Question about Craps and Variance
August 13th, 2010 at 3:22:09 PM
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I have a question about craps, regarding upward and downward fluctuations. (Variance)
Pretend you have 100k as a total bankroll and that you must gamble with ALL of it. Which method would have the greatest fluctuations downward or upward.
Assuming you are playing the pass line and double odds.
1. Placing 100k in bets by playing with only $50 units. (Meaning you're betting about $150 each roll)
or
2. Placing 100k in bets by playing with $300 units. (Meaning you're betting about $900 each roll)
In both scenarios you much place a grand total of 100k in bets.
Would the variance be the same?
Pretend you have 100k as a total bankroll and that you must gamble with ALL of it. Which method would have the greatest fluctuations downward or upward.
Assuming you are playing the pass line and double odds.
1. Placing 100k in bets by playing with only $50 units. (Meaning you're betting about $150 each roll)
or
2. Placing 100k in bets by playing with $300 units. (Meaning you're betting about $900 each roll)
In both scenarios you much place a grand total of 100k in bets.
Would the variance be the same?
August 13th, 2010 at 4:14:46 PM
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First of all, placing 100k in bets does not usually require a bankroll of 100k.
Second, for the same total amount wagered on the same kind of wagers, as you described, the larger individual wagers will lead to a larger variance.
Third, I think you should focus more on standard deviation than variance, since it is in the same units as the wager; i.e., dollars rather than dollars squared.
Finally, and completely off-topic from your question, I want to take this opportunity to apologize to members of this forum for my poor use of terminology in past posts. When describing a gambling session in which the results were better than should be expected, I referred to that as "positive variance". Variance is always non-negative. I think I should have been using the term "positive deviation" from expectations. Maybe some day I will learn.
Second, for the same total amount wagered on the same kind of wagers, as you described, the larger individual wagers will lead to a larger variance.
Third, I think you should focus more on standard deviation than variance, since it is in the same units as the wager; i.e., dollars rather than dollars squared.
Finally, and completely off-topic from your question, I want to take this opportunity to apologize to members of this forum for my poor use of terminology in past posts. When describing a gambling session in which the results were better than should be expected, I referred to that as "positive variance". Variance is always non-negative. I think I should have been using the term "positive deviation" from expectations. Maybe some day I will learn.
