Yes, sorry I didn't catch that contradiction before posting.
Assume you can make multiple bets on the same spin.
Now I wonder if any of the interviewees passed this test, given how muddled the conditions were stated.
What is your strategy?
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Assume you can make multiple bets on the same spin.
Now I wonder if any of the interviewees passed this test, given how muddled the conditions were stated.
You postulate that Kelly doesn't apply because of the limited number of trials, but then proceed with the 100,000 trials simulation to come up with a more legitimate answer?
Both Kelly and Expectancy are invariant with respect to the number of trials. Think of it this way: you can play only 10 times, but what if there are 1 million players? Who is the most likely to make the most money, based on the strategy that they selected?
Yes, sorry I didn't catch that contradiction before posting.
Assume you can make multiple bets on the same spin.
Now I wonder if any of the interviewees passed this test, given how muddled the conditions were stated.
It's still a good interview question. What matters here is how the interviewee thinks, and not how accurately he/she understands the assumptions of the stated problem. And indeed, it's very directly related to the problem of the optimal capital allocation in the portfolio of strategies.
k*E == (% of bankroll wagered)*(expected return per unit bet)
== expected return to bankroll.
Correct.
Yes, although I am not sure if it should be adjusted for volatility (risk), or if it's already adjusted for volatility by incorporating the Kelly. From what I remember, cutting Kelly by 50% reduces the risk by 75%. So, if we are seeking the maximum risk-adjusted return, perhaps we should account for risk.
This is a guesstimates without any fancy formulas. Just estimating so math might be off. In regular roulette the odds of a black or red landing is like 48% or so. So the house gets a few % advantage. The odds of a single number hitting is 2-3%. There are 4 R-16's so 10%...ish but the payout is 35 times. So if you have a 10% chance of getting a 35 to 1 payout and $100 in your pocket, idk maybe bet $5 per spin. You could do $10 but if the odds don't play out exactly you could be SOL. That will give you 20 spins. Even if it takes you till the last spin you will make like 75% on the initial capital or so. Seems like the best way to play to me, the odds are much higher that you will make much higher than that though. Then do whatever after that with the profits. My math might be wrong in there but seems reasonable I think.
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