Sample Size Needed To Determine Accuracy

Programs like the Wizard's VP application or WinPoker will keep running statistical information about how accurately you play hands. What number of hands do you think I need to play to get a good idea of my accuracy? My gut says I would be there in about 2000 hands, what say you? To be specific, I am looking for the "% of Best Play" number to be reasonably accurate, say within a tenth of a percent. Go ahead and throw out a guess, I think this is something where the wisdom of crowds will point me in the right direction.

99.9% of hands played to be correct? That's a pretty good rate. I am not that good usually. I think the amount that errors cost you is a better metric. Being 99.9% accurate in terms of return is a much easier goal to accomplish, but still takes a good amount of practice/discipline.

Or are you meaning the amount of hands needed to have your hands result to be reliable to +/- 0.1% to your expected accuracy? If that's the case, it's a lot more than 2000 hands.

I think 2k hands is a good start generally speaking though. I get bored fast myself and rarely practice more than 400 hands at a time.

Quote: bigfoot66

Go ahead and throw out a guess..

4

This is a nice and simple university level stats question. Your % best play score has a binomial distribution, and you want to find a confidence interval for it. The confidence interval half-width for a binomial distribution (using the normal approximation) is:

+- z * sqrt{ p (1-p) / n }

where z is based on the level of confidence you want. So let's say you want to 95% confident you have your score (use z=1.96) and your best play score is 99%. Then we solve the following for n:

0.001 = 1.96 * sqrt { .99 * 0.01 / n }

I get 38032 hands. Note that this formula depends on your best play score. So if you make the best play 99.5% of the time, and want to confirm that to within 0.1%, with 95% confidence, you need only 19111 hands.

^ I haven't done the numbers but I agree the order of magnitude.

Another way to look at is is suppose you had a deck with 1000 cards, where most are Red but (say a friend) has put 5 Black cards in the deck. Your aim is to determine how many Black cards your friend put in.

You shuffle the cards and pick one to see whether it is Red or Black. Repeat this many times to get an idea - how many times do you need to do it to get an accurate estimate.

If you do it 2000 times then you can see your estimate isn't that close and 90% it's between 2.5 and 7.5.

Total Black	Your Est	Pr
0	0.0	.000 044
1	0.5	.000 445
2	1.0	.002 235
3	1.5	.007 480
4	2.0	.018 765
5	2.5	.037 644	<
6	3.0	.062 897	<
7	3.5	.090 034	<
8	4.0	.112 712	<
9	4.5	.125 361	<
10	5.0	.125 424	<
11	5.5	.114 022	<
12	6.0	.094 970	<
13	6.5	.072 981	<
14	7.0	.052 051	<
15	7.5	.034 631	<
16	8.0	.021 590
17	8.5	.012 662
18	9.0	.007 009
19	9.5	.003 674
20	10.0	.001 829

whereas with 20000, you can be 90% confident of being between 4.2 and 5.8...

Total Black	Your Est	Pr
84	4.20	.011 176
85	4.25	.013 159
86	4.30	.015 313
87	4.35	.017 613
88	4.40	.020 028
89	4.45	.022 517
90	4.50	.025 033
91	4.55	.027 522
92	4.60	.029 929
93	4.65	.032 194
94	4.70	.034 261
95	4.75	.036 076
96	4.80	.037 588
97	4.85	.038 758
98	4.90	.039 555
99	4.95	.039 959
100	5.00	.039 961
101	5.05	.039 565
102	5.10	.038 788
103	5.15	.037 654
104	5.20	.036 200
105	5.25	.034 470
106	5.30	.032 510
107	5.35	.030 374
108	5.40	.028 115
109	5.45	.025 783
110	5.50	.023 428
111	5.55	.021 096
112	5.60	.018 825
113	5.65	.016 649
114	5.70	.014 595
115	5.75	.012 683
116	5.80	.010 925

Quote: bigfoot66

What number of hands do you think I need to play to get a good idea of my accuracy? My gut says I would be there in about 2000 hands, what say you? To be specific, I am looking for the "% of Best Play" number to be reasonably accurate, say within a tenth of a percent.

If you play the majority of hands right, errors are rare events (say at rate p). You need to play long (1/p) to catch an error, and then you need even longer to estimate their frequency.

So you play 1/p hands for each error you want to catch. This is Poisson statistics. The Variance of errors will be the number of errors you expect to do. Hence in order to get any reasonable error rate, you need your standard deviation to be your expected error rate (or better, way smaller).

With variance = stddev^2 I would guess you need to play 1/p^2 hands to get any reasonable result.

If your aim is 99.9% accuracy, p=0.001. You would need to play a *million* hands.

Quote: bigfoot66

Programs like the Wizard's VP application or WinPoker will keep running statistical information about how accurately you play hands. What number of hands do you think I need to play to get a good idea of my accuracy?

i say it first depends on the game played
JOB vs TDB should have different error rates i would thinks so

and then on how difficult the hand is to play
if every hand was a dealt Royal for example - no errors

this is from Video Poker for Winners
"The Hands tab tells you how many hands you've played, breaking them down into Beginner, Intermediate, and Advanced.
These are somewhat arbitrary designations
based on
how big the difference is between the best play and the second-best play. It also gives your overall score in a percentage."

ok
maybe not so good a metric
there is more
"The Return tab is the most valuable information presented in the Overall Play window.

It compares the expected value in coins from your actual plays,
designated by Your Return,
to the expected value of the perfect play, designated by Best Return.
The difference between the two is shown in the Cost In Coins field. Return % indicates your overall accuracy of play."

that sounds much better to me
the number of hands to play?

more is better?
IS more better?
play with a strategy card for the game and the number of hands to play should be meaningless
so I would think

Sally

i hope you don't rack your brain trying to play perfect video poker. it is a machine and it does have a payout setting in it. if you are playin deuces wild and throw away a deuce you won't get 4 deuces. play the machine with some intelligence and if its ready to hit a rf or 4 deuces it'll give it to ya if its not ready your not gettin it no matter how well you play.

Quote: mustangsally

more is better?
IS more better?

The sample spaced is small enough (134459 unique starting hands, modulo suit permutations) that "more is better" runs into the practical limitation of exhausting the cycle.

Quote: champ724

i hope you don't rack your brain trying to play perfect video poker. it is a machine and it does have a payout setting in it. if you are playin deuces wild and throw away a deuce you won't get 4 deuces. play the machine with some intelligence and if its ready to hit a rf or 4 deuces it'll give it to ya if its not ready your not gettin it no matter how well you play.

So this only applies to those Class II(?) machines. Real video poker doesn't work this way.

Quote: teliot

The sample spaced is small enough (134459 unique starting hands, modulo suit permutations) that "more is better" runs into the practical limitation of exhausting the cycle.

This is an interesting point, but I wonder if seeing the same hand laid out in a different way would cause you to play it differently at high speeds. I'm pretty sure I've made a mistake because of the order I process cards in.

Thank you all for the input. I am trying to learn a deuces wild game that I've never played before and want to be able to determine when my edge is sufficient to justify playing the game. So often we simply use the theoretical perfect return on a game and I know I don't play perfectly, so I simply want to determine what MY return is. I really do appreciate the input, I figured I could get a "good enough" number at about 2000 hands, so it is good to know that I was off by an order of magnitude.

Quote: teliot

4

BTW Your book just showed up in the mail from Amazon, I can't wait to read it.

Quote: bigfoot66

Thank you all for the input. I am trying to learn a deuces wild game that I've never played before

which one?

Quote: bigfoot66

and want to be able to determine when my edge is sufficient to justify playing the game.

wow
WOW
just start playing with a strat card!

this sounds so grade school to me

ands
which expert vp player (please name names) says or suggests to do this?
i mean
"determine when one's edge is sufficient to justify playing the game"

that makes the use of a strategy card (free or paid versions) useless i says
ands
you also mention (men) nothing about how many hands per hour you want to crush

do you have a vp book you got this info from?
if yes, name the book?

a webpage?
i can not and will not believe this is from a personal thought only

are you writing your own vp book?
i might write my own and have a video version to share

Quote: bigfoot66

So often we simply use the theoretical perfect return on a game

is not that the only thing that matters?
and all other thoughts and plans are just an illusion
nothing for fun or entertainment like this hit of mine
i was getting no winning hands so i changed games and pressed the buttons at the right time

a win is a win
Max bet would not have resulted in a Royal as i took me time to make my bet (i was giving 3 hands and out B4 WSOP event #3)

Quote: bigfoot66

and I know I don't play perfectly

exactly, how do you know this is true?
if it is true, can you play slower and perfectly with a strat card

0% errors at slow play can be worth more than .5% error rate at fast play in my opinion
unlesssssss

one plays for speed only
it is an addiction
i hear
Sally

The game is DW 44 that returns 99.95%. During certain times I can get 3/4% cash back plus mailers so the edge is not that great to where I can play with a lot of errors, and I have never played DW before so I am still learning the basics. The other playable game is 10/6 DDB which I know very well so I am continuing to play that relatively quickly, I would prefer to learn the DW game so that I can cut the variance in half.

Quote: bigfoot66

BTW Your book just showed up in the mail from Amazon, I can't wait to read it.

Awesome! Please let me know what you think.

Quote: bigfoot66

The game is DW 44 that returns 99.95%.

nice
here in SoCal we have the 20/12/9 (Yahoo!) version that i have hit many many many Royals on (more than Alan Mendelson in his long lifetime of play)
so many (i am lucky) i lost count in memory but have it written down

Quote: bigfoot66

to where I can play with a lot of errors, and I have never played DW before so I am still learning the basics.

Ah, yes the point of your thread

you asked for a sample size and one poster said 4 hands

i still say 0 hands are needed
as practice has to be a non-factor to play perfectly any vp game

a strat card is all that is required (and HOPE it is a good one)
you disagree with this for some unknown reason, that is ok too (1+1)

do (DUE) have fun no matter what
i always say
i guess Royals are fun
Sally

Well I got 2 dealt royals in the past 3 weeks so that is a lot of fun! I could play with a strategy card but financially it makes more sense to learn 95+% of the hands cold first so I can play relatively quickly.

Quote: bigfoot66

Well I got 2 dealt royals in the past 3 weeks so that is a lot of fun!

i agree there
i have just one of those dealt to me name

Quote: bigfoot66

I could play with a strategy card

and in my opinion you should
because

Quote: bigfoot66

but financially it makes more sense to learn 95+% of the hands

i think you are sharing you opinion here and not a proven fact
not that all opinions are not facts...

in DW, i thinks, most times you throw away your starting hand
i think there is a post about that (maybe not your game of choice or no-choice)

and i would also think abouts 95% of all the dealt hands (in DW) are no-brainers
i could B a few %points off here, just a feel-guess

Quote: bigfoot66

cold first so I can play relatively quickly.

i say
it still depends on the kind of errors you make

how large and how often do you make them

(of course, not all errors result in a loss over a weeks worth of 24/7 play for example.
some errors would win a hand and some correct plays could lose too. this is part of the law of large numbers no one ever talks about)


how do you know the errors you make?
do you video your vp sessions (easy to do)
that sounds like a good idea too
Yahoo!
Sally

well
so
i take back the part about most hands are thrown away, just from my sample video
still, most hands (95%+) are easy to play correctly, imo

Quote: mustangsally

in DW, i thinks, most times you throw away your starting hand
i think there is a post about that (maybe not your game of choice or no-choice)

and i would also think abouts 95% of all the dealt hands (in DW) are no-brainers
i could B a few %points off here, just a feel-guess
i say
i take back the part about most hands are thrown away, just from my sample video
still, most hands (95%+) are easy to play correctly, imo

Yes, you are right. Having never played DW though it is not always clear when to hold a deuce and 2 suited cards, for example. If 95% of hands are no-brainers then I will be stopping every 20 hands to look something up, and this will take away significantly from an anticipated $6 per hour opportunity. While I do seek out advantage opportunities, this is mostly recreational gambling and its just not fun to stop and look every 20 hands, and it is also not fun to worry about if I am actually playing the hands correctly. I would rather just get to the point that I am confident that I am playing with a 99.7% return and play through quickly to take the 3/4% cash back plus $300+ freeplay monthly and food comp .