vpFREE2 Forums

PDF example: not normal

#1

I dug around on my computer and found some PDF's that I computed some
years ago for
pick'em poker. [I couldn't find the Job or DW, so I will have to
recompute somwday]. I've
uploaded the graph to the files section. Here are some selected
figures one can get from
the PDF (CDF)

# Hands 10% 90% 50% Most Likely EV (theory)
100 -145 120 -35 -50 -0.23
500 -390 495 -95 -170 -1.16
1000 -600 690 -115 -285 -2.32
2000 -910 970 -125 -305 -4.64

some details: I computed the PDF's for 5 coins/max bet. To speed up
the computation, I
set the SF payout to 1200 (from 1199). This introduces a negliable
error. Optimal
statgey assumed (no errors)

note: Pick'em can be played very quickly, >=1000 hands/hour. Even
with perfect play, my
computation shows that a player has about a 20% chance of being up or
down more than
$3K (on a $5 machine) in 1 hr or so! More importantly, most of the
time, the player is in
the red (the PDF's show this clearly). Unless one plays a very long
time, one should
basically ignore the return of a royal. That puts the game at
approx. 99.5%, or similar to
JoB, but without the worry of hitting a royal. So why play this
game? Given a high enough
comp %, the return can be positive, and since the play is fast (one
can easily play 2
machines at a time!), the hourly rate can be quite high, >>$100/hr.
Or at least it used to
be, before Mohegan Sun killed the comp rate.

#2

At 99.5% you have to worry about hitting SF, which is hit in PKM with
about the same frequency as hitting RF in JoB.

JBQ

···

On 8/23/05, cdfsrule <groups.yahoo@verizon.net> wrote:

pick'em poker.

#3

Jean-Baptiste Queru wrote:

At 99.5% you have to worry about hitting SF, which is hit in PKM with
about the same frequency as hitting RF in JoB.

Yes, to an extent. Recognize that the SF contributes less than a 1/3
of the JB RF.

Exclude both the RF and SF from your expected pick'em return and
you're looking at an ER of 99.0%. The number of hands before which
you have a strong confidence of achieving a minimum of 99% return in
PE play is considerably less than the number of hands required for a
similar confidence in games such as JB or DB because of the higher
contribution to return of very infrequent hands in these latter games.

- Harry

#4

Could you explain how you computed these PDFs? Hopefully, a program
that could be shared.

···

--- In vpFREE@yahoogroups.com, "cdfsrule" <groups.yahoo@v...> wrote:

I dug around on my computer and found some PDF's that I computed some
years ago for
pick'em poker. [I couldn't find the Job or DW, so I will have to
recompute somwday]. I've
uploaded the graph to the files section. Here are some selected
figures one can get from
the PDF (CDF)

#5

Harry : Indeed. And the next rarest pay is a lot more frequent than in
JoB. Certainly those two factors help PKM immensely in the comparison.

JBQ

···

On 8/23/05, Harry Porter <harry.porter@verizon.net> wrote:

Yes, to an extent. Recognize that the SF contributes less than a 1/3
of the JB RF.

#6

Don't forget that MS used to give 1.1% points. At that rate, one
could fall behind on SF's and still be positive (son long as the 4oak's
were in line, etc) The challenge was turning the points into cash. I
usually aimed for $0.50 to $0.75 on the point. Though most players
lost on the game itself, the casino cliams it was hurtin a bit on the
points and so downgraded the game (first the pay table, then restored
the paytable and cut the point rate)

Harry : Indeed. And the next rarest pay is a lot more frequent than in
JoB. Certainly those two factors help PKM immensely in the comparison.

JBQ

> Yes, to an extent. Recognize that the SF contributes less than a

1/3

···

--- In vpFREE@yahoogroups.com, Jean-Baptiste Queru <jbqueru@g...> wrote:

On 8/23/05, Harry Porter <harry.porter@v...> wrote:
> of the JB RF.

#7

Could you explain how you computed these PDFs? Hopefully, a

program

that could be shared.

Sure (though I will not be sending any code to this list at the
moment).
Computing the PDF's is quite straight forward. [Though the method I
used is accurate and simple, it has it limitations.]

(1) First, start with the Paytable. For each payout entry, you need
the probability of occurance. You can these numbers from your
favorite
VP software. You also need the probability for the "nothing" result.

Now you have a two colomn table. One column for payouts, including
zero (nothing) and one column for probability. (Make sure the
probabilites add up to 1!). I will call this data table the
"starting
point", it is a list of Payout[i] and Prob[i]

Now Subtract the bet (in the correct unit) from each payout entry.
The
resulting two columns is your PDF for 1 hand. I will call this PDF1 =
{money[1,n],prob[1,n]}. There is another way f looking at
this:before
we start, we have a probability of 1 of having no loss or gain. so I
would describe our state as (0,1), where 0 is our current loss/win
and
1 is the probability. Then we bet, and our state looks like, if we
bet
5 coins, (-5,1), that is before we know the outcome. Now we take
this single point and add the win/loss
(-5 in this case) to every payout entry in the starting data set and
mulitply the prob (1 in this case) with every starting prob. entry.
The
result is 1 data point for each row in the starting table.

2) To compute the PDF for the next hand, start with the two column
data
from the previous hand. You are going to take each row in the table
(1
set of payout value & proability) and operate on them. So if there
are
10 rows in the table, you are going to do the following 10 times.
Each
row in the table represents a possible state. Take that state, and
subtract the bet (from the win/loss value). Then add it to each
payout
value in the original table, and likewise, mulitply the
probabilities.
This produces another, say, 10 states. Now repeat this for each
state
(row) in the PDF for one hand. If there were 10 rows in the first
PDF,
there would be now 100 rows in the PDF for hand 2 [there are 10
possible outcomes for of the original 10 possible state]. Now, mwe
might be able to simplify these results some. For example, we can add
together the probabilities that occur for the same win/loss value. At
this point it might not matter much if we do this, but after a lot of
hands it does!

3) Now repeat the procedure in 2 for each hand. Take the PDF from
the
last hand. Take each entry, subtract the bet, multiply the prob. by
the starting data table. When done, collect all the results and
simplify. BTW, without the simplification step outlined above, the
size of the PDF goes up geometrically. 10,100,1000,10000,... and
will
soon overwhelm your computer!

AS for code to do this, I am toying with the idea of making some
MATLAB
or similar code available

Hope this helps...if someone wants I can give a numerical example for
a few hands

#8

Cool! That could help in de-bugging.

Thanks.

bl

···

--- In vpFREE@yahoogroups.com, "cdfsrule" <groups.yahoo@v...> wrote:

Hope this helps...if someone wants I can give a numerical example for
a few hands

#9

No Problem:

Game paytable used (1200 instead of 1199)

0 0.668459
10 0.228375
15 0.0620877
25 0.0300147
55 0.00506554
75 0.00318887
90 0.00235632
600 0.00042358
1200 2.60071e-05
6000 2.84238e-06

Below values are (coins won/loss,probability);(coins won/loss, probability)...
Note: data formatted to keep this email as short as possible, and only 4 sig. fig's given.
Sum of all probabilites for each state (hand) should =1
You can convert into data that excel likes by: removing all white space, replacing ";" with
returns and "," with tabs, then removing "(" & ")"

···

--- In vpFREE@yahoogroups.com, "bornloser1537" <bornloser1537@y...> wrote:

Cool! That could help in de-bugging.

Thanks.

bl
--- In vpFREE@yahoogroups.com, "cdfsrule" <groups.yahoo@v...> wrote:
>
> Hope this helps...if someone wants I can give a numerical example for
> a few hands

------------------------
Starting state:
(0,1);
-------------------------
Non-Zero Prob's after hand 1:
    (-5,0.6685);(5,0.2284);(10,0.06209);(20,0.03001);(50,0.005066);(70,0.003189);
(85,0.002356);(595,0.0004236);(1195,2.601e-05);(5995,2.842e-06);
-------------------------
Non Zero Prob's after hand 2:
   (-10,0.4468);(0,0.3053);(5,0.08301);(10,0.05216);(15,0.06849);(20,0.003855);
(25,0.01371);(30,0.003727);(40,0.0009009);(45,0.006772);(55,0.002314);(60,0.000629);
(65,0.004263);(70,0.0003041);(75,0.001457);(80,0.003546);(90,0.001268);
(95,0.0002926);(100,2.566e-05);(105,0.0001414);(120,3.231e-05);(135,2.387e-05);
(140,1.017e-05);(155,1.503e-05);(170,5.552e-06);(590,0.0005663);(600,0.0001935);
(605,5.26e-05);(615,2.543e-05);(645,4.291e-06);(665,2.701e-06);(680,1.996e-06);
(1190,3.495e-05);(1200,1.188e-05);(1205,3.229e-06);(1215,1.561e-06);
(1245,2.635e-07);(1265,1.659e-07);(1280,1.226e-07);(1790,2.203e-08);
(2390,6.764e-10);(5990,3.8e-06);(6000,1.298e-06);(6005,5.865e-07);
------------------------
Non Zero Prob's after hand 3:
  (-15,0.2987);(-5,0.3061);(0,0.08323);(5,0.1046);(10,0.0971);(15,0.01964);(20,0.03721);
(25,0.01012);(30,0.004936);(35,0.00436);(40,0.007138);(45,0.0006172);(50,0.004808);
(55,0.001261);(60,0.005094);(65,0.001041);(70,0.002979);(75,0.004161);
(80,0.0005556);(85,0.002813);(90,0.0006373);(95,0.0005513);(100,0.0005198);
(105,4.483e-05);(110,0.0001103);(115,9.113e-05);(120,2.31e-06);(125,2.85e-05);
(130,5.389e-05);(135,2.039e-05);(140,1.926e-05);(145,1.141e-05);(150,3.216e-05);
(155,2.15e-06);(160,1.121e-05);(165,1.393e-05);(170,2.455e-07);(175,5.157e-06);
(180,1.034e-06);(185,1.814e-07);(190,6.545e-07);(205,2.284e-07);(210,3.243e-08);
(220,8.438e-08);(225,7.188e-08);(240,5.312e-08);(255,1.308e-08);(585,0.0005678);
(595,0.000388);(600,0.0001055);(605,6.628e-05);(610,8.703e-05);(615,4.899e-06);
(620,1.742e-05);(625,4.736e-06);(635,1.145e-06);(640,8.606e-06);(650,2.94e-06);
(655,7.993e-07);(660,5.417e-06);(665,3.864e-07);(670,1.851e-06);(675,4.506e-06);
(685,1.611e-06);(690,3.718e-07);(695,3.261e-08);(700,1.797e-07);(715,4.105e-08);
(730,3.034e-08);(735,1.292e-08);(750,1.91e-08);(765,7.055e-09);(1185,3.522e-05);
(1195,2.394e-05);(1200,6.51e-06);(1205,4.069e-06);(1210,5.359e-06);
(1215,3.008e-07);(1220,1.07e-06);(1225,2.908e-07);(1235,7.029e-08);
(1240,5.311e-07);(1250,1.805e-07);(1255,4.908e-08);(1260,3.343e-07);
(1265,2.372e-08);(1270,1.136e-07);(1275,2.779e-07);(1285,9.891e-08);
(1290,2.283e-08);(1295,2.002e-09);(1300,1.104e-08);(1315,2.521e-09);
(1330,1.863e-09);(1335,7.934e-10);(1350,1.173e-09);(1365,4.332e-10);
(1785,4.426e-08);(1795,1.509e-08);(1800,4.104e-09);(1810,1.984e-09);
(1840,3.348e-10);(1860,2.108e-10);(1875,1.557e-10);(2385,1.37e-09);
(2395,4.634e-10);(2400,1.26e-10);(2410,6.09e-11);(2440,1.028e-11);(2460,6.471e-12);
(2475,4.781e-12);(2985,8.595e-13);(3585,1.759e-14);(5985,3.81e-06);
(5995,2.603e-06);(6000,8.639e-07);(6005,1.249e-06);