Well, time for me to learn something again.

Jeff, if J Random makes a bet and that pushes, how does that not
increase the total wagered?

I'm a bit confused because of French roulette with the en prison rule (
https://wizardofodds.com/games/roulette/basics/#toc-FrenchRules ). 
Namely, if you make an even money wager and the spin comes up on zero,
you _don't immediately lose your wager_.  As the name suggests, it's
imprisoned (forced to play on next spin) and if it comes up on the next
spin, your original bet is returned, thus halving the basic house edge
of 2.7% on those bets.

By your logic, neither of those would count.

Alex

On 9/3/20 6:21 am, Jeff Zeitlin wrote:
> 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!
>
> ®Traveller is a registered trademark of
> Far Future Enterprises, 1977-2020. Use of
> the trademark in this notice and in the
> referenced materials is not intended to
> infringe or devalue the trademark.
>
--