How Real are Dollar-per-Hour Figures?
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Bob Dancer's Latest CasinoGaming.com Column
In http://www.casinogaming.com/columnists/dancer/2004/0713.html Bob
Dancer writes:
If I calculate a game is worth $20 per hour, I don't expect that
playing the game for five hours will let me be $100 ahead. (But I
would expect playing the game for 500 hours would put me $10,000
ahead. Nobody can define "long term" exactly, but 500 hours is
probably long enough.)
Actually, there is a good definition for "long term" and that is N0
which is the number of hands played at which point the expected
return catches up to the variance.
N0=variance/(er-1)^2 hands
For full pay deuces wild with 0.25% cashback:
N0=25.83/(1.0076+.0025-1)^2=253,210 hands (422 hours at 600
hands/hour)
For 15/10 loose deuces wild:
N0=70.31/(1.0097-1)^2=747,263 hands
At N0 hands your odds of being a net winner are 84%, at 4xN0 your
odds go up to 98%
in case anyone is curious about the math, it's pretty straightforward:
er(hands)=(er-1) x hands
standard deviation(hands)=sqrt(variance x hands)
the point at which expected return equals one standard deviation is:
(er-1) x hands = sqrt(variance x hands)
using algebra:
((er-1) x hands)^2= variance x hands
(er-1)^2 x hands = variance
hands=variance/(er-1)^2
one standard deviation means 15.87% is less, meaning 100-15.87=84.13%
is positive (net winner)
two standard deviations means 2.28% is less, meaning 100-2.28=97.72%
(the 2 gets squared so you must play 4 x N0 hands to get 2 standard
deviations)
--- In vpFREE@yahoogroups.com, "nightoftheiguana2000"
<nightoftheiguana2000@y...> wrote:
···
In http://www.casinogaming.com/columnists/dancer/2004/0713.html Bob
Dancer writes:
>If I calculate a game is worth $20 per hour, I don't expect that
>playing the game for five hours will let me be $100 ahead. (But I
>would expect playing the game for 500 hours would put me $10,000
>ahead. Nobody can define "long term" exactly, but 500 hours is
>probably long enough.)Actually, there is a good definition for "long term" and that is N0
which is the number of hands played at which point the expected
return catches up to the variance.N0=variance/(er-1)^2 hands
For full pay deuces wild with 0.25% cashback:
N0=25.83/(1.0076+.0025-1)^2=253,210 hands (422 hours at 600
hands/hour)For 15/10 loose deuces wild:
N0=70.31/(1.0097-1)^2=747,263 handsAt N0 hands your odds of being a net winner are 84%, at 4xN0 your
odds go up to 98%
this formula works for negative games also, but the meaning is
reversed:
9/6 double double bonus, er=.9898, variance=41.98
N0=variance/(er-1)^2=41.98/(.9898-1)^2=403,499 hands
meaning by 403,499 hands you have an 84% chance of being a net loser
6/5 jacks or better, er=.95, variance=19.04
N0=variance/(er-1)^2=19.04/(.95-1)^2=7,616 hands
meaning by 7,616 hands you have an 84% chance of being a net loser
--- In vpFREE@yahoogroups.com, "nightoftheiguana2000"
<nightoftheiguana2000@y...> wrote:
···
In http://www.casinogaming.com/columnists/dancer/2004/0713.html Bob
Dancer writes:
>If I calculate a game is worth $20 per hour, I don't expect that
>playing the game for five hours will let me be $100 ahead. (But I
>would expect playing the game for 500 hours would put me $10,000
>ahead. Nobody can define "long term" exactly, but 500 hours is
>probably long enough.)Actually, there is a good definition for "long term" and that is N0
which is the number of hands played at which point the expected
return catches up to the variance.N0=variance/(er-1)^2 hands
For full pay deuces wild with 0.25% cashback:
N0=25.83/(1.0076+.0025-1)^2=253,210 hands (422 hours at 600
hands/hour)For 15/10 loose deuces wild:
N0=70.31/(1.0097-1)^2=747,263 handsAt N0 hands your odds of being a net winner are 84%, at 4xN0 your
odds go up to 98%