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Best of Alan Krigman

Gaming Guru

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The More You Try to Make, The Less Your Chance of Success

29 March 1999

One of the simplest yet poorest perceived principles of casino gambling is that the more you try to earn, the less your chance of success and the more vulnerable you are to failure. Nothing you can do -- no potpourri of wagers, no betting progressions, no hunches about riding streaks -- changes the fundamental effect.

I'll demonstrate how this works by examining the net wins and losses for three million hopefuls making 10 bets of $10 on different propositions at single-zero roulette. A million solid citizens each put their money on red, four-number corners, and single numbers. To the casino, all three million patrons are equivalent because they'll each bet $100 with a 2.7 percent edge.

At odds of 1.06-to-1, $10 on red pays $10. The list below shows how the million players are expected to finish 10 rounds.

 Wins in 10 trials Net win (+) or loss (-) Number of players
 0  -100 1,275
1 -80 12,079
2 -60 51,496
3 -40 130,094
4  -20  215,682
5  0  245,196
6  +20  193,576
7  +40  104,793
8  +60  37,229
9  +80  7,838
10  +100  742

At odds of 8.25-to-1, $10 on corners pay $80. The following list shows where the million players are expected to be after 10 bets.

 Wins in 10 trials Net win (+) or loss (-) Number of players
 0  -100 318,509
1 -10 386,072
2 +80 210,585
3 +170 68,068
4  +260  14,438
5  +350  2,100
6 +440  212
7  +530  15
8  +620  less than 1
9  +710 less than 1
10  +800  less than 1

At odds of 36-to-1, $10 on single numbers pay $350. The next list indicates what the million players can expect after 10 tries.

 Wins in 10 trials Net win (+) or loss (-) Number of players
 0  -100 760,340
1 +260 211,205
2 +620 26,401
3 +980 1,955
4  +1,340  95
5  +1,700  3
6 +2,060  less than 1
7  +2,420  less than 1
8  +2,780  less than 1
9  +3,140 less than 1
10 +3,500  less than 1

Figures within each class of bet are one way to show that the higher the win, the fewer who can expect to reach it. For instance on corners, 68,068 out of a million should net $170, 14,438 should earn $260, and 2,100 should walk away with $350.

Among classes, the data show that more solid citizens can expect to win any given amount as odds get longer, but susceptibility to loss simultaneously rises. As an illustration, 7,838 out of every million should win $80 on red, whereas 210,585 should hit this goal betting corners. However, of those who bet on red, only 1,275 should forfeit their whole stakes and 410,626 should lose at least something. Of those who bet on corners, 318,509 should lose everything and 704,581 should end up somewhere in the hole.

Again among classes, greater longshots mean higher possible prizes but more players who'll lose all or some of their bankrolls trying. See this by comparing bets on corners and single numbers. Corners can yield only up to $800, but 318,509 players can expect to lose $100 and another 386,072 can expect to finish $10 in the hole. Single numbers promise up to $3,500 but 760,340 players should lose $100 trying.

You can opt for any point along the spectrum from a good shot at a small haul to a remote chance at a big bonanza. Which is best? You decide. Whether a goal is wise or foolish is an individual issue, tied up in factors like your personal motivation to gamble and how often you indulge your casino fantasies. But, once you set your objectives, understanding the trade-offs helps you pick a playing style consistent with them. Sumner A Ingmark, the Geoffrey Chaucer of judicious choice, said it this way:

By dreams of riches we are oft deceived,
With foolproof plans that beg to be believed.
But dreamers are most apt to be aggrieved,
While modest goals are easiest achieved.
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.