69 video poker math question

The payout on a typical 6 9 video poker is let's say .995 if playing a pretty sound game according to max strategy. But that payout includes the probability of getting a royal flush betting max chips. Since this happens so rarely, I was wondering what would be the payout assuming there were no royal flush- both at the single coin bet and for the max coin bet. Thanks!

A royal at max bet is worth 800 credits and it happens about every 40,000 hands. So, you would lose 800/40,000 if you never hit a royal, or about 2%. This would be the same payout at minimum bet if you are assuming that you won't hit a royal. The return would be approximately 0.975 .

Since the payout on 1 coin is 250 and max coin is 4000, by this logic then the correct number for 1 coin should be 1 minus 250/40000 or .625 and for max coin 1 minus 4000/40000. That would imply odds of .995-.00625 or .98875 for single coin and .995- .1 or .895 for max coin. Now I am really confused.

The return percentage is listed per coin wagered, so the max coin royal win is 4000/5 coins = 800 credits. This is why I subtracted 800/40000 and not 4000/40000.

For one coin, you are correct that you subtract 0.625% from the minimum return. But, the minimum return is not 0.995, it is already less because of the lower paying royal flush. The return for 9/6 jacks at minimum bet is 98.3735%. If you subtract the 0.625% for the royals, you get 97.7485%.

For max bet, the return is 99.544%. If you subtract 2%, you get 97.544%.

So, for min you get 97.75 and for max, you get 97.54 if you assume that you will never hit a royal. I simply said they were about the same because in both cases, you are assuming that you will get no royal pays.

Got it thanks!