Question for VP Expert !

[DOUBLE B]

I asked the following question on another web site without much luck in getting a response. I probably should have posted question here to begin with. We have two VP machines side by side. One is 10/7 DB and one is 9/6 Jacks Better. Both are quarter ($.25) machines. Both players will play max coins in and have perfect play. After 1 million hands have been played on each machine.........do the odds say that both machines should have the same (or very close to it) number of Royal Flushes. Or, is there a reason that one machine should have more have more RF than the other because of the difference in games (10/7 vs 9/6)?

[Eduardo]

Odds of a royal flush are about 1 in 40,000. So expect around 25 royals on either game in that time. But a million hands is still a pretty small sample for such a rare event.
 
I'm only guessing here but the likely range could probably be anywhere between 18 and 32 or so for either machine. I doubt strategy changes between DB and JOB are different enough to impact the number of expected royals very significantly over a million hands.
 
So if you are only counting royals, expectations could be about the same on both of these machines for a million hands or so, would be my guess.

[Eduardo]

Also, it wouldn't make any difference if you played two machines side by side, or played a million hands of JOB on one machine then switched it over to DB and played another million on the same machine in the other game type.

[DOUBLE B]

Thanks Eduardo----Right or wrong thats the info I was looking for! Thanks Again!

[Eduardo]

Let's hope for "right" then.
 
There are people much more "expert" than me here. Wait for one of them to chime in before doing anything rash like playing a million hands on two machines.

[faygo]

Winpoker: 10/7 DB, RF occurs once in 48048.04 hands.  Flush is 10.47% of the return.
9/6 JOB, RF occurs once in 40390.55 hands. Flush is 6.61% of return.
 
It stands to reason that the Royal  in 10/7 DB  would occur less often due to the increased value of the Flush to the overall return , which in turn changes a number of holds.

[Eduardo]

Yikes. That big a difference? Wow.

[DOUBLE B]

Ah Shucks ! I was going to play a million or so hands this afternoon and hit the RF somewhere between 18 and 32 times! Now you tell me to wait! Now--to get serious! The only thing that I question is the 40,000 plus/minus hands for a RF the same for 10/7 and 9/6 and any other VP game??? It just seems to me that if 40,000 was for 10/7 then 9/6 should take more hands on the average to hit the RF since payback is less than %100. Since the pay back for 10/7 DB is over 100% for perfect play then 9/6 should take (on the average) more than 40,000 hands to hit the RF. In my simple way of thinking I wonder if 40,000 (approx) is the magic number for all VP RF's...regardless of the game. i.e. 10/7, 9/6, etc. I hope to heck I am writing clearly what I am thinking/asking!

[New2vp]

Yes, Faygo's right of course.  But there is some truth to what Eduardo said as well in that the results from the two games might be about the same.  You would expect 24.76 royals with Jacks or Better and 20.81 royals with 10/7 Double Bonus in a mathematical sense, so one could expect about 4 more royals in a million hands playing Jacks or Better if you used a strategy that tried to maximize the expected value of each hand.But it is far from a sure thing.  If you run such an experiment, expected value will take you only so far in getting an answer.  There is only a 69.5% chance that Jacks will beat DB.  Certainly this is the most likely outcome but there is still a substantial 25.5% chance that DB will yield more royals and a 5.0% chance that you will end with the same number of royals.

[New2vp]

Ah Shucks ! I was going to play a million or so hands this afternoon and hit the RF somewhere between 18 and 32 times! Now you tell me to wait! Now--to get serious! The only thing that I question is the 40,000 plus/minus hands for a RF the same for 10/7 and 9/6 and any other VP game??? It just seems to me that if 40,000 was for 10/7 then 9/6 should take more hands on the average to hit the RF since payback is less than %100. Since the pay back for 10/7 DB is over 100% for perfect play then 9/6 should take (on the average) more than 40,000 hands to hit the RF. In my simple way of thinking I wonder if 40,000 (approx) is the magic number for all VP RF's...regardless of the game. i.e. 10/7, 9/6, etc. I hope to heck I am writing clearly what I am thinking/asking!It's the relative ratios between the payouts for royals and the other lines that determine how many royals a strategy will yield, not the percent returns for the various games.If you compared a regular 9/6 Jacks game with a 4000 royal to a 6/5 Jacks game with an 8000 royal, the latter game would produce about 24% more royals but only yield 97.30% vs. 99.54%.