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Best of Alan Krigman

Gaming Guru

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How Betting Systems Affect Your Session Chances

18 January 1999

Betting systems abound for casino games that pay even money -- 1-to-1 -- or close to it. While particulars vary greatly, the systems fall into three general categories.

  1. Flat: keep bets constant, waiting for a streak of successes.
  2. Negative progressions: raise bets after losses, trying to recover on an eventual win.
  3. Positive progressions: raise bets after wins, hoping to use "their money" to spiral toward a big payout.

No such systems can alter house advantage in games of independent trials. So, over the long run, the casinos' pound of flesh will equal the product of edge times handle -- total wagers booked.

Few solid citizens, however, will place enough bets in their lifetimes to satisfy statistical criteria for "the long run." Certainly, no single game, not even a marathon match with the gambling gods, will come anywhere close. And it is in sessions of reasonable duration, where some players win and others lose, that betting systems have their impact.

For a given bet, flat wagering leads to sessions with the closest odds of success and failure as well as the narrowest, most balanced, range of expected wins and losses. Negative progressions yield more chance for victory than defeat in any particular instance, but many small wins are offset by occasional large losses. Positive progressions offer more likelihood of an adverse than a favorable session, but intermittent rich rewards help compensate for frequent small routs.

Idiosyncrasies of sessions depend on the details of each game and the unique twists players apply to their betting systems. But computer analysis of three archetypal strategies in a specific game show the trends. Sessions were 100 rounds each, except that those based on progressions ended immediately if the next required bet exceeded 256 units. Wagers examined are Red at double-zero roulette. The systems, which aren't necessarily practical but emphasize the effects of the approaches, are:

  1. Flat: single units are bet and the amount never varies.
  2. Negative progression (Martingale): bets are doubled after every loss and reduced to single units after every win.
  3. Positive progression (parlay): bets are doubled after every win and reduced to single units after every loss.

The following figures are the outcomes of a particular 2,000-session computer run using each technique. Note that with negative and positive progressions, starting at 1 unit, average bets are 5.2 and 3.8 units respectively. This is important both to gauge the absolute effect of bet size on profit and loss, and also to compare projected performance in the alternate cases. The column of equivalent wins and losses shows how much would be involved if the base flat and parlayed wagers were raised so the averages were the same as with Martingale betting.

     Pct of Sessions  Average Win/Loss  Equiv Win/Loss
  Flat (1 unit average bet)
   Break even  1.45    
   Win  38.70  7  37
   Lose  59.85  9  48
 Negative/Martingale (5.2 units average bet)  
   Break even  0.00    
   Win  85.35  56  56
   Lose  14.65  412  412
 Positive/parlay (3.8 units average bet)
   Break even   0.05    
   Win  9.60  359  492
   Lose  90.35  43  59

The data show the trade-off opportunities. Consider these figures in developing an approach to suit your own gaming goals. However, recognize that other factors may bias expected session results. Of these, the most critical is the ratio of the bankroll you're willing to risk to the profit at which you'll quit.

Actual wins or losses, of course, depend on whether you get lucky. Still, as Sumner A Ingmark lyrically lamented, life would be lovelier if choices going into a situation were clear:

Tell me what's right, I'll do what's correct,
Just say what's wrong, and that I'll reject,
Don't make me guess, I'll never select.
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.