Note that the formula listed in the article is the Kelly formula for when you lose 100% of your stake if you lose the bet, which isn’t always the case.
The Kelly formula is derived from the starting point of:
bankrolln=(1+b∗wager)pn∗(1−a∗wager)(1−p)n
Essentially, after a sufficiently large number of n wagers, you expect to have won pn times and lost (1-p)n times. Each time, your previous bankroll is multiplied, either by (1 + b*wager) if you won, or by (1 - a*wager) if you lost.
Often, a = 1. Sports betting, poker tournament, etc—if you lose your bet, you lose your entire wager.
Sometimes, though it isn’t: For something like an investment with a stop-loss, for example, the downside risk could be something like 20% instead of 100%.
If you leave it as “a” instead of assuming a=1, you end up dividing that first term by it:
Note that the formula listed in the article is the Kelly formula for when you lose 100% of your stake if you lose the bet, which isn’t always the case.
The Kelly formula is derived from the starting point of:
bankrolln=(1+b∗wager)pn∗(1−a∗wager)(1−p)n
Essentially, after a sufficiently large number of n wagers, you expect to have won pn times and lost (1-p)n times. Each time, your previous bankroll is multiplied, either by (1 + b*wager) if you won, or by (1 - a*wager) if you lost.
Often, a = 1. Sports betting, poker tournament, etc—if you lose your bet, you lose your entire wager.
Sometimes, though it isn’t: For something like an investment with a stop-loss, for example, the downside risk could be something like 20% instead of 100%.
If you leave it as “a” instead of assuming a=1, you end up dividing that first term by it:
wager=pa−1−pb