Mythological Moment: Progression systems Ė part 2
Copyright 2001, The Mayor
When Einstein came up with his famous E = mc2 he did not suddenly invent a new law that didnít exist previously. He used mathematics to rigorously derive the equation, and left it to a future generation to realize its potential applications. Mathematics helps us model reality, and can be used to make reliable predictions about the effects of certain actions we take.
Other not so famous mathematicians long ago arrived at their own theorems in statistics and probability theory, which bear directly on money management and betting schemes. Here are the basic results:
To put this to the test, I wrote a computer program to model a very simple game. In it, a coin is tossed repeatedly. If the coin comes up heads you win, tails you lose. Begin by betting $1, and double your bet until you win. After a win, begin over again by betting $1. Thus, if the sequence is tails, tails, tails, heads, you will have bet $1, $2, $4, and $8. You won your final $8 bet, but you lost the previous $1 + $2 + $4 = $7. Thus, you are ahead $1.
What happens if we toss the coin exactly 20 times? Iíll call that a "session." Here are the results of a typical session:
How many tosses: 20
High point: $7 at toss 20
Low point : -$250 at toss 16
Final total: $7
I then ran this program for one hundred million sessions, consisting of 20 tosses each, and accumulated the statistics. Here they are.
Average high point during session: $10.00
Average low point during session: $-83.68
Maximum high point for all sessions: $20.00
Maximum low point for all sessions: $-2,097,151
Number of winning sessions: 86,188,733
Number of losing sessions: 13,811,267
Average win at a winning session: $7.39
Average loss at a losing session: $46.12