I posted a simple explanation of the M progressive on videopoker.com and a poster there did all the math work and exceeded my level of accuracy, topping me hands down. Nothing pleases me more than when people take the ball and run with it.
Here's the repost from the thread on the other forum. It is relevant to the new M progressive.
FK:
I calculate the average high Royal to be around $10,600. And by that time that hits at around $11,400 the next one in cue will be $10,600. $12,000+ will be common, but not all the time.
Reply by new2vp:
Well, good. Our calculations are close then. I found the equilibrium point for the highest royal hitting at 10,653.13 coins. My simplifying assumptions were (1) that the overall average cycle time to build each jackpot would be equal to the sum of the average cycle times of each game, (2) every play would be on the game with the highest royal flush at the time, (3) every play would use computer perfect strategy AS IF the jackpot was ALWAYS at the average value.
I know that there will be deviations from my assumptions. For example, the game with the highest royal is not always the best play. The computer perfect strategy will change during the quest to take down each royal, the "average" strategy may not be the average of the actual strategies, and people will not always choose the best game when they wager their coins. The assumptions were set up so that I could find a solution using relatively easy math with the hope that the assumptions were robust enough so that the actual expected results would not vary too much from those derived from the assumptions.
And we can be confident that the AVERAGE actual jackpot hit must be related to the AVERAGE actual number of plays per royal because the average meter rise to be added to the reset comes directly from the AVERAGE actual number of plays per royal or average experienced cycle time, if I can call it that.
If I used the 10,653 figure for each of the 8 games as the average size of a royal, I was able to balance out the meter rise as equal to 1/2% x 5 coins x [Cycle time for Game 1 + Cycle time for Game 2 + Cycle time for Game 3 + ... + Cycle time for Game 8]. Each game is played only part of the time, but is accumulating a rising jackpot on each play including that of the other games. The cycle times are (for each game at 10,653 coins):
16-13 Deuces Wild 37257.06
15-7 Kings or Better Joker Wild 37696.14
6-5 Bonus Poker 31871.05
8-5 Double Double Bonus Poker 31630.92
9-6-4 Double Bonus 31734.78
6-5 Super Double Bonus 32059.91
7-5 Jacks or Better 31902.52
7-5 Bonus Poker Deluxe 31972.98
Total 266125.37
with the last figure off in the 2nd decimal place due to rounding error in the individual entries.
266125.37 plays x 0.5% x 5 coins per play = 6653.13 coins added on to the reset value of 4000 coins yields 10653.13 which balances to the average jackpot size in each calculation.
I can follow that your value would change during play if you started at 10,600 to 11,400 if you assumed 32,000 plays (32,000 x 0.5% x 5 = 800 coin difference) for each take down WHILE COINS ARE WAGERED ON THAT GAME. That would mean that you had an average of 6600 meter rise (from 4000 to 10600) accumulated WHILE COINS WERE WAGERED OTHER GAMES. This, in turn, would imply that you had an average of 264,000 plays (6600 divided by 5 coins divided by 0.5%) while playing the other 7 games. But that would mean that you averaged 37,714 plays for the OTHER games, but only 32,000 on EACH GAME that you were playing. I think that may be a bit of an inconsistency in the calculation somewhere that is too big to be explained by rounding. Your figures would be more consistent and work better if 10,600 is closer to the (rounded) average number at which the royal hits, instead of the average number at which play begins on a particular game. It seems to me at least that the meter rise during play of OTHER GAMES should on average be 7 times the meter rise during play of THE CURRENT GAME before it hits.
Nevertheless, I think this multi-game progressive concept will be very entertaining and I hope that M doesn't decide to pull the games too quickly. This looks to me like quite an accomplishment on your part.
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