VP JoB multi-line simulator

[Zoozie]

The content of this post has probably little interest for the mainstream gambler, so be warned, but I think it is theoretically interesting.

I was interested in watching the variance(up/down-swings) when playing multi-line VP. Knowing the EV and variance did not really tell me what could happen. So basically I wanted to see what happened if you try to wager 10000$ at bet 2.5$ on 50-lines instead of wagering 10000$ at bet 0.5$ on 10-lines. (Some MG casinos now have coin size 0.01$ on 10-hand also). Running this simulation several times in a row gave me a good picture of what to expect. I recorded the minimum bankroll, maximum bankroll and the final bankroll of course. The minimum bankroll was also important because of the possibility of going bust before finishing. You can now play 1000-lines multihand poker or even higher if you like (for playmoney...).

I made a JoB program playing optimal strategy (full pay table) for this and then running the tests. It is capable of 5000 hand-keeping decisions every second. It is fast because the optimal strategy is hard-coded (the 39 steps algorithm from WizardOfOdds) instead of calculating it in real time.

The program is included as attachment in this post. Just unzip all files (it will create a new folder) and press the .bat file to start it. It is pure java, no adware or anything. You can edit this .bat file (use notepad etc.) and change the parameters and run the simulation again. Futher more is a little bonus program that decide what cards to hold that you can use from a dos-promt. The program is in java, so it can also be used from Mac/Linux. There is NO GUI, just a promt interface. It added the install path to system-path so I always have this program available in my dos-promt.

Here is an example of a single simulation (10000 games, 10 lines, logging data every 1000 games). If bet-size is 0.5$ then this would be equal to 5000$ wagering. The bankroll is coin units, but it is also given in bet-units, which in this case would be 0.5$.


C:\JoBSimulator>java poker.JoBSimulator 10000 10 1000
Starting Jack or Better Video poker simulator. #games=10000,#number of lines=10,#loginterval=1000
---------------------------------------------------------------------------------------
Iterations:1, running for 0.0 seconds
Start hand:[A(s), 2(c), 7(d), J(h), 9(h)], Held[A(s), J(h)]
Hand 1:[A(s), T(c), 4(c), J(h), Q(d)] win=0
Hand 2:[8(d), A(s), 8(c), 4(c), J(h)] win=0
Hand 3:[A(s), T(s), 7(s), 2(h), J(h)] win=0
Hand 4:[A(s), 6(c), 2(s), J(h), 3(s)] win=0
Hand 5:[Q(h), A(s), A(c), 7(h), J(h)] win=1
Hand 6:[A(s), 6(c), 7(s), 2(h), J(h)] win=0
Hand 7:[A(s), 3(d), 6(d), 2(s), J(h)] win=0
Hand 8:[A(s), 2(d), 9(s), 8(s), J(h)] win=0
Hand 9:[A(s), 6(d), 5(d), 6(h), J(h)] win=0
Hand 10:[Q(h), A(s), A(c), 3(d), J(h)] win=1
Added wins for hand=2
Current bankroll:-8 (~ 0 units) after 1 games
Maximum bankroll:0 (~ 0 units) after 0 games
Minimum bankroll:-8 (~ 0 units) after 1 games
Maximum win :2 (~ 0 units)
Payout=0.2

---------------------------------------------------------------------------------------
Iterations:1000, running for 1.5 seconds
Start hand:[Q(s), K(h), 2(c), 3(h), A(h)], Held[K(h), A(h)]
Hand 1:[J(s), K(h), 9(s), K(s), A(h)] win=1
Hand 2:[4(h), K(h), T(h), 5(s), A(h)] win=0
Hand 3:[J(s), K(h), 9(c), 6(h), A(h)] win=0
Hand 4:[9(d), K(h), A(c), 8(s), A(h)] win=1
Hand 5:[K(h), A(c), 3(d), 7(h), A(h)] win=1
Hand 6:[K(h), 8(h), 7(h), 5(h), A(h)] win=6
Hand 7:[K(h), 3(d), Q(c), A(h), J(d)] win=0
Hand 8:[K(h), 6(d), 6(h), 2(s), A(h)] win=0
Hand 9:[K(h), 3(d), 7(d), 4(c), A(h)] win=0
Hand 10:[Q(h), K(d), K(h), 9(s), A(h)] win=1
Added wins for hand=10
Current bankroll:-102 (~ -10 units) after 1000 games
Maximum bankroll:400 (~ 40 units) after 246 games
Minimum bankroll:-118 (~ -11 units) after 993 games
Maximum win :250 (~ 25 units)
Payout=0.9898

---------------------------------------------------------------------------------------
Iterations:2000, running for 2.9 seconds
Start hand:[8(d), 3(d), 5(s), 5(h), 3(s)], Held[3(d), 5(s), 5(h), 3(s)]
Hand 1:[3(d), 4(s), 5(s), 5(h), 3(s)] win=2
Hand 2:[3(d), 5(s), 5(h), 2(h), 3(s)] win=2
Hand 3:[Q(s), 3(d), 5(s), 5(h), 3(s)] win=2
Hand 4:[3(d), 6(c), 5(s), 5(h), 3(s)] win=2
Hand 5:[K(d), 3(d), 5(s), 5(h), 3(s)] win=2
Hand 6:[3(d), 9(c), 5(s), 5(h), 3(s)] win=2
Hand 7:[3(d), 5(s), 5(h), 9(h), 3(s)] win=2
Hand 8:[7(c), 3(d), 5(s), 5(h), 3(s)] win=2
Hand 9:[3(d), 5(s), 5(h), 3(s), J(d)] win=2
Hand 10:[3(d), 5(s), 5(h), 2(s), 3(s)] win=2
Added wins for hand=20
Current bankroll:-135 (~ -13 units) after 2000 games
Maximum bankroll:400 (~ 40 units) after 246 games
Minimum bankroll:-165 (~ -16 units) after 1983 games
Maximum win :250 (~ 25 units)
Payout=0.99325

---------------------------------------------------------------------------------------
Iterations:3000, running for 4.2 seconds
Start hand:[A(s), 7(c), Q(c), 6(d), 2(h)], Held[A(s), Q(c)]
Hand 1:[A(s), Q(c), 5(d), 7(s), 3(s)] win=0
Hand 2:[A(s), 4(h), Q(c), A(h), 3(s)] win=1
Hand 3:[A(s), 3(d), Q(c), 7(s), 3(s)] win=0
Hand 4:[A(s), 4(h), 8(h), Q(c), 4(d)] win=0
Hand 5:[A(s), 5(c), Q(c), 4(d), 5(d)] win=0
Hand 6:[A(s), 5(c), K(c), Q(c), 5(d)] win=0
Hand 7:[A(s), T(c), T(d), Q(c), 6(h)] win=0
Hand 8:[6(s), A(s), 4(s), Q(c), 2(s)] win=0
Hand 9:[Q(s), A(s), Q(c), 5(d), 5(h)] win=2
Hand 10:[9(d), A(s), Q(c), 5(h), 9(h)] win=0
Added wins for hand=3
Current bankroll:-36 (~ -3 units) after 3000 games
Maximum bankroll:400 (~ 40 units) after 246 games
Minimum bankroll:-458 (~ -45 units) after 2155 games
Maximum win :250 (~ 25 units)
Payout=0.9988

---------------------------------------------------------------------------------------
Iterations:4000, running for 5.6 seconds
Start hand:[3(d), 6(c), K(c), 8(s), 6(h)], Held[6(c), 6(h)]
Hand 1:[6(c), 9(c), 4(d), 6(h), 9(h)] win=2
Hand 2:[8(d), 7(c), 6(c), T(d), 6(h)] win=0
Hand 3:[2(d), 6(c), 4(c), 2(s), 6(h)] win=2
Hand 4:[8(d), 6(c), 6(h), 3(s), J(d)] win=0
Hand 5:[6(c), A(d), T(h), K(s), 6(h)] win=0
Hand 6:[6(s), J(s), 6(c), 6(h), J(d)] win=9
Hand 7:[6(c), 3(h), 9(s), 6(h), J(d)] win=0
Hand 8:[A(c), 6(c), 6(d), 6(h), J(d)] win=3
Hand 9:[J(s), 6(c), 2(c), 5(d), 6(h)] win=0
Hand 10:[2(d), 5(c), 6(c), 7(s), 6(h)] win=0
Added wins for hand=16
Current bankroll:-324 (~ -32 units) after 4000 games
Maximum bankroll:400 (~ 40 units) after 246 games
Minimum bankroll:-458 (~ -45 units) after 2155 games
Maximum win :250 (~ 25 units)
Payout=0.9919

---------------------------------------------------------------------------------------
Iterations:5000, running for 7.0 seconds
Start hand:[A(d), 9(s), 5(d), K(s), 6(h)], Held[A(d), K(s)]
Hand 1:[Q(s), 5(c), A(d), 4(d), K(s)] win=0
Hand 2:[6(s), A(d), 8(s), K(s), A(h)] win=1
Hand 3:[8(d), 8(h), 7(h), A(d), K(s)] win=0
Hand 4:[8(h), A(d), 5(s), K(s), 4(c)] win=0
Hand 5:[6(s), T(h), A(d), 2(c), K(s)] win=0
Hand 6:[8(d), K(c), A(d), 3(h), K(s)] win=1
Hand 7:[A(s), T(c), A(c), A(d), K(s)] win=3
Hand 8:[5(c), A(d), 7(s), K(s), J(h)] win=0
Hand 9:[T(s), A(d), 3(c), 7(s), K(s)] win=0
Hand 10:[Q(h), 8(h), A(d), 3(h), K(s)] win=0
Added wins for hand=5
Current bankroll:-556 (~ -55 units) after 5000 games
Maximum bankroll:400 (~ 40 units) after 246 games
Minimum bankroll:-666 (~ -66 units) after 4888 games
Maximum win :250 (~ 25 units)
Payout=0.98888

---------------------------------------------------------------------------------------
Iterations:6000, running for 8.6 seconds
Start hand:[Q(h), T(s), Q(c), 4(c), 3(s)], Held[Q(h), Q(c)]
Hand 1:[Q(h), 4(h), 8(h), T(h), Q(c)] win=1
Hand 2:[Q(h), Q(c), 3(h), 8(s), 6(h)] win=1
Hand 3:[Q(h), 4(h), 3(d), Q(c), 5(h)] win=1
Hand 4:[Q(h), A(c), 7(h), 9(c), Q(c)] win=1
Hand 5:[6(s), Q(h), A(d), 9(c), Q(c)] win=1
Hand 6:[Q(h), K(c), Q(c), 7(s), 2(s)] win=1
Hand 7:[J(s), Q(h), Q(c), 5(d), 8(s)] win=1
Hand 8:[Q(s), 8(d), Q(h), 4(s), Q(c)] win=3
Hand 9:[Q(h), T(c), 7(h), Q(c), 9(h)] win=1
Hand 10:[Q(h), Q(c), 4(d), 7(s), 7(d)] win=2
Added wins for hand=13
Current bankroll:-741 (~ -74 units) after 6000 games
Maximum bankroll:400 (~ 40 units) after 246 games
Minimum bankroll:-994 (~ -99 units) after 5855 games
Maximum win :250 (~ 25 units)
Payout=0.98765

---------------------------------------------------------------------------------------
Iterations:7000, running for 10.0 seconds
Start hand:[Q(s), 4(h), 2(d), A(d), 3(h)], Held[Q(s), A(d)]
Hand 1:[Q(s), 4(s), A(d), J(c), 2(s)] win=0
Hand 2:[Q(s), A(s), T(h), A(d), 2(h)] win=1
Hand 3:[9(d), Q(s), T(c), A(d), 7(d)] win=0
Hand 4:[6(s), Q(s), K(h), A(d), 7(d)] win=0
Hand 5:[Q(s), J(s), 7(c), 8(c), A(d)] win=0
Hand 6:[6(s), Q(s), 4(s), A(d), 6(h)] win=0
Hand 7:[Q(s), 3(d), 9(c), A(d), 3(s)] win=0
Hand 8:[Q(s), T(s), A(d), 2(c), 7(d)] win=0
Hand 9:[Q(s), A(d), 5(s), 3(c), 2(h)] win=0
Hand 10:[Q(s), A(d), 4(d), 7(s), 3(s)] win=0
Added wins for hand=1
Current bankroll:-620 (~ -62 units) after 7000 games
Maximum bankroll:400 (~ 40 units) after 246 games
Minimum bankroll:-994 (~ -99 units) after 5855 games
Maximum win :804 (~ 80 units)
Payout=0.9911428571428571

---------------------------------------------------------------------------------------
Iterations:8000, running for 11.4 seconds
Start hand:[K(h), A(c), 7(h), T(h), J(d)], Held[K(h), A(c), T(h), J(d)]
Hand 1:[K(h), 5(c), A(c), T(h), J(d)] win=0
Hand 2:[K(h), A(c), T(h), 3(s), J(d)] win=0
Hand 3:[K(h), A(c), T(h), 2(h), J(d)] win=0
Hand 4:[J(s), K(h), A(c), T(h), J(d)] win=1
Hand 5:[K(h), A(c), T(h), 3(c), J(d)] win=0
Hand 6:[K(h), A(c), K(c), T(h), J(d)] win=1
Hand 7:[K(h), 8(c), A(c), T(h), J(d)] win=0
Hand 8:[K(h), A(c), T(h), 6(h), J(d)] win=0
Hand 9:[K(h), A(c), T(h), 8(s), J(d)] win=0
Hand 10:[K(h), A(c), T(h), A(h), J(d)] win=1
Added wins for hand=3
Current bankroll:-1118 (~ -111 units) after 8000 games
Maximum bankroll:400 (~ 40 units) after 246 games
Minimum bankroll:-1313 (~ -131 units) after 7849 games
Maximum win :804 (~ 80 units)
Payout=0.986025

---------------------------------------------------------------------------------------
Iterations:9000, running for 12.7 seconds
Start hand:[T(s), K(h), 2(d), Q(c), 9(s)], Held[K(h), Q(c)]
Hand 1:[J(s), K(h), 6(c), Q(c), 2(h)] win=0
Hand 2:[A(s), K(h), J(c), Q(c), Q(d)] win=1
Hand 3:[K(h), 9(c), Q(c), K(s), 3(s)] win=1
Hand 4:[K(h), 3(d), A(d), 3(c), Q(c)] win=0
Hand 5:[8(d), K(h), 7(h), Q(c), J(d)] win=0
Hand 6:[A(s), K(h), 4(s), Q(c), 3(s)] win=0
Hand 7:[4(h), K(d), K(h), T(d), Q(c)] win=1
Hand 8:[4(h), K(h), A(d), 5(s), Q(c)] win=0
Hand 9:[6(s), K(h), J(c), Q(c), 2(s)] win=0
Hand 10:[Q(s), Q(h), K(d), K(h), Q(c)] win=9
Added wins for hand=12
Current bankroll:-913 (~ -91 units) after 9000 games
Maximum bankroll:400 (~ 40 units) after 246 games
Minimum bankroll:-1325 (~ -132 units) after 8694 games
Maximum win :804 (~ 80 units)
Payout=0.9898555555555556

---------------------------------------------------------------------------------------
Iterations:10000, running for 14.1 seconds
Start hand:[A(s), K(c), T(d), 7(s), 2(s)], Held[A(s), K(c)]
Hand 1:[A(s), 3(d), K(c), A(d), 6(d)] win=1
Hand 2:[Q(h), A(s), T(s), K(c), J(h)] win=4
Hand 3:[9(d), A(s), K(c), 3(c), A(h)] win=1
Hand 4:[A(s), K(c), T(h), 2(c), 8(s)] win=0
Hand 5:[A(s), K(c), 4(d), K(s), A(h)] win=2
Hand 6:[Q(s), A(s), K(c), 5(d), A(h)] win=1
Hand 7:[6(s), A(s), 6(c), K(c), A(d)] win=2
Hand 8:[9(d), A(s), T(c), K(c), 3(s)] win=0
Hand 9:[A(s), T(s), A(c), 5(c), K(c)] win=1
Hand 10:[A(s), K(c), 4(d), 3(s), 9(h)] win=0
Added wins for hand=12
Current bankroll:-718 (~ -71 units) after 10000 games
Maximum bankroll:400 (~ 40 units) after 246 games
Minimum bankroll:-1325 (~ -132 units) after 8694 games
Maximum win :804 (~ 80 units)
Payout=0.99282

---------------------------------------------------------------------------------------
Iterations:10000, running for 14.1 seconds
Start hand:[A(s), K(c), T(d), 7(s), 2(s)], Held[A(s), K(c)]
Hand 1:[A(s), 3(d), K(c), A(d), 6(d)] win=1
Hand 2:[Q(h), A(s), T(s), K(c), J(h)] win=4
Hand 3:[9(d), A(s), K(c), 3(c), A(h)] win=1
Hand 4:[A(s), K(c), T(h), 2(c), 8(s)] win=0
Hand 5:[A(s), K(c), 4(d), K(s), A(h)] win=2
Hand 6:[Q(s), A(s), K(c), 5(d), A(h)] win=1
Hand 7:[6(s), A(s), 6(c), K(c), A(d)] win=2
Hand 8:[9(d), A(s), T(c), K(c), 3(s)] win=0
Hand 9:[A(s), T(s), A(c), 5(c), K(c)] win=1
Hand 10:[A(s), K(c), 4(d), 3(s), 9(h)] win=0
Added wins for hand=12
Current bankroll:-718 (~ -71 units) after 10000 games
Maximum bankroll:400 (~ 40 units) after 246 games
Minimum bankroll:-1325 (~ -132 units) after 8694 games
Maximum win :804 (~ 80 units)
Payout=0.99282
C:\JoBSimulator>pause
Press any key to continue . . .


It can be seen the the result of the simulation (wagering 5000$) was -71 units which is equal to -71*0.5$=35.5$ in this case.

Here is some examples of how to use the hand-decision program from a promt:
C:\JoBSimulator>java poker.JoBHold 8c Tc Jd Kd Qc
Start hand:[Q(c), K(d), J(d), T(c), 8(c)], Hold[Q(c), K(d), J(d), T(c)]

C:\JoBSimulator>java poker.JoBHold 8c Tc Ad Kd Qc
Start hand:[Q(c), K(d), A(d), T(c), 8(c)], Hold[K(d), A(d)]

C:\JoBSimulator>java poker.JoBHold 8c Tc Ah Kd Qc
Start hand:[K(d), Q(c), A(h), T(c), 8(c)], Hold[Q(c), T(c), 8(c)]


Maybe someone else has interest in the program and I happy to share it. All source code also included (Java). It also includes the framework for my poker (Texas Hold'em) simulator if are into that. Just contact me if you have any questions.

Zoozie

 

[Simmo!]

Blimey. I'm starting to wish I hadn't been behind the bike sheds smoking during Math lessons now

 

[vinylweatherman]

For real (well for fun really).

Some while ago I carried out this simulation "for real" in a Ruby Fortune fun money account. This was in conjunction with a bonus at Jackpot Factory that did not allow BJ, but theory showed it might be worth some +EV if taken on the 50-Hand Jacks or Better, a game which many MG casinos exclude.
I tabulated my results on an Excel spreadsheet, but the one thing I did find out was that even with a good deal of wagering the +EV is a lot less than the theoretical 99.54%
I believe that this is due to the amount contributed to this by the very rare PAT hands of Straight and Royal flushes. With a 50-Hand game, these PAT deals are less likely to hit on that all important decision hand.
I believe that 50 hands is too many for "doing a bonus", and that either single or 4 hand is best. The problem is that in most MG casinos these two games limit minimum coin to 0.25, but allow the 50 and 100 hand games at 0.01 coin. I believe that 4 hand at 0.01 would produce less variance than 50 hand at 0.01 coin, which is the opposite of what I had initially thought when the game first came out.

Interestingly, does my run show results close to this simulator? This could be worth looking at to see how "random" the traditionally streaky MG software is.

 

[Zoozie]

I believe that 4 hand at 0.01 would produce less variance than 50 hand at 0.01 coin, which is the opposite of what I had initially thought when the game first came out.
Interestingly, does my run show results close to this simulator? This could be worth looking at to see how "random" the traditionally streaky MG software is.

4 hand at 0.01$ is indeed a lot better than 50 hands at 0.01$. But if the 4 hands was at 0.1$, what then? Of course variance calculations for this can be found on WizardOfOdds, but I wanted to see it in action.

At the moment Roxy casino has 10 hands JoB at 0.01$ limit so it costs 0.50$ for maximum bet.

Running my simulation for hours shows payout converge to 99.5% which basically just shows that the program holds the cards correct. This results shown on my simulator seems in perfect agreement with what I have seen on MG. I used 50-line JoB to clear wagering, so I have done alot of that.

Zoozie

 

[Zoozie]

When playing VP I noticed that a good part of my RF's came when I held 3 cards. Actually I had suspected it would be when I held 4. But getting 3 to a RF is far more likely than getting 4 to a RF though you need to hit 2 cards instead of just 1 and this could make up for it.

So I made the simulation (6M iterations,JoB optimal strategy) and actually it was the case. The statistical data is limited, but it does show the tendency. So now you know this also.


Results:
#number of cards held:#number of RF
0 held:0
1 held:2
2 held:31
3 held:55
4 held:44
5 held:12
Iterations:6000000, running for 1480.2 seconds
Current bankroll:-30727 (~ -30727 units) after 6000000 games
Maximum bankroll:158 (~ 158 units) after 328394 games
Minimum bankroll:-31300 (~ -31300 units) after 5915252 games
Maximum win :800 (~ 800 units)
Payout=0.9948788333333334

Zoozie

 

[Zoozie]

I made the simulation run over night

Iterations:173000000, running for 57957.4 seconds

0 held:14 (0.35%)
1 held:153 (3.78%)
2 held:826 (20.4%)
3 held:1670 (41.3%)
4 held:1125 (27.8%)
5 held:257 (6.35%)

Zoozie

 

[retlaw]

Very interesting Zoozie,

I am not very good in statistics, but I expect that you would get most RF's when you held 4.

Now I see that holding 2 is only a little worse than holding 4

Do you have an explanation for this?

 

[Zoozie]

Very interesting Zoozie,
Now I see that holding 2 is only a little worse than holding 4
Do you have an explanation for this?

I am counting the number of RF and then recording how many cards I held WHEN I hit the RF.

You get 2 to a RF (which you hold according to optimal strategy) very often. A few of these do connect because you get so many chances though it is a hard to hit (1 to 12000 or something).
Getting 4 to a RF is a rare start-hand though you connect much easier. (1 to 47)

Zoozie

 

[winbig]

Thanks

Nice....this is sure to get me an A for all the java stuff in class this fall


Just kidding, but nice program

 

[Zoozie]

Nice....this is sure to get me an A for all the java stuff in class this fall
Just kidding, but nice program

Source code included, use it as you wish. I tried to make the code for the 36 step algorithm very easy to read. (Making use of Set's (HashSet) and using set-operations like containsAll(cards), getNumberOfAKind(CardValue.ACE), getNumberOfASuit(CardSuit.CLUBS), getSpread(cards) on the set of cards)
etc.

Zoozie

 

[Zoozie]

I made a simple GUI and turned the JoB multi-line simulator into an Applet.

Old / Expired Link

Next project is of course the make the slot-simulator into an applet also, which should be done within a few days if I work on it. I plan to make several other tools I have developed into applets as well, so all can access them easy.

Last week I made my all-in calculator into an applet as well.
Old / Expired Link

Zoozie

 

[Nifty29]

Very interesting stuff Zoozie!!

I wonder how 4-hand Double Double Bonus Poker (MG) would hold up?

Ive always had suspicions about that game. It seems very very difficult to hit any 4 of a kind, and the starting hands seem to be worse than JoB or Aces and Faces. It should be no harder to hit 4OAK than the others, but it does seem to be the case. I know its higher variance, but the amount of 4OAKs etc should surely be the same (regardless of what they pay)

Keep up the good work

 

[happygobrokey]

nice, so in 1.73x10^8 deals you got 257 pat royals, and 14 royals randomly after discarding everything. wild!

and in response to retlaw, you get a lot of royals off of two cards because often you will hold two suited paints (or JT, QT) just looking to pair up, but on occasion you get rewarded with a flush, straight, or the elusive royal.

fun stuff.

 

[vinylweatherman]

nice, so in 1.73x10^8 deals you got 257 pat royals, and 14 royals randomly after discarding everything. wild!

and in response to retlaw, you get a lot of royals off of two cards because often you will hold two suited paints (or JT, QT) just looking to pair up, but on occasion you get rewarded with a flush, straight, or the elusive royal.

fun stuff.

This is what I find odd, surely there should be as many, if not more, RFs when everything is discarded than are dealt PAT from the full 52 card deck. The discards from when all 5 are thrown away are not going to include ANY, Aces or faces, as these would he held, and drawing a pat RF from a 47 card deck with all the faces and Aces available, and only ever one "10" short, should be easier.

 

[Zoozie]

This is what I find odd, surely there should be as many, if not more, RFs when everything is discarded than are dealt PAT from the full 52 card deck. The discards from when all 5 are thrown away are not going to include ANY, Aces or faces, as these would he held, and drawing a pat RF from a 47 card deck with all the faces and Aces available, and only ever one "10" short, should be easier.

I think you forget the weight by how often you actually discard all cards. On every hand you have a chance of hitting a PAT RF. And only in rare case where you discard everything, you have a chance of hitting a 'discard all RF'. So you have much less attemps to hit this 'discard all RF'.
However you are probably right that IN THE CASE YOU DISCARD EVERYTHING, the chance of hitting the RF is higher than getting dealth from a fresh deck.
My own RF distributions actually match my results. (I have only had 1 discard everything RF so far though, and 2 PAT RF).


It is also because of the weight that you hit RF about the same number of times with 3 or 4 card held.

Zoozie

 

[Zoozie]

I made a simulation that showed you discard everything in JoB only 3.2%.
An in this case it is almost twice as likely to hit a RF.

The whole point of the simulation was to see where you RF's came from over the long run.

Calculating RF probablity given you hold 0,1,2,3,4,5 is much easier and has been done many times before and this could be done without a simulation.

Zoozie