Standard deviation - determine your possible profit.

[mr.ore]

What is your possible profit if flat betting constant amount of money(WAGER) on an option with probability p and PAYOUT from {1,2,5,8,11,17,35} with unit size = UNIT?

BOUNDARY(x) = -WAGER/37 + x*(PAYOUT+1)*sqrt(WAGER*p*(1-p)*UNIT)

Let's say you bet WAGER=5000 and UNIT 1, and you bet on single (PAYOUT=35)

68% of time your profit will end up in an interval <BOUNDARY(-1), BOUNDARY(1)>

BOUNDARY(-1) = -5000/37 - 1*(35+1)*sqrt(5000*1/37*(1-1/37)*1) = -548
BOUNDARY(1) = -5000/37 + 1*(35+1)*sqrt(5000*1/37*(1-1/37)*1) = 277


95% of time your profit will end up in an interval <BOUNDARY(-2), BOUNDARY(2)>

BOUNDARY(-2) = -5000/37 - 2*(35+1)*sqrt(5000*1/37*(1-1/37)*1) = -961
BOUNDARY(2) = -5000/37 + 2*(35+1)*sqrt(5000*1/37*(1-1/37)*1) = 690


99,7% of time your profit will end up in an interval <BOUNDARY(-3), BOUNDARY(3)>

BOUNDARY(-3) = -5000/37 - 3*(35+1)*sqrt(5000*1/37*(1-1/37)*1) = -1373
BOUNDARY(3) = -5000/37 + 3*(35+1)*sqrt(5000*1/37*(1-1/37)*1) = 1103


Now what about having WAGER=5000 and UNIT 5, and you bet on single (PAYOUT=35)

68% of time your profit will end up in an interval <BOUNDARY(-1), BOUNDARY(1)>

BOUNDARY(-1) = -5000/37 - 1*(35+1)*sqrt(5000*1/37*(1-1/37)*5) = -1058
BOUNDARY(1) = -5000/37 + 1*(35+1)*sqrt(5000*1/37*(1-1/37)*5) = 787


95% of time your profit will end up in an interval <BOUNDARY(-2), BOUNDARY(2)>

BOUNDARY(-2) = -5000/37 - 2*(35+1)*sqrt(5000*1/37*(1-1/37)*5) = -1981
BOUNDARY(2) = -5000/37 + 2*(35+1)*sqrt(5000*1/37*(1-1/37)*5) = 1710


99,7% of time your profit will end up in an interval <BOUNDARY(-3), BOUNDARY(3)>

BOUNDARY(-3) = -5000/37 - 3*(35+1)*sqrt(5000*1/37*(1-1/37)*5) = -2904
BOUNDARY(3) = -5000/37 + 3*(35+1)*sqrt(5000*1/37*(1-1/37)*5) = 2633

The greater unit means greater risk, but also possible reward.  Enjoy the formula.

[VLS]

Thanks Mr. Ore, this is something people must understand in full, since the larger the sample the harder that is *not* to fall within these ranges: 3 STD range.

[Toby]

Mr. ore: playing 5 units means you play less spins or you wagw more.


Wagging 5000 1 unit each spin or 5 units 1000 spins.


Playing 5 units at the same level of the example you gave us for 1 units mean to wage 25,000 instead of 5000.


It seems that bounderies playing strait bet go from -27.5% to +22%(3sd) of the total waged.


Same formula for a double street play is:


BOUNDARY(-3) = -5000/6.1666 - 3*(31+1)*sqrt(5000*6/37*(1-6/37)*1) =
BOUNDARY(3) = -5000/6.1666 + 3*(31+1)*sqrt(5000*6/37*(1-6/37)*1) =
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[/size]It is that correct?
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[/size]Do they keep similar bounderies?(strait bet and DS)
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