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Thread: pm: SD question

  1. #11
    Don Schlesinger
    Guest

    Don Schlesinger: Perfect!

    > Am I doing this right? If I have a wager with a 30%
    > winrate and a 3 to 1 payback, and I bet $1000 here 10
    > times, then:

    > Average squared result = [(0.30 * $3000^2) + (0.70 *
    > (-$1000)^2)] = $3,400,000

    Right. Easier to call $1,000 your "unit," do all the calculations with the smaller numbers, then convert at the end. But, then, I didn't do it that way in my example, above, so can't find any fault with your approach.

    > Variance for 1 bet = $3,400,000 - $200^2 = $3,360,000
    > S.d. for 1 bet = $3,360,000^0.5 = $1833.03

    Right.

    > Variance for 10 bets = $3,360,000 * 10 = $33,600,000
    > S.d. for 10 bets = $33,600,000^0.5 = $5796.55 (or just
    > $1833.03 * 10^0.5)

    Right.

    > Also, just to confirm, in the chapter 2 s.d. tables,
    > the variances listed in that one column assume a 1
    > unit bet per hand played and we then multiply by the
    > bet squared to get the variance for that particular
    > number of units, correct?

    Yes. But, there are some two-hand wagers, where the variance is increased by the covariance (roughly 0.50).

    > And I think I have this right, but just to confirm:
    > 1) Once all the variances in the table have been
    > summed, we divide by the sum of the frequencies
    > because we aren't playing all 100 hands; we just take
    > out the 26.77% divisor for each TC frequency as
    > common, correct?

    Right.

    > 2) If we didn't divide by the sum of the frequencies,
    > the resulting s.d. would be for 100 hands played &
    > observed, correct?

    Not sure about this one. If you didn't divide by the sum of the frequencies, in the above examples, then you'd get the wrong answer. :-) The resulting s.d. wouldn't be for 100 hands played, because the frequencies don't add to 100%. I think what you meant to write was, "If this were for 100 hands played (the frequencies add to 100%), then we wouldn't have to bother to divide by the sum of the frequencies."

    > (Sorry, I keep saying last question and I always have
    > a few more; feel free to cut me off anytime.)

    Be my guest. You're doing great.

    Don

  2. #12
    pm
    Guest

    pm: Re: Perfect!

    I'm elated; I actually understand some of the fundamentals now. The reason I was asking was because I'm concocting some cover plays that can't be simmed, so the only way I can figure out what effect they'll have on my risk of ruin and e.v. is by doing the calcutions by hand. Hopefully I won't screw anything up too badly now.

    Thanks; I'm sure I'll have some more questions along the way.

    pm

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