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# Playing It Smart: Does winning big in a casino prove you're a good gambler?

5 August 2008

Ralph goes to a casino once a month. He starts in January with \$1,000, his loss limit. He wins \$1,000, then quits. To put some numbers on the probability of this scenario, pretend he plays blackjack using perfect Basic Strategy and bets uniformly at \$50 per hand. These conditions give him 46 percent chance of success.

Thinking he's on a roll, Ralph goes in February with his \$2,000 and bets \$100 per hand. He's resolved to win \$2,000 or bust out trying. The chance he'll succeed is also 46 percent. Say he does.

Carry this reasoning through the year, assuming Ralph doubles-up and triumphs every month. In December, he brings \$2,048,000, bets \$102,400 per round, and earns \$2,048,000. His December prospects are still 46 percent. The chance he'll win 12 times in a row is 46 percent multiplied by itself 12 times, one out of 11,140.

Here's another way to look at it. Suppose 100,000 solid citizens go to a casino in January with \$1,000, determined to win \$1,000 betting \$50 or go broke in the attempt. A 46 percent likelihood of success, based purely on chance, means 46,000 can be expected to make it. Those 46,000 return in February and pit their \$2,000 on double-or-nothing sessions with \$100 bets. Since the chance of success doesn't change, on the average 46 percent of the 46,000 will prevail. That's 21,160 players following perfect basic strategy, still purely by chance. Take the 46 percent survival rate through to December. Statistically, four out of the initial 100,000 would finish looking like wagering wonderkinder.

Of course, there was no way to know which four of the original 100,000 would be the winners. Further, from the previous reasoning, no special skill was involved. However, you can be sure that, like ants over a picnic lunch, the bosses would be on top of anyone who parlayed \$1,000 into well over \$4 million in 12 visits. And the surveillance staff would be clocking up overtime scrutinizing tapes of this bettor's every move. They'd be positive that the player was cheating or onto a hitherto unknown branch of mathematics because of the mind-boggling degree to which it appeared he or she had beaten the odds.

True, those who'd earned \$4 million had overcome steep 99,996-to-4 odds. But from the casino's perspective, they'd have had impossible winning runs. Doubt that this could be done would be so great that in examining tapes of the action, some hero would detect characteristics they all shared. Maybe, always playing in the third position, starting games after 11:00 pm, and leaving any table where another player ordered a scotch-and-soda. This discovery would be anointed with technical veracity by calling it "data mining." But it would be hogwash. Look long and hard at enough data and you can always pick out cues that fit a known result, in retrospect, regardless of cause-and-effect. This, partly because you examine only winners and neither know nor can test whether the same precursors also fit losers.

Blackjack buffs who follow perfect Basic Strategy are underdogs. But only marginally. House edge is slightly shy of 0.5 percent. A weak blackjack player might give the casino about 1 percent edge. This would yield roughly 42.25 percent chance of success in any double-or-nothing session with the indicated bets. At this rate, the probability of a 12-month streak would drop to one out of 30,909. At that level, one out of the 100,000 initial patrons could be expected to hit the \$4 million mark. But that player, a lousy gambler at 1 percent, would be respected and feared.

Ponder this, next time The Wall Street Journal acclaims the wisdom and far-sightedness of star traders who picked all the right stocks the past quarter. Most of them won't have been in the limelight three months before, nor will they be three months hence. Largely, they were luckier more than smart. The hotshots are feted going up like rockets. They're forgotten, even fired, coming down like sticks. The smart ones, who trade conservatively for respectable steady profits, don't make for good press. Or, as that lyricist of luck, the laudable Sumner A Ingmark, wrote:

'Though you may score big wins in tandem,
It doesn't mean your fate's not random.

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Best of Alan Krigman
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.