Best guess

[pokeherguy]

Lets see who can come the closest to guessing the outcome to the following video poker scenario.
The game $2 Double Double Bonus at max play ($10 hand) with a payback percentage of 98.8%, near perfect play, 150,000 hands played. Whats your best guess as to how many royals and and misc. quads hit?
 
Royals=
Aces w/kicker=
Aces and 2,3,4 w/kicker=
2,3,4=
straight flush=
misc. quads=

[TEXACO]

ROYAL FLUSH APPROX. 3.67 TIMES
ACES WTH KICKER APPROX. 10 TIMES
 
2,3,4 WITH KICKER APPROX. 22 TIMES
 
ACES NO KICKER APPROX. 26 TIMES
 
2,3,4 NO KICKER APPROX. 58 TIMES
 
STRAIGHT FLUSH APPROX. 17 TIMES
 
QUADS 5 - KINGS APPROX 245 TIMES
 
ALL BASED ON 150,000 HANDS WITH NEAR PERFECT PLAY, AS STATED IN MOST DISCLAIMERS, "YOUR RESULT'S MAY VARY".

[cddenver]

Lets see who can come the closest to guessing the outcome to the following video poker scenario.
The game $2 Double Double Bonus at max play ($10 hand) with a payback percentage of 98.8%, near perfect play, 150,000 hands played. Whats your best guess as to how many royals and and misc. quads hit?

 
Roughly:
 
Royals=4
Aces w/kicker=9
Aces w/o kicker and 2,3,4 w/kicker=49
2's-4's w/o kicker=58
Straight Flush=17
Misc. Quads (5's-K's)= 243

[Eduardo]

Royals= 0 to 12
Aces w/kicker= 2 to 14
Aces and 2,3,4 w/kicker= 20 to 70
2,3,4= 20 to 100
straight flush= 2 to 20 (I think people screw these holds up a lot)
misc. quads= 200 to 400

[New2vp]

The DDB games at 98.8% that I'm aware of are the ones that pay only 1600 for quad aces with kicker, either 8-6-5 or 8-7-4 for full house-flush-straight (as opposed to the 98.98% game, common in some places, that pays 2000-9-6-4).Selecting the first machine (1600-8-6-5), I'll put in ranges that should be at least 95% accurate in containing your actual results on a line by line basis (presuming that you did not select this question simply because you thought your results were unusual).Royals=  0 to 8
Aces w/kicker= 4 to 15
Aces w/o kicker and 2,3,4 w/kicker= 34 to 61
2's-4's w/o kicker= 43 to 73
Straight Flush= 9 to 25
Misc. Quads (5's-K's)= 213 to 274Surprisingly (to some), even with such wide ranges, around 19% of typical results will miss at least one of the ranges above.  That is why this is a popular game; typical results can vary enough to allow you to win money with moderately better than average luck.  Of course, with bad luck, this game can kill you.The actual game will matter in selecting these ranges if I presumed the wrong pay schedule.  For example, you can expect 15% fewer royals with the 8-7-4 schedule because you would try for flushes with 3-royal draws much more often.(Edited:  ***Eduardo, sorry about posting ranges apparently right after you.  As you might be able to tell, your post had not been made while I was preparing mine.***)

[Eduardo]

 Glad I posted mine first then. The point of course is that it can be fun to guess, but to expect any exact number or close to an exact number would be irresponsible mathematically since that isn't how probabilities work. There will always be a range of outcomes and you might be on the better or worse side of that range.
 
It's mathematically possible that you would hit zero quads in 150K hands, but very very very unlikely (so unlikely that suspicion would be in order). Of course, we all have our own acceptable range before we would be suspicious of things... some such ranges being more educated than others.
 
Someone just posted about a hot streak at the M that was way better than average. I'll bet they aren't suspicious of the machines there.
 
But 150K hands is a good amount. I would expect most of the numbers to fall within a reasonable range. Of course, I also don't know what "near" perfect strategy is or what results are being impacted by the incorrect holds. Like I said, I think a lot of people goof on straight flush holds so that number is maybe the most likely to be low, other than royals and kickers which could also be very low since they are relatively infrequent.
 
When we're looking at a valid sample statistically, 150K sounds like a lot, but an expected 3.67 royals is not a lot. Play enough hands where the expected royals would be 150K and then you will be within a fairly tight percentage across the board I would imagine. There is still a lot of volatility in 150K hands in DDB.
 
So, even though I posted a range to be a smart-tush, it's still just a guess and i could be way off.

[New2vp]

In competing with Texaco's and cddenver's guesses, I will enter the following point estimates, with the winner being decided on the basis of who is closest in the most categories.Royals= 3
Aces w/kicker= 8
Aces w/o kicker and 2,3,4 w/kicker= 47
2's-4's w/o kicker= 57
Straight Flush= 16
Misc. Quads (5's-K's)= 242Of course, I reserve the right to change my guesses if either cd's or Texaco's change or if we have new entries.

[cddenver]

In competing with Texaco's and cddenver's guesses, I will enter the following point estimates, with the winner being decided on the basis of who is closest in the most categories.

 
I withdraw from the contest.    Both you and Eduardo quite correctly pointed out that over a limited number of hands it's better to look at ranges than specific values, especially when it comes to hands that occur less frequently, like RF's.   Much better answers than mine.
 
It didn't surprise me to see your initial range post, but I was  to see Eduardo's.  Eduardo, did you take a smart pill today? 
 
We'll see what PG says about these posts when he checks back in.

[New2vp]

 Glad I posted mine first then. The point of course is that it can be fun to guess, but to expect any exact number or close to an exact number would be irresponsible mathematically since that isn't how probabilities work. There will always be a range of outcomes and you might be on the better or worse side of that range. "Irresponsible mathematically" may be a tad harsh in describing this.  Do you refuse to enter March Madness brackets if the tiebreaker is the total number of points scored in the championship game?  That number is a bit harder to estimate than some of these vp results when you don't even know who is going to be in the game.  But, you're right, in that the odds of getting this exactly correct are low, but someone has to be closest (unless there is a tie).The odds of getting these numbers exactly right might be about the same as winning some state lotteries.It's mathematically possible that you would hit zero quads in 150K
hands, but very very very unlikely (so unlikely that suspicion would be
in order). Of course, we all have our own acceptable range before we
would be suspicious of things... some such ranges being more educated
than others.
The odds of this happening are about 1 in 10 vigintillion.  If you have never heard of "vigintillion,"  don't worry.  It's safe to say that events with such remote probabilities, although still positive, essentially never happen...at least not in our lifetimes (or even most estimates of the lifetime of our planet).If you played this game and had 0 quads after 150000 hands, either the machine is biased or you're making the wrong holds with 100% certainty.  That is unless you see a difference between 100% and 99.9999999999999999999999999999999999999999999999999999999999999%.
When we're looking at a valid sample statistically, 150K
sounds like a lot, but an expected 3.67 royals is not a lot. Play
enough hands where the expected royals would be 150K and then you will
be within a fairly tight percentage across the board I would imagine.
There is still a lot of volatility in 150K hands in DDB.

 Play
enough hands where the expected royals would be 150K and then you will...be very old.  It would take 25 people playing 800 hands per hour, 12 hours per day, every day for 70 years to play enough hands.So, even though I posted a range to be a smart-tush, it's still just a guess and i could be way off.

I like it.  "Tush" doesn't get you flagged by politically-correct software.  Hope you don't mind if I use that jargon since many of my posts, especially this one, are entirely aimed at removing any doubt whether or not I suffer from chronic smart-tu****is.(Edit:  DARN!!!! The software still got me!   I tried to add the suffix "-itis" to smart-tush and the software knocked out part of my word!!!)

[New2vp]

 
I withdraw from the contest.  
We'll see what PG says about these posts when he checks back in.You shouldn't withdraw.  My numbers just will hurt you in a fair contest.  You should simply cheat.  Bribe PG 1/2 the prize fund to post numbers which just happen to be exactly equal to your guesses and you will win!Of course, Eduardo and I might be somewhat suspicious of such results.