You didn't clarify what chance you want there to be of winning the $1000. You seemed to only be concerned with minimizing the chance of losing the $1 million, which makes the answer simple. Maybe the assumption that playing in such a way that maximizes the chance of winning the $1000 before losing the $1 million should be incorporated, in which case a Martingale that starts out at $1000 is probably the ideal approach. The chance of winning is probably close to the ratio of the 2 possible results, 999 out of 1000.
----- Jeff McDaniel <jmcdaniel@dmtechlaw.com> wrote:
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>Four days at home with a nasty spring cold have left me with time to ponder gambling imponderables and gambling fantasies. After you read my question below, you might think the cold has left me one taco short of a combination plate.
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> I have a hypothetical question that has probably been asked in various forms over the years. I think it ultimately is mostly or completely a math question. Maybe it is a risk of ruin question or a derivative thereof.
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> Assumptions:
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> 1. You have a million dollar bankroll.
> 2. You can only play negative EV games. For the hypothetical, assume you give the casino a half of one percent edge on every bet you make.
> 3. You play games that have a maximum bet of $25,000. You, however, are free to play games with lower limits if you wish.
> 4. You play every day with the objective of winning $1,000. You stop for the day as soon as you have won $1,000.
> 5. You are willing and able to risk the entire bankroll on any given day to win $1,000.
> 6. You play perfect strategy, albeit only on negative EV games.
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> Questions:
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> 1. How many days are you likely able to play before you encounter that fateful (inevitable?) day when you lose your million dollar bankroll?
> 2. Are there specific strategies such as betting strategies or bankroll management strategies that you could use to improve your longevity (i.e., putting off the day that you lose your bankroll)?
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> If I am leaving out any key assumption or not asking the right question, kindly supplement as necessary.
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> Thanks,
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> Jeff
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