On Mon, 9 Mar 2020 12:21:54 +1000, Alex Goodwin
<xxxxxx@multitel.com.au> wrote:

>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.

There is an important difference between French Rules/'en prison' and the
'push' in Dhe: in a "French push", the _payout_ changes - that is, if your
number comes up on the second spin, you only get $1 handed to you for each
$1 you placed on the mat (your original bet only), instead of the usual $2
(representing your original bet plus equal winnings). In Dhe, the payout
doesn't change. If the house plays "pushes ride", and you win on the second
roll, you still get the 9:1 payout.

Think of it this way: In Dhe, the mat is "cleared" after every roll, and
the house throws it all into the pot. If your number didn't come up at all,
you get handed $1 for each $1 that you placed on the mat. That's null to
the house; they neither win nor lose (25 of every 36 bets). If your number
comes up on one die only, the house keeps your bet (a win for them, 10 of
every 36 bets), and if it comes up on both dice, you get handed $10 for
every $1 you put on the mat (your bet, plus the 9:1 payoff - a loss for the
house, 1 of every 36 bets). The various rules regarding how the "null" bets
- the 25-of-36 - are handled really are controls on how the players may bet
for the next roll: if the rule is "pushes ride", you must bet again, same
amount, same number. If the rule is "may change number", you must bet
again, same amount, you choose the number. Finally, if the rule is
"withdraw permitted", you're not under any constraints - you may sit out,
or bet any amount on any number. In any case, those bets neither contribute
to the house's bottom line, nor take from it.

Now, I happen to disagree with that site's analysis of how 'la partage' and
'en prison' affects the house's edge; as I see it, the house edge isn't
affected at all. Suppose that the house played it 'straight' - no 'en
prison', no 'la partage'. You make two consecutive $1 bets on the same
color. The first time, you lose; the house keeps your bet. The second time,
you win. You've put down $2; the house has handed you $2 - except that the
_correct_ payout, for break-even, should be 37:18 (or 38:18 if the wheel
has a double-zero). It's that difference that pays for all the lights. With
the 'en prison' rule, you make a $2 bet on your color, the zero comes up,
so the bet has to ride. The second time, your color comes up, but the house
doesn't pay the usual amount; you only get your bet back. So, you've put
down $2, the house has handed you $2.  Gee, that looks a bit familiar,
doesn't it?  Same edge to the house, yes?

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