My question has to the with the pool size and kelly sized bets and bettors' current bankroll
I read the following
"...Even if a bettor possesses infinite wealth, there is a maximum bet producing the greatest expected profit, and any amount above lowers the expected profit.
The maximum bet can be calculated by writing the equation for expected profit as a function of betsize, and solving for the bet size which maximized expected profit.
Example:
calculated probability = 6%
dividend (Decimal odds) = 20
edge = 0.20
total pool size = 100,000
maximum er bet = $416
expected profit = 39.60
.. in the above example the maximum expected profit is a bet of 416. If one made a bet of 2/3 of the maximum, i.e. $277, the expected profit will be $35.5 or 90% of the maximum."
I don't know how they derived the maximum er bet, i.e: $416 and the expected profit of 39.60. Can anyone explain how they arrive at their values ?