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Best of Alan Krigman

Gaming Guru

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Trying to Recoup Past Losses Can Cloud Your Judgement

3 February 2000

Anything can happen to a bankroll in a casino. Everyone seeks a boon and dreads a bust, of course. For the majority of games and betting strategies, though, these extremes are rare. Most gamblers, at least those who last long enough to be considered experienced, accordingly develop intuition about the gains or losses they can anticipate during normal gambling sessions. And, this instinct usually underlies the quitting decisions they make.

Usually. Not always.

The exceptions can be most damaging when solid citizens have suffered painful upsets in previous games, then encounter sessions in which luck seems to be going their way. So, rather than quit with what they'd ordinarily regard as healthy profits, they forge ahead attempting to recoup earlier extraordinary losses. Sometimes it works, sending the players home convinced they possess great gifts for gambling. More often it doesn't, turning partial recoveries into extensions of prior routs.

I'll illustrate with some numbers on a typical blackjack situation; the reasoning applies as well to other games and amounts. Pretend you have a $500 session bankroll. You bet $10 the bulk of the time, now-and-then pressing to $15 and $25 -- either when you think the table is hot, or you've lost a few hands and get brave trying to catch up. You generally quit after a shoe that leaves you over $150 ahead, but scamper away with less if you've come out of a hole after a long struggle. You hit and run when you can, although you'll "grind it out" if you fall behind -- knowing you'll often recover, and occasionally lose your entire stake. With this approach and at these levels, you can expect to win at least three quarters of your games.

Note that nothing's magical about winning an average of $150 in 75 percent of your sessions and depleting a $500 bankroll in the rest. The casino still finishes sightly ahead in the long run.

Now picture this situation. You've come to the casino for a day of blackjack. In the morning, you butted your head against the wall for over three hours. Nothing went right. And you lost your $500 limit. After consoling yourself with a comp for the all-you-can eat buffet, you find an empty blackjack table and play the dealer heads-up. Voila! Nothing goes wrong. You're $255 ahead at the end of the first shoe, 50 rounds.

Ordinarily, you'd happily color-up, toke the dealer $5, and hit the cashier's cage. Overall, $255 profit isn't unusually high for your game. Were you to play until you win this much or lose $500, your success rate would be about 60 percent. It's outstanding for a 50-round session, however. With your bets, you only have 5 percent chance of doing this well in one heads-up shoe. Either way, it's normally more than enough to meet your objectives.

What if, aspiring to recover from your morning's loss, you keep playing instead of quitting as you ordinarily would? There's no correlation between your lucky first shoe and what might follow. You could do better, as well, or worse. Perhaps you tell yourself you'll risk the $255 you just won, but no more, striving to get back the original $500. What are your chances?

Now, you've effectively got a $255 bankroll -- half the stake to which you're accustomed -- and are trying to win $245 before losing it. Independently of session length, you have less than 40 percent likelihood of success. Further, you're facing almost 20 percent chance of exhausting the $255 in two more shoes.

Most proficient players start each session at psychological ground zero. They don't approach a new game thinking they're already in the hole, and playing until they climb back out. If $255 is more than enough to quit the first game of a casino visit, it's more than enough to quit the last game -- regardless of what happened in the interim. Sumner A Ingmark, a bard on whom bettors can always bank, said it this way:

Though history your goals may rearrange,
It doesn't cause the laws of chance to change.

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.