Who's to Blame when You Draw Bad Cards at Blackjack?

Gamblers who win sometimes credit luck or whatever occult forces in their personal universes they hold responsible for miracles. More often, though, they attribute success to their own punting prowess. Solid citizens who lose commonly look for, and usually find, innocent bystanders to blame. As if, for instance, cocktail servers passing by can influence the last reel of a slot machine, sending a giant jackpot to oblivion. Or a roulette tablemate knocking over a stack of checks can urge the ball off 28 where there's a big bet, and finish in 14 where there's zilch.

The possible effect of someone else's actions gets muddier in a game like blackjack. There, bezonians who don't follow "the book" -- Basic Strategy -- are apt to be faulted for anything from ruining the whole table by changing the rhythm of the shoe to feeding either bad cards to the next player or good ones to the dealer. Such accusations are almost invariably groundless.

One person violating Basic Strategy doesn't impact anybody else's chances. This, because its rules are predicated on the presumption that cards still to be drawn are not in some vaguely tenuously predictable series but are randomly distributed. Were this not true, were there in fact an order to the cards in a shoe, Basic Strategy wouldn't be the optimum way to play. As those who practice card counting and shuffle tracking know.

The idea can be illustrated with a strictly hypothetical, highly simplified situation involving a player at "third base" (the last person to act before the dealer). Make believe this person has a 16; the dealer has six-up, and while nobody knows it yet, 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 -- 3/4 or 75 percent.

What happens if the player hits? 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 -- player five AND dealer 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:

It's simplistic to a mystic: Gambling is deterministic.