I'd love to Chief, however I think a lot of work went into this post, & I'm
sure it means something to someone, so, I'm going to resist temptation & not
make a comment.
However........Ponder this.............
If a Hen & 1/2, lays an egg & 1/2 in a day & 1/2......what's the price of
oranges?
CF
"There is no data on the future"
Laurel Cutler
Cardfather, can you please double check this? Thanks.
the derivation of N0 (which does rely on clt) is pretty
straightforward:the -2sd curve is:
(er-1) x hands - 2sqrt(variance x hands)
for full pay deuces wild it is:
.00762 x hands - 2sqrt(25.83462 x hands)
this can be ploted using a spreadsheet
to find the minimum take the first derivative and solve for zero:
(er-1) - 1/sqrt(variance x hands) = 0
hands = variance/(er-1)^2
which is also the formula for N0 which is the x-intercept of the -1sd
curveto find the loss at the minimum, plug N0 into the -2sd formula:
(er-1) x variance/(er-1)^2 - 2sqrt(variance x variance/(er-1)^2))
variance/(er-1) - 2variance/(er-1) = -variance/(er-1)
which is also the formula for the kelly bankrollso, for the -2sd curve (2.28% of results are worse assuming clt) the
highest loss is a kelly bankroll (variance/(er-1) bets) and it occurs
at N0 (variance/(er-1)^2) hands, for full pay deuces wild 5-coin
quarters this would be $4,238 at 444,930 hands
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