Stations Casinos have a popular promotion which awards players
$50 in free slot play if the Jumbo Jackpot hits during their play
session. The jackpot starts at 100,000 and is guaranteed to hit by
150,000.
This analysis will focus on the RTP for free slot play first
then combine the jackpot award into the RTP. If we assume the jackpot
has an equal chance to hit during any time of the day (which may not
be the case) then the win frequency for the free slot play is
proportional to the number of hours played during the month times the
number of jackpot hits per month.
The number of hours in a month assuming 30 days per month is 720
so we have the following:
HF(FS) = (x * N) / 720,
where x = number of hours played per month,
N = number of jackpots hit per month.
Our monthly EV in dollars can be then be calculated:
EV(FS) = (50 * x * N)/ 720 = 0.0694 * x * N.
Similarly for the Jumbo Jackpot assuming each active player has the
same chance to win the prize (which might not be the case) the EV is:
EV(JB) = ((125,000 * x * N) / 720 )* (1/p),
where p = number of players active when the jackpot hits.
= (173.61 * x * N) / p.
Out total expectation for this promotion is therefore:
EV = EV(FS) + EV(JB) = x* N * (0.0694 + 173.61/p).
Now our RTP can be calculated:
RTP% = (EV / CI) * 100,
where CI = Coin in per month.
CI = x * R,
where x = number of hours played per month.
R = Coin in per hour.
RTP % = (N * (6.94 + 17361/p))/R,
where N = number of jackpots hit per month.
R = Coin in per hour.
p = number players active when jackpot hits.
With this formula we can now calculate how much this promotion
adds to our RTP. Let's say the jackpot hits on average 4 times per
month and when it hits on average 10,000 players are active and
assume a video poker player is playing 700 hands per hour single line
game with 5 coin max bet then the table below shows the added value
this promotion has for different denominations.
denom wager rtp (free slot play) rtp (Jumbo) rtp (total)
1¢ 35 0.7931 0.1984 0.9916
5¢ 175 0.1586 0.0397 0.1983
25¢ 875 0.0317 0.0079 0.0397
50¢ 1750 0.0159 0.0040 0.0198
$1 3500 0.0079 0.0020 0.0099
We see that this promotion adds more to the overall return
percentage the less you bet per hour. I would guess that a good
proportion of slot and video poker players at Station properties fall
within the $175-$875 coin in per hour range. For these players
(using the parameter values from above) this promotion is essentially
a cash back program which yields ~0.2% - 0.04% respectively.
Unfortunately for higher level players the promotion doesn't offer
much.