Are you sure about R in this case? Double or nothing is 1 to 1 payout or 2 for 1, not 2 to 1. i.e. R should be 1, and based on Kelly criterion the fraction would be 33%
Yes, I must've been thinking about the other side of the bet. That's why one should always check the math before posting. Regardless, the Kelly criterion is based on certain odds of the game so that is not analogous to stock market, as odds are constantly fluctuating. However, for a dice roll, yes 66%.
I did a random number calculator in excell using a 40% adjusted bet. In other words, my first bet is 40% of 500K, but my second bet is 40% of the remainder. So if I lose, my second bet is 40% of 300K, and if I win, it's 40% of 700K. I did 20 trials of 50 rolls of the die. After 50 years rolling the die once per year, my lowest trial yielded $2,116,400,000 and my highest trial yielded 341,558,100,000. So between 2 trillion and 341 trillion. The biggest draw down was 5 sixes in a row in any of the trials. So, if I got 5 sixes in a row on my first 5 rolls, I would be reduced to 38,000 from the original $500,000. Crappy start, but the law of averages pulled me back up to at least 2 trillion by the end of the 50 years regardless of the string of losers. Law of Averages wins. Moral of the story? Don't after a string of losers.
If i were supposed to face such a hypothetical situation then for sure i would bet anything more than 70% of my total assets to double the income, and the rest would be to cover up the basic living cost if i lost it.
Less than 10%... Never bet the farm as they say. If something can happen then all you need to do is give it enough opportunities to happen and one day it probably will. Bet almost all your net worth time after time again and one day you'll probably lose the lot. My advice, don't do this...
Expected time to death plays role here. Also what % of 500K are yearly living costs. And what is current other income. Assume 100K p/a costs and one expects 30 healthy years ahead and has no other income. Clearly one HAS to take risks, else run out of money which will mean substantially decreased quality of life. Lets jut call it no life. If betting 40% and lose, then after year 1, balance will be 200K. Another loss in 1 year, end of life. Priority is to ensure survival for 30 years, before thinking of making big. 100K you bet, you win and cover expenses until year comes when you lose and balance is down to 300. You can repeat same thing again until balance falls to 100. On average say 12 years. But extremely unlikely you will live 30. One can bet 150K. In this case balance will grow. Person will die if first 2 trades are losses, which is 1:36 chance. Too lazy to create spreasheet but I say optimum is around 170K. If first trade loss, second bet 130.
if one works or have spouse to cover expenses then I think fixed % best to bet. After 5 years at 40% bet EQ after 5 yrs % Chance 0.18 ------------------0.3% 0.42 ------------------3.6% 0.99 -----------------15.7% 2.30 ------------------41.0% 5.38 ------------------39.5% So one has 39% chance to 5x increases balance. and 41% chance to more than double. Only 3.9 % chance to lose. Increasing or decreasing % will magnify max and min numbers but % chance will remain. ==>> BET AS BIG AS YOU CAN AFFORD WHEN OPPORTUNITY PRESENTS ITSELF. 70% bet does not appear to be that appealing. you have 20% chance to show large negative return after 5 years. EQ after 5 yrs %---- Chance 0.01 ------------------0.3% 0.08 ------------------3.6% 0.44 -----------------15.7% 2.51 ------------------41.0% 14.2------------------39.5% 10% bet - don't bother EQ after 5 yrs %---- Chance 0.72 ------------------0.3% 0.88 ------------------3.6% 1.08 -----------------15.7% 1.31 ------------------41.0% 1.61------------------39.5%