Recently, I was having a debate with an internet friend on progressions. He felt that his "up as you lose progression" would out perform my "up as you win progression" - when the player has the edge.
Furthermore, the recent discussion regarding the Martin Blakey system has left many people confused as well, since Martin's system also used an "up as you lose progression".
In order to clear up the confusion, and because there's so much bad information out there (written by some hoity-toity pretentious individuals), I've decided to create a comparison of the two progressions, and one showing the results of flat betting. This way, people can learn what really performs the best.
In the example below, we're going to provide the players with a 6% edge over the casino. All three players will have a starting bankroll of $1,000 and will play off and on, over a series of several weeks, for a total of 10,000 spins.
1. Player one will run an "up as you lose progression", based on the Fibonacci "like" sequence 10, 15, 23, 35, 53, 80, 120. If the player looses the sequence, he simply starts the sequence over.
2. Player two will flat bet $50 at every spin.
3. Player three will run an "up as you win progression", betting just 1% of his bankroll at each spin. His initial bet will be only $10.
Which player will win the most money?
1. Player one, after 10,000 spins, will likely win the following: (.06 edge) x (average bet of $48) x (10,000 spins played) = $28,800. Not bad, but the player will likely go broke before playing all 10,000 spins because of variance.
2. Player two, after 10,000 spins, will likely win the following: (.06 edge) x (bet of $50) x (10,000 spins played) = $30,000. Not bad.
3. Player three, after 10,000 spins, will likely win the following: (1.0006)^(10,000 spins played) = $402,703. Such is the power of compounding interest! As you can see, betting an "up as you WIN progression" is vastly superior, and the player was far less likely to go bust, since his bets would decrease during losing periods, and increase during winning periods. Mathematically it's vastly superior to an "up as you lose progression" and flat betting!
At this point, common sense should have many asking why would a supposed mathematician ever advocate using an "up as you lose progression" in the first place? The answer is, of course, he/she wouldn't!
If you believe that you may have the edge, mathematically it will always make the most sense to run an "up as you win progression", based on a percentage of your bankroll.