Correct. Except that it was analyzed by the game designer, Walker
Digital Gaming, before it was every sold to IGT. According to Jay
Walker, principle owner of WDG, the computer-and-programming costs to
get the numbers in this game were in the tens of millions of dollars.
That sounds sus to me. Surely you can just brute force hundreds of
players playing a wide variety of strategies for a lot less than that
sort of money.
IGT has very skilled mathematicians with a big budget for computer
software when required. This particular game taxed their resources
considerably.
Well, if that's true, then what I say next hasn't much chance of being
right.
It seems to me that you should *never* "rebuy" (cash out early). I'm
assuming that the game is positive expected value, considering comps,
cash back, and your "entertainment value", so even after a royal
flush, you should play out the remainder of your $20 as the start of
the next royal cycle. So when you cash out, you use it to buy more
plays (look at these as insurance, or better yet at opportunities for
drawing a royal flush.) Rebuys are just too expensive.
The key here is that the number of plays per dollar is fixed. Lets say
that the best you could hope for on a Jacks or better style of game is
400 plays for $20 (quarter game, 5 credits per bet). So that's a cost
of 5 cents per play. If you play regular strategy, the royal cycle
will be about 40,000 plays, for a cost of 40,000/400 * 20 = $2000 to
buy a $1000 jackpot.
The 5c per play cost is regardless of the strategy you use; you can be
as wild as you like with the strategy; there is no extra cost for wild
strategies, as there is for regular play. For example, playing a
"royal or bust" strategy shortens the cycle from say 40,000 to perhaps
half that (I can't find the actual figure quickly, perhaps 28,000 is
more realistic), but at regular games, it costs you an arm and a leg
because you are breaking hands like quad tens to keep one of the tens
(1 to a royal). If you could play a stragegy wild enough to bring the
cycle length down to 20,000 plays per royal, it becomes break even
(neglecting cash back etc).
So I believe the right stragegy is close to that: play *every* play
for the maximum chance of a royal flush. A lot of the time, you will
be throwing away 5 cards, whether they are paying or not. This
guarantees the minimum number of times you pay the $20 tax to keep
playing. Only a royal flush will bring you positive enough to end the
cycle.
I do see one possible exception to this: in the rare cases where you
are up whatever it cost you, you have the opportunity to have a
winning session, which can reduce your overall cost. Suppose you are
up 100 credits and it costs 80 credits for a rebuy; perhaps you should
switch to regular strategy towards the end of a set of 400 hands to
"protect" your profit. This will cut back dramatically on your chances
of a royal for those plays, but with the profit you can buy more wild
strategy opportunities at 5c per play.
Perhaps you really want the optimal strategy to produce a profit of 16
bets (your $20 investment) or more over 400 hands. If you are down 80
bets with 50 plays to go, you need a strategy that maximises the
chances of winning 96 bets profit (your 16 bet investment plus your
accumulated loss of 10 bets) in those 50 plays. That might mean
playing initially for any quads or higher (keep only pairs, trips, or
dealt quads, and perhaps 4SF and 4RF), switching to straight flush or
better in the middle (keep (guessing) 67s over an ace), and finally
playing royal or bust (keep only the ace from an ace-low straight flush).
Then again, keeping the straight flush when your goal is 96 bets will
get you half way to your goal, and you can probably switch to a less
wild strategy to make the the other half. Tricky.
OK, I can begin to see where you might be able to spend $10M on
analysing this. I still think I could do it for a fair bit less, though.
- Mike
···
--- In vpFREE@yahoogroups.com, "Bob Dancer" <bob.dancer@...> wrote: