Wednesday, October 20, 2010

Progressive Betting

For the past few months (or longer), B-Dawg's been trying to find ways to make lots of money with minimal energy.  He's so hellbent on this that he's willing to go through the trash to find cans so he can get a deposit.  He may try to deny it, but don't let him fool you...I've seen him in action.

Discussing this with him inevitably led to discussion about the movie "21" and eventually casinos in general.  After some theoretical discourse, I made some back of the envelope calculations to put numbers to the ideas.  By far, the most intriguing strategy we talked about at length was progressive betting.  To simplify the discussion, I will focus on Roulette because it is easy to determine the odds of winning (and more importantly, losing), and it has independent trials (unlike blackjack).

The basic betting strategy would involve betting a certain amount on every play regardless of a win or a loss.  In this case, playing any of the one to one payoff bets (1-18, 19-36, black, red, odd, or even) carries a 47.4% chance of winning (9/19).  Betting this strategy, one ought to expect to lose a little over five cents on the dollar.  In this case, the player is betting on each individual independent trial.

Progressive betting, on the other hand involves incrementally increasing one's bet after a loss.  The idea is that after a win (regardless of how many losses), if one doubles his bet after every loss, he will have increased his chip stack by the amount of the original bet.  Playing a progressive betting strategy, the gambler is essentially not betting on any one roll.  Instead, he is betting against a particular sequence of outcomes.  The reason is that the only way to lose is to lose a number of bets in a row to the point where you cannot double your bet again without exceeding the table maximum.  Since rolls are independent, the odds of losing x number of rolls in a row is equal to the odds of losing raised to the x power or (10/19)^x.

Example:  If the table has a $5 minimum and a $500 maximum, one can absorb six losses before exceeding the table max (the bet would be $320 on the seventh roll).  The odds of losing on seven consecutive plays is (9/19)^7 or 1.1%.  Thus 98.9% of the time, the gambler can expect to win $5.  While the player can lose a considerable amount of money, the odds are that they will not.  This strategy also reduces the expected loss per roll from 5.26 cents to 0.35 cents on the dollar (although the variance is considerably higher).

There are variations that can diminish the risk of a total loss at the expense of expected win frequency, and there are other games with somewhat more difficult odds to determine.  I have worked out similar variants for other games that are strictly superior to the one described above, so they certainly do exist (if there is demand, I would be glad to elaborate some in future posts).  The above was just the easiest example to describe what is really going on with progressive betting.



  1. I don't know if this changes anything, but you forgot about 0 and 00!

  2. I've got ya covered. There are 36 spots plus the 0 and the 00 for a total of 38 possible outcomes on any roll. There are 18 ways to win betting the 1 to 1 payout bets. Thus, the odds of winning with those bets is 18/38 = 9/19. -MSG

  3. Seems scary to me!

    A negative progression system has you increase your bets when you lose in hopes of getting back to even after a loss. The is the Martingale System calls for you to double your bets after each loss. This is very dangerous and you should NEVER do it.