Steve Cotten wrote:
Casino West at the Riverside Resort will double the payout on the
first 20 natural club royals beginning April 1st. The only playable
game is NSUD at the dollar level.
The Casino also pays double for natural quad 4s: Four 4s pays $40,
and four 4s with a duece pays $150.
Can anyone help me with the ER and Var of this game?
Tom Robertson replied:
An extremely, if not perfectly, accurate, way to get the ER is to
take the average of all the values of the games, assuming there are
4 different games, one with each suit. 3 of the 4 games would pay -
.27% and the one with clubs would pay 1.74%. The only way this
wouldn't be completely accurate is if there are hands for which
there is some gain by keeping the club royal draw that there
wouldn't be in the games that would be played with the other suits.
Not a bad suggestion, Tom. I took a "Q&D" approach that assumes the
player wants to go at this without changing strategy. Not as
accurate, but it might well be a more realistic assumption.
To get an idea of what might be given up without changing strategy for
the double club royal, I looked at an earlier workup of the 8000rf 9/6
DB game that can be found in AC. In that case, if you play the 4000
cr. rf strategy, you give up .33%.
While not a perfect measure of what you sacrifice if you make no
strategy change here for the clubs, I'm quite satisfied with it.
Allow for the lower RF contribution in a wild card game and that
you're only talking about 1 suit vs. all 4 in the example above, and
I'd say that you're looking at giving up less than .07%. Running a
handful of test hands through Winpoker or Frugal hand analysis and you
should be able to get a grip on the strategy changes that would recoup
most of that .07%.
So, using the Deuces Deluxe game template in WinPoker (which
accomodates natural quads), and simply doing a pro rata allocation of
the RF, 5K, and 4K hand occurance to split out 1/4 of the RF hands as
clubs and 1/12 of the quads as naturals (I roughed the 5K with natural
quads as 1/12 * 1/12 of the natural quads), I arrive at an ER of
100.25% and variance of 36.8.
Because of the infrequent occurance of natural quad 4's and the fairly
low bonus relative to that infrequency, the quad bonuses only add
about .07% to the ER. You're getting .46% out of the RF bonus. As
noted, there's up to an additional .07% to be picked up through some
decent strategy changes -- likely involving things like dropping a
deuce when you have 3 club RF cards. (To be honest, I'd expect it's
closer to .04% -- in DBDJ, one of the most frequent strategy change
involves breaking a high pair for any 3 RF ... I wouldn't think there
would be any change nearly as frequent in this NSUD game.)
- Harry