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Best of Alan Krigman

Gaming Guru

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How Betting Strategies Let You Balance Your Prospects

29 November 1999

Many table players think that sizing bets based on past results is the key to gambling success. They're wrong in that outcomes averaged over many players, or for one bettor over many rounds, depend only on house edge and total amount wagered. They're right in that betting strategies affect the bankroll swings individuals are apt to experience during sessions of reasonable length.

In general, betting uniformly best equalizes chances of nominal wins and losses. Raising bets when losing -- looking for recovery -- improves chances of modestly successful sessions but opens prospects of occasional larger penalties. And pressing when ahead -- hoping to catch hot streaks with "the house's money" -- offers outside chances at bigger scores while increasing the potential for small losses.

To envision the effect, imagine flipping a coin four times and betting on each toss. Heads (H) wins even money and tails (T) loses. The game has no house advantage and players "expect" to break even. There are 16 possible heads-tails combinations.

Say that three groups, each comprising 16 solid citizens, take part in different sessions of this game. Make believe the distribution of results proves to be statistically correct in every case. That is, each player gets one of the combinations.

The following list shows how the players will fare for three betting modes. Players all start with $1. A risk-neutral group bets $1 flat. A risk-averse group doubles up after every loss and returns to $1 after a win. A risk-prone group doubles up after every win and returns to $1 after a loss. You can check my arithmetic yourself with pencil and paper. As a model, the sixth row -- (HHTT) -- will get (+1 +1 -1 -1) for a total of 0 betting flat, (+1 +1 -1 -2) for a total of -1 doubling after every loss, and (+1 +2 -4 -1) for a total of -2 doubling after every win.

result
flat
double
after a loss
double
after a win
HHHH
+4
+4
+15
HHHT
+2
+2
-1
HHTH
+2
+3
0
HTHH
+2
+3
+2
THHH
+2
+3
+6
HHTT
0
-1
-2
HTHT
0
+1
-2
HTTH
0
+2
-1
TTHH
0
+2
+1
THTH
0
+2
-1
THHT
0
+1
-2
TTTH
-2
+1
-2
TTHT
-2
0
-3
THTT
-2
-2
-3
HTTT
-2
-6
-3
TTTT
-4
-15
-4

Tallying these results shows the effects of the alternate strategies. Each group of 16 stalwarts broke even, as you can see by summing the separate columns. The distinctions arose in the numbers and amounts of wins and losses within the categories.

  • Betting flat yielded one $4 and four $2 wins; six pushes; and one $4 and four $2 losses. This mode of play exhibited equal numbers of moderate victories and defeats.

  • Doubling after losses lead to one $4, three $3, four $2, and three $1 wins; one push; and one $15, one $6, one $2, and one $1 loss. This yielded 11 moderate wins with one large, one intermediate, and two small losses. More but slighter triumphs, fewer but worse tragedies.

  • Doubling after wins generated one $15, one $6, one $2, and one $1 win; one push; and one $4, three $3, four $2, and three $1 losses. This approach produced one large, one intermediate, and two small wins, offset by 11 moderate losses. Fewer but greater conquests, more but pettier routs.

The moral of the story is that gamblers can select betting strategies consistent with their goals and the penalties they're willing to accept. Do you want to trade off moderate potential gains and losses? How about a good chance at a small win and a small prospect of getting stung? Maybe a long shot at a big payout and a strong likelihood of a small loss? Or somewhere in between? Choose accordingly, with these cases as guides. And, as you decide, ponder these pearls from the poet, Sumner A Ingmark:

Among a gambler's dearest talents,
Is keeping win and loss in balance.
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.