Question about standard deviation.

[FrankieT]

I ran the conditions of a particular blackjack game through the CVCX online viewer

Here are just a few of the conditions followed by a few of the results:


CONDITIONS
Bankroll: $10,000
Amount of hands bet per round: 2


RESULTS
$/HR = $87
Standard Deviation per hour= 134 betting units



True count............Bet amount
....<=0........................2x5
.......1........................2x10
.......2........................2x25
.......3........................2x50
.......4........................2x50
.......5........................2x75
....>=6........................2x100

Standard Deviation per hour in $ = 134 x $5 = $670





Ok, just to clarify:
Bankroll=$10,000
$/HR= $87
Standard Deviation in dollars = $670


According to the aforementioned standard deviation, bankroll, and $/HR,
after one hour of play you should have:

a 68% chance of ending up with $9,417 < $10,087 < $10,757

a 27% chance of ending up with $8,747 < $9,417 or $10,757 < $11,427

a 4% chance of ending up with $8,077 < $8,747 or $11,427 < $12,097


After two hours of play you should have:

a 68% chance of ending up with $9,504 < $10,174 < $10,844

a 27% chance of ending up with $8,834 < $9,504 or $10,844 < $11,514

a 4% chance of ending up with $8,164 < $8,834 or $11,514 < $12,184


And so on and so on.....


Is my understanding of standard deviation correct or skewed somehow?

 

[Sonny]

Everything for the first hour looks good given the following:

100 hands per hour
SD/Hand = 13.4 units ($67)
SD/100 hands = 134 units ($670)

For the second hour I get:

SD/200 hands = 189.5 units ($947.50)

After two hours of play you should have:
a 68% chance of ending up with $9,226.50 < $10,174 < $11,121.50
a 27% chance of ending up with $8,279 < $9,226.50 or $11,121.50 < $12,069
a 4% chance of ending up with $7,331.50 < $8,279 or $12,069 < $13,016.50

-Sonny-

 

[FrankieT]

Everything for the first hour looks good given the following:

100 hands per hour
SD/Hand = 13.4 units ($67)
SD/100 hands = 134 units ($670)

For the second hour I get:

SD/200 hands = 189.5 units ($947.50)

After two hours of play you should have:
a 68% chance of ending up with $9,226.50 < $10,174 < $11,121.50
a 27% chance of ending up with $8,279 < $9,226.50 or $11,121.50 < $12,069
a 4% chance of ending up with $7,331.50 < $8,279 or $12,069 < $13,016.50

-Sonny-

Oh yeah it's 150 hands per hour, probably should have included that , std deviation per hand=10.9 (according to the CVCX online viewer)

 

[Sonny]

Oh yeah it's 150 hands per hour, probably should have included that , std deviation per hand=10.9 (according to the CVCX online viewer)

So the SD for 2 hours = 10.9 * Sqrt(300) = 189 units instead or 189.5. I was pretty close.

-Sonny-

 

[FrankieT]

So the SD for 2 hours = 10.9 * Sqrt(300) = 189 units instead or 189.5. I was pretty close.

-Sonny-

Ahhhh, thanks! Much appreciated

 

[Kasi]

I guess all the above is Ok, especially as the dollars go.

But let's face it, his average bet unit is nowhere near $5.

Just seems a little weird to think ur making 18 units an hour or could lose 134 units in 150 hands as 1 standard deviation.

Can't happen without arbitrarily re-stating ur unit.

But nothing wrong with it either, if that's how u like to look at it.