The approach to this problem that I would suggest is to start by calculating the proportion of events of each type (label them 1 through 4).

Then analyse the distribution of winnings for each event type (probably

using an contingency tree to keep track of the results). (I assume that

there are no additional stakes involved for the staged jackpot phase).

As the type of an event is independent of that of the proceeding event

we need only calculate the probability of each event type for a single

sequence of wagers ending at an event.

The probability that the event occurs on the -th wager is the probability

that it has not occured on any of the preceeding wagers times the

probability that it occurs on this one:

So the probability of a type 1 event:

,

which is a geometric series and so:

,

Similar arguments show that:

From these and the results of the analysis of the return when an event of each type occurs

we can calculate the mean return in a long run (say N) of wagers, as there are N/500 events

and we know the amount wagered ($3N).

It would also be wise to support this type of analysis with a simulation to make sure that

no hidden invalid assumption/s have creapt in

RonL