Originally Posted by random_person
Am I correct in thinking that the math for the strategy for this machine is the same as the strategy for the average jackpot?
Yes, for strategy purposes, I would assume this is the best course of action. If this is not technically optimal, I am almost certain it is the best practical approximation we can make. Optimal strategy may not be tied to the average jackpot if strategy errors are significantly more severe in one particular direction.
We can briefly explore this idea through example. Let's say there are two jackpots, one at 1500 credits and one at 1580.4 credits. So the average jackpot is 1540.2 credits. We are dealt A
. At 1540.2 credits we are indifferent to either holding AA or AKT suited. At 1500, holding AA is superior by 0.03719 credits, while at 1580.4 credits, holding AKT suited is superior by 0.03719 credits. So, yep, using the strategy for the average jackpot is definitely best.
Like you say, when the average jackpot is above $1944 (1555 credits), then the machine becomes +EV. And then to answer your other question what is the expected +EV value if you only play the machine when the average jackpot is $1944 or higher? Well, the easiest way to estimate this is to determine the average number of hands it will take you to hit a royal. Unfortunately oyal probabilities change as the oyal payouts increase.
But studying various game states, the probability of hitting a royal in any given hand is roughly 1 in 32,300 when the machine is between 100% and 101% return. So we would see about 3230 deals on average before getting a royal. And would gain 3c x 3290 = $96.90 from the royal payout that you end up hitting on average while chasing it. So this adds $96.90/$1.25/32,300 ~ 0.24% return on average. Now in this scenario, the machine may still be +EV even after you hit a royal if that royal's jackpot that was hit was lower than average. But I'm just indicating what the average return would be if you just chased until you hit any royal.
Generally speaking, going back to your OP, if this machine consistently adds 3 cents per hand played to the progressive royal bank, this machine basically depends on player error to turn a profit.