On Mon, 9 Mar 2020 04:45:19 +1000, Alex Goodwin
<xxxxxx@internode.on.net> wrote:

>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%.

No; the house edge is 10% - the "null" results don't affect play - or the
house take - either way, regardless of whether the rule is "you can
withdraw after a null", "you can't withdraw, but you can change number
after a null", or "you have to let it ride after a null". See, each roll is
independent of history - if you are rolling fair dice, the odds of a
particular double are always and invariably 1/36 - the statistical data
doesn't change the probability for _this_ roll; it only describes the
long-term history, and says that _from this point forward_, you can expect
to see a similar pattern. You can't "bridge" the past and present into the
future; if you could, the dice wouldn't be "fair".

>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.

More like Cr10,000 per Cr100,000. See my separate analysis.

>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.

Mister Dodgie is going to become very wealthy until his players catch on -
his edge isn't a piddling 5.6%; it's a nice, comfortable 20% - one credit
out of every five is going right into his pocket!

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