vplaxlover wrote:
3) If a JoB machine has a progressive with a $4700 reset (for $1
coins), what is the approximate return on the machine? My gut feel
tells me that the machine probably hits on average at about $5500,
which is a 37.5% "bonus" on a $4,000 royal. The royal flush accounts
for about 2% of the return on JoB, so .2 x .375 is .075, turning JoB
into a 99.54 + .075 = 100.29% game (played optimally). Am I
extremely far off?
Dennis confirmed that this is a very decent estimate of game return,
based upon the assumption that the game does hit at an average meter
of $5500 and that game strategy used is one that's optimized for a
$5500 meter at all times (implicit within the winpoker calculation
with the RF set to $5500).
I wanted to set out the calculations one might employ if you wanted to
fine tune that number, simply as a matter of laying out the variables
involved.
I'll note that as a shortcut, the return on a progressive is often
ballparked as the game return at reset plus the meter advance rate.
There are two primary variables in calculating the actual return:
- Average meter when hit
- The ER of your play given that average meter plus an assumption re
the play strategy you employ.
···
------------
You don't cite what you based the $5500 approximation for the average
hit on. Perhaps anecdotal observation. The actual average meter will
be dependent upon how much of each wager is added to the meter (meter
advance rate) and the average number of hands played by all players on
the bank between hits.
I've seen JB banks where the meter advances by as much as 1% (e.g.
$.05 per each $5 played on a $1 bank). However, it's general more
modest than that, and given a starting meter that resets at an
advanced value of 4700 credits I'd look for an even slower meter.
Let's assume 0.5% or $.025/play on the $1 bank.
Once you estimate the number of plays between royals on the bank, it's
a simple matter to determine the total average meter advance expected
when a royal is hit. That number of plays is determined not by your
play strategy, but instead the average play strategy employed by all
players.
If players tend to use a standard 9/6 JB strategy, then that number is
40400. If players averaged out at a strategy that on average
approximated the optimal strategy for the starting meter of $4700,
that number falls to 38100. If players anticipate the hit at a higher
level and play more aggressively for the royal (or, what I expect is
more likely, simply play more aggressively out of a competitive spirit
in desiring to have a greater shot at a hit than others) that number
falls further. At something that would approximate an optimal
strategy for a $5500 meter, the number goes to 34000.
So, using the assumption that general player strategy yields a 34000
hand cycle on the bank, the meter can be expected to advance by $850
on average at each hit. That would be an average hit meter of $5550,
which is in line with your estimate.
------------
Your actual expected return on play will be a function of that average
$5550 hit and the strategy that you personally employ.
That is, of course, player dependent. You might use a standard 9/6
strategy, optimize strategy to the average $5550 hit, adjust strategy
at various breakpoints as the meter climbs, etc.
The ER will reflect the strategy related to the meter that is targeted
on average, with an adjustment to the meter at which the actual hit is
expected.
So, by example, let's assume a fixed progressive strategy that some
players use as a default -- one based upon an assumed JB meter of 4800
(this ties very close to a breakeven game value).
At 4800, the expected game return is 99.95% when the actual hit is for
$4800. The RF will contribute 2.61% to that return. If the actual
payoff is $5550, then the incremental return from the greater meter is
.41% (total RF contrib of 3.02). The adjusted total play ER would be
100.36%.
That is, of course, the same number Dennis arrived at in a
straightforward manner using Winpoker. As I indicate, my intent here
wasn't to confirm anyone's calculation -- but instead to offer a grasp
of the specific variables involved and how one might come to a value
under varying assumptions (for example, an average player bank
strategy of standard 9/6 Jacks). A shorthand method such as Dennis
used is more than adequate for most purposes.
- Harry
