G'day Cian,

Are you sure about that?  I suspect Jeff zinged me with something very
similar a few years ago - if I've made a similar error again, please
point and laugh.

From my reading, with a punter betting on a given number, N, out of the
36 possible results, the punter has:

double N - 1 result : 9x bet payoff

single N - 10 results : -1x bet payoff  (chances calculated by
subtracting double N and no N results from 36)

no N - 25 results : 0x bet payoff

By my read, that's a net result of -1x bet over 36 such bets, for a
house edge (edge being net result divided by total bet) of ~ 2.8%.

Thus, over a sufficiently long run (and remembering things being "due"
to turn up happens in the denominator, not the numerator), the house
would expect to net Cr2,800 out of every Cr100,000 wagered.

Dhe, as written, has a fairly high variance - although J. Random Punter
would expect to lose 2.8% of his bet per hand, the standard deviation of
per-hand returns is ~158% of his bet.

The length of the short run (defined as N0, the number of hands required
to accumulate expected gain equal to the accumulated standard deviation)
would be 3,275 hands.  At 100 hands per hour (to keep the numbers
simple), that obviously drops out to just under 33 hours - a bit over
four 8-hour shifts - for a given table to reach its long run.

On an hourly basis, a table would expect to take 280% of a single bet,
but the standard deviation of hourly returns is 1580% of a single bet. 
(Standard deviation accumulates in quadrature, unlike expectation which
accumulates linearly).

However, over at Dodgie Brothers Casino, Dry Cleaning and Eye Care, ol'
Desmond Dodgie (a fine, upstanding sophont without a criminal record or
other stain upon his character - that you know about) offers a "variant"
of Dhe that, shorn of the member-of-Parliament-level bollocks-smithing,
shaves the double-N payoff to 8x the amount bet.

House edge becomes 5.6%, and standard deviation of per-hand returns
becomes 143% of the amount bet.  The Dodgies' Dhe tables reach their
long runs in 665 hands - 4x reduction from the original game's 3275
hands-to-long-run is due to the doubled house edge, while the final
~1.25x is from the variation reduction.

Alex

On 9/3/20 3:53 am, Cian Witherspoon wrote:
>
>
> On Sat, Mar 7, 2020 at 23:29 Timothy Collinson - timothy.collinson at
> port.ac.uk <http://port.ac.uk> (via tml list) <xxxxxx@simplelists.com
> <mailto:xxxxxx@simplelists.com>> wrote:
>
>
>
>     On Sun, 8 Mar 2020 at 01:12, Jeff Zeitlin
>     <xxxxxx@freelancetraveller.com
>     <mailto:xxxxxx@freelancetraveller.com>> wrote:
>
>         The March/April 2020 issue of Freelance Traveller is now
>         available for
>         download!
>
>     (Snip)
>     And yes, math(s) challenged as I am, I'm still working out the
>     odds of Dhe.  But great idea - it will be just the thing for an
>     NPC to suggest when the Wolblutn is in Jump.
>
>     Cheers
>     tc
>
> For which ever number you pick, that’s a 1:36 chance of winning, a
> 5:36 chance of losing, and a 30:36 chance of maintaining. Over a
> statistically perfect series of 36 rounds, player vs house, with a bet
> of 1 unit, you will lose 5 and gain 9, for a net gain of 4. Once other
> players get involved... on a max of six players vs house,  a player
> gets kicked the first round 35:36 rounds (the only exception is a win
> on round one). The odds of a specific player pulling that off is
> 1:216, and the odds of a specific player getting kicked is 5:216
> (betting on players in a game of chance is a chancy business). The.
> The odds tighten up as players are eliminated - 5 players face a win
> odd of 1:180, 4 players 1:144, 3 players 1:108, and 2 players 1:72. Of
> course, for the overall chances of someone winning a round, that’s the
> same as 1vH - 1:36. If a Dhe round ends only by elimination by win or
> loss, the house pulls a lot of money. 
>
>
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