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Best of Alan Krigman

Gaming Guru

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When the Best Game in Town Proved to be Too Good

4 June 1996

A few weeks ago, I told you about a casino whose gaming gurus goofed in ordering and operating a keno system. It was a costly gaffe. They gave big bucks away to a solid citizen who found out the computer was picking the same random numbers every day.

OK, you say. Casinos shouldn't have to know the nitty gritty of computers. They pay experts for that when they buy systems. Just as you and I shouldn't have to know the nuts and bolts of fuel injectors; we pay experts for that when we buy cars.

Not quite. True, civilians shouldn't have to fathom fuel injectors. But the Uniform Commercial Code presumes organizations to be expert in all phases of their businesses. So casinos should comprehend the computers behind their games.

Well, you say, anyone can flub a first foray into cybergames. But the casinos surely have the classics - baccarat, roulette, craps, and blackjack - down to a pure money-making science.


Sorry, this isn't quite right, either. I'll tell you about a mistake a casino made recently in spreading what they wanted to tout as the "best blackjack in town." Until the bosses tallied their losses, realized the game was too good, and pulled the plug.

The single-deck blackjack was played with the casino's otherwise regular rules. Bettors got cards face-up; the dealer took one up and one down. Players could split but not resplit pairs, and could double down on any two cards including hands formed by splitting pairs. Blackjack paid 3-to-2. Insurance paid 2-to-1.

Being paranoid about card counters and shuffle trackers, though, management took steps to keep players from detecting favorable conditions and betting high when they got an edge. Only one round was dealt between shuffles, and bets were kept at $5 to $100.

What was wrong? Two things, actually.

Primarily, single-deck blackjack normally disallows doubling after splits; it sometimes bans doubling on any "soft" hands. By offering both options in single deck games, this casino gave straight "basic strategy" players an automatic 0.11 percent edge.


Secondly, the casino didn't fully grasp how certain players use information about changes they detect in the probabilities of cards to be drawn. Shuffling between rounds obviated exploiting this knowledge to vary bet sizes. But most single-deck blackjack is dealt with player cards face-down. Exposed hands let bettors see a third or more of the cards removed from the deck, and optimize their decisions based on the proportions of what remained.

Insurance shows plainly how this could add to players' edge. Insurance is usually a sucker bet. But if 14 player cards, a dealer up-card, and a burn card are exposed and none is a 10, insurance favors the bettor by over 33 percent. Even if three of the 16 face-up cards are 10s, the player has over 8 percent edge.

A more complex example involves count-dependent basic strategy improvements. To cite a few favorable changes when more low than high cards have been removed from a deck: stand rather than hit 12 against dealer three; double rather than hit nine against two; and double rather than stand on soft 19 against five or six.

What happened? Nobody broke the bank. But the house took the heat. Precisely what the math predicts. The potential for big individual wins depends on volatility, which wasn't greatly affected by the rules. But, the central limit theorem of statistics says the casino should expect a loss closely tied to the player's edge - 0.11 percent of the aggregate bet in this case.

The casino's error is elegantly elucidated in the punting punditry of the immortal poet, Sumner A Ingmark, who wrote:

Entering into a game without sense is,
Likely to bring on some bad consequences.

Alan Krigman

Alan Krigman was a weekly syndicated newspaper gaming columnist and Editor & Publisher of Winning Ways, a monthly newsletter for casino aficionados. His columns focused on gambling probability and statistics. He passed away in October, 2013.
Alan Krigman
Alan Krigman was a weekly syndicated newspaper gaming columnist and Editor & Publisher of Winning Ways, a monthly newsletter for casino aficionados. His columns focused on gambling probability and statistics. He passed away in October, 2013.