playing blackjack they are are going to be blamed for ruining the whole table by changing the rhythm of the shoe and feeding either bad cards to the next player or good ones to the dealer. These accusations are groundless.
If someone at the table isn’t following basic strategy then it doesn’t have any effect on the other player’s chances. The cards that are still to be drawn have no relation to one another, it is all based on random distribution. If this wasn’t the case and there was an order to the cards in the shoe, then you shouldn’t use basic strategy but play more like card counters do.
Let’s take a look at an example to illustrate. A player is sitting at “third base” (the last person to act before the dealer), with a 16; the dealer has six showing, and while nobody knows it yet, there is a 10 in the hole. This being hypothetical and simplified, to keep the figures easy to envision and manipulate while not changing the logic or the conclusions, further pretend only four cards are left in the shoe: one is a five, the other three are sixes.
Assume the player follows the hallowed dictum of Basic Strategy for 16 against a six and stands. The chance the dealer will draw a six and bust is then three out of four or 75 percent.
What happens if the player hits instead of stands? The chance is one out of four (1/4) of drawing the five, leaving the dealer with three chances out of three (3/3) of pulling a six and busting. The joint probability of this state of affairs the player getting a five AND the dealer getting a six is found by multiplying (1/4) x (3/3), which yields 1/4. Conversely, the chance is three out of four (3/4) that third base will receive a six. If this happens, the dealer is left with two chances out of three (2/3) of pulling one of the sixes still in the shoe. The probability of this combination — player six AND dealer five — is the product (3/4) x (2/3) which equals 2/4.
The chance that the dealer will bust if the player hits is the probability that one OR the other of these outcomes will happen. This is found as the sum of the two scenarios. That is, (1/4) + (2/4) which equals 3/4 or 75 percent. It’s no coincidence that this is the same as the 75 percent chance of the dealer busting when the person at third base stood rather than hit.
The wicket gets sticky because mere mortals have trouble reconciling the difference between immediate cause-and-effect, and the impact of an action on the chances of a particular result. So if the third base player in the example pulls a six and feeds the dealer a five for a total of 21, when standing at third base would have meant the dealer got the six and busted, everybody gets angry. But, why blame the player, say, rather than the dealer who shuffled the cards for the shoe, or the previous run-through, such that the six got interleaved ahead of the five?
Oh yes, about the cocktail server and the slots. If you pause or even break the cadence of your punching the button to ask for a drink, the random number generator in the machine will whiz on and give you a different result than you’d have otherwise gotten. Unlike blackjack, where you can usually see the next card, you’ll never know what you missed. Maybe that way’s more equanimous. For, as that placid poet, Sumner A Ingmark, poignantly penned:
