I posted last year about progressives and I am still having trouble wrapping my head around them. I understand that if a game pays back 99% and the meter rise is 1% and I am the only person who ever plays this game then the overall return of the game is 100%. Where I am getting confused is if I am not the only one to play it and I stop playing it sometimes without the jackpot hitting.
For instance, say the game is 99% base, and I only ever start playing it when the meter is already high enough to make it 100%, then if I am the only one to play it from there on out, the machine is clearly returning 101%. Now, suppose I am not the only one playing it, but others are as well. I may or may not hit it, and at some point, whether or not I hit it or someone else hits it, I will leave. I'm not clear on the EV of such a machine now.
Let's say there's some video poker that has a 99% return, a 1% meter, and a cycle of 10k hands. I only ever sit down at the reset and I play 100 hands. If I play 100 sessions I will expect to hit the jackpot 1 time, and that one session I should expect to get back 0.5% of my total bets (I could hit it at the beginning or the end, but on average in the middle of that 100 hands). So even though I have played a total of 10k hands, the value I get from the game being progressive is not 1% of 10k bets, but 0.5% of 100 bets, which is a far lower EV gain than just being additive.
This scenario can trivially be extended to play 1-hand sessions in which case the EV gain is even less, or it can be extended to where the session is the full cycle. If you also adjust it to say that you hit the jackpot at the end of the cycle then it's clear the EV is additive.
I am thinking the EV of a progressive is only additive if, once you start playing, you only stop once the jackpot is hit -- whether you hit it or someone else hits it. Say you and someone else play on a progressive bank until one of you hits it, then one player gets the entire 1% contribution of both players, but over a bunch of trials you will hit it half the time so you get 1% of both players half the time, which is 1% overall (assuming both players play at the same speed, etc.).
It seems logical to me from the above reasoning that the longer you play on a progressive, the higher the EV, with the maximum occurring when playing a session until it is hit, in which case the EV = (return of the base game) + (return from whatever the meter started at when you sat down) + (return from meter rise), and the EV can never be truly additive if you quit a session and the jackpot was not hit (by you or anyone else).
Additionally, I don't see how extending this out infinitely improves things. One simply cannot keep playing a progressive until it hits, as there must be time for sleep, food, etc. So your best sessions will be the additive EV when it is hit, and your other sessions where it is not hit will be lower than additive.
The only way I can even think that the EV is truly additive is if you play a progressive without regard for the meter. That is to say, you disregard the current meter value (so long as it meets your threshold) and play it whenever you feel like it. Sometimes the meter will be at the base, sometimes other players will have put in enough money for it to be higher. Then, on a 99% machine with a 1% meter rise, the overall EV will be 100% -- sometimes when you start it will be at 99% but sometimes at 103% or 105%. Of course you would like the meter to be higher for any individual session, but prior to all sessions if you have made the play/no play decision based on the meter being above a specific level (say 101%) then you are "locked in" to the long term EV of that specific level plus the meter rise (1%) for your overall EV (101% + 1% = 102%), even if in that one particular session it could be higher than this.
I have no math to back it up, but it seems like this is the only way it makes sense for progressive value to truly be additive.
The reason I'm wondering about all this is that I'm trying to figure out my estimated long term win rate on a progressive. Surely I can play a bunch of sessions and for each individual session I know what the game returns at the moment I sit down -- sometimes it's better than others but because of the above arguments I do not think I can say "OK the machine is returning 102% now, the meter rise is 1%, so I expect to earn 103% for this one hour long session." Perhaps I can actually figure out the EV gain of a progressive where I know I will play a session that is 25% of the cycle long, hit or no hit. This is certainly a useful result.
However if I can actually figure out my estimated long term win rate by using (my minimum meter requirement) + (meter rise) then I can forget about worrying about how much I expect to make for an individual session and simplify it by knowing how much I am making long run and that is also a useful result.
Any thoughts?
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