
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 twohand 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

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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