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Best of Alan Krigman

Gaming Guru

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How Progressive Betting Affects Your Chance of Staying in the Game

26 July 2000

Gamblers tend to take a lot on faith. And no aspect of table play involves faith more than betting progressions. Practitioners all think they're onto secrets for overcoming edge the casino bosses don't want anyone to know. They can point to sessions proving they're right, too. And conveniently forget those that didn't quite work out. Limitless betting strategies are possible, but three general classes of approach cover most of the field.

A) Raise after losses and pull back after wins, for a strong shot at a small profit.

B) Keep bets constant, for reasonable prospects of respectable earnings.

C) Go up after wins and down after losses, for a small chance of a big score.

In practice, for solid citizens having sufficient sense to set and stick with gambling stakes they can afford, the offsetting factor is the loss of a bankroll. Monetarily, the downside is therefore identical for all three approaches.

But even gamblers who know they'll take a bath once in a while don't want it to happen too soon. A premature crash landing takes away the fun and excitement of the action. Worse, it's an inducement to find the cash or credit card machine in the lobby, the pawnshop on the corner, or the guy in the stretch Mercedes down the street reputed to lend money at rates just above prime.

Given this situation, it helps to know how betting progressions affect the probability a poke will persist through the dips expected during sessions of specified duration. And, how downsizing bets relative to bankroll can enhance durability.

Particulars depend on the details of the game and the betting strategy used. To see the idea, consider a coin toss. Heads win even money -- minus 2 percent commission. Tails lose the bet. The chances are 50-50; the house edge is 1 percent.

The following chart compares three betting strategies. For each, it shows the chance the indicated bankroll will last for the desired number of rounds. The average wager in both progressions is $25, so that's the amount of the flat bet. The house has the same theoretical earnings in all three cases -- $0.25 per round.

A) The negative progression starts at $10 and rises to $20 after one loss, $40 after two, $80 after three, then holds at $80 if more losses occur; a win returns the bet to $10.

B) The flat bet is $25 regardless of past outcome.

C) The positive progression starts at $10 and rises to $20 after one win, $40 after two, $80 after three, then holds at $80 if more wins occur; a loss returns the bet to $10.

bankroll  rounds  chance of survival
    negative
progression
flat
bets
positive
progression
   
250 100 56% 69% 66%
500 100 83% 96% 94%
750 250 80% 93% 87%
1000 500 76% 90% 81%
2000 750 94% 99% 98%

Note that any stake is most apt to be enough for the desired session with flat bets, less with the positive progression, and least with the negative progression. Comparing the first two rows across further shows the key to increasing longevity. For any desired playing time, having twice the cushion for equal bets -- or, equivalently, betting half as much for the same bankroll -- significantly improves the outlook for staying in action.

Ultimately, gambling strategies involve compromises. Betting flat offers the most likelihood of surviving the session in each instance. But it turns out to yield the least chance of reaching any specified profit level. Which is more important? That's a decision players must make for themselves -- although most do it by default rather than design. Then they wonder why, trying to have it both ways, they usually end up with neither. As the troubadour of trade-off, Sumner A Ingmark, tellingly attested:

Those who set priorities are few,
Most jump in without a single clue.

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.