Was i really right when admitting i was wrong regarding Kelly betting on horse racing? - Page 2 - Gambling and Probability

The probability of being reduced to X% of your bankroll when wagering c*f, where c is a constant and f is the kelly stake, is

X^{2/c - 1}

In real life there is a minimum wager. Let's say it's 0.2% of your current bankroll, so you're broke if your bankroll goes below that. Let's pick a smaller percentage, say 0.1%.

P(ever fall to 0.1% when betting 2x kelly) = .01^(2/2 - 1) = .01^0 = 1

Since .2% and .1% were arbitrary examples, we can say that no matter how large your bankroll and how big your edge, if there is a minimum wager then your chance of going broke when betting 2x kelly is 100%. Any small number raised to the 0 equals 1.

(But you don't need a formula to see why that's true.)

Your arbitrary imaginary constraints lead to "going broke" at any non-zero wager size, genius.

Warren Buffett puts up $3B vs $1B on a fair coin flip. By your genius definition, you're "broke", genius.

Quote

02-12-2015 , 12:42 AM

#27

heehaww

Pooh-Bah

Join Date: Aug 2011 Posts: 5,081

Quote:

Originally Posted by RickySteve

Your arbitrary imaginary constraints lead to "going broke" at any non-zero wager size, genius.

The only imaginary thing is a casino/racetrack/sportsbook with no minimum wager constraint. If you can find one, then I'll concede that you don't go broke with 0 growth.