The surest way to hit the expectation of -$500 after $100,000 total bet is to bet as small as you can and flat bet. Ideally that means 10,000,000 bets of 1 cent each. That is most likely not practical or possible. The smaller the bet the closer you expect to come to your expectation. Flat betting limits variance as the luck of what happens to your bigger bets no longer has an effect on the outcome. Look at it in reductio ad adsurdum negating blackjacks, doubles and splits. You could bet $100,000 as one bet but the variance would be huge. You would either win $100,000 or lose $100,000. If you made two bets of $50,000 each 49.995% of the time you lose nothing , 24.354% you win $100,000 and 25.5025% you lose $100,000. Hopefully I don't need to go any further. The tails of the spread become rare and the center becomes more and more likely and quickly approaches the EV of a $500 lose as the number of bets increase. It is most certain at the smallest bet possible and the variance is the smallest. ie you have a better chance of being closer to expectation.
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