There is a difference between mean loss and median loss in a game that
doesn't have a normal distributuon. The most likely loss is the median value of
about 750$.
My wife and i did it in laughlin and got lucky and broke even.
Bob from Pennsylvania
[Non-text portions of this message have been removed]
See comments below.
There is a difference between mean loss and median loss in a game
that doesn't have a normal distributuon.
Right on: For a normal disribution, the mean (simple arithmetric
average) = median (50% probability point) = mode (most likely
outcome).
The most likely loss is the median value of about 750$.
Not right: by definition, the most likely outcome is the MODE. For
VP, unless you play forever (really forever), the median, and the
mode are all less than the mean (or EV), even if the game is
positive.
That means we are, a priori, always more likely to win less (or lose
more) than the EV. Oh well.
I guess I should hurry up and compute the PDFs for JoB. I imagine
the pictures will tell a nice story.
Any preferences for the # of hands? (I am only going to do SL now)
--- In vpFREE@yahoogroups.com, BOBBJ@a... wrote:
Here are some JoB statistics for a 9/6 FP machine. Values are per coin, unless otherwise
noted.
Results are non-linear in # of hands except for EV (mean).
100 500 1000 2000 4000 Hands
mode -45 -100 -165 -290 -550
median -30 -80 -135 -245 -445
EV -0.456 -2.280 -4.561 -9.121 -18.244
10% -130 -335 -510 -795 -1255
90% 110 230 315 460 1655
Prob<EV 61% 63% 66% 69% 73%
For comparison purposes, here are some values for Pick'em:
100 500 1000 2000 4000 Hands
mode -50 -170 -285 -305 -335
median -35 -95 -115 -125 -150
Pick'em has a return of 99.95%, higher than JoB's 99.54%. Nonetheless, for a (very) small
number of hands, the most likely outcome for JoB is better than for Pick'em. This has
nothing to do with the RF cycle or its contribution (the RF has almost no effect on the
mode; results for mode are the same with or without RF). BTW, if I had the choice, I'd
always play Pick'em over JoB. For some reason though, most VP players I've spoken to
prefer JoB. (Perhaps Pick'em is too boring? )
So which is the more risky game? I guess it depends upon what you mean by "risk" and
how many hands you play.
So what is the required bank roll to play either 5 coin JoB or Pick'em with 100% certainty of
not going broke for 4000 hands? Easy: 4000*5 = 20,000 coins, since that is the most you
could ever lose after 4000 hands. (This was a trick question and it has nothing to do with
log-optimal betting or RoR)
Homework: Compare JoB to a game with higher variance and better EV, like FPDW or NSUD
.