bigfoot66
Joined: Feb 5, 2010
• Posts: 1581
June 21st, 2015 at 10:50:22 AM permalink
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.
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tringlomane
Joined: Aug 25, 2012
• Posts: 6270
June 22nd, 2015 at 5:18:10 PM permalink
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.
teliot
Joined: Oct 19, 2009
• Posts: 2159
June 22nd, 2015 at 6:40:50 PM permalink
Quote: bigfoot66

Go ahead and throw out a guess..

4
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dwheatley
Joined: Nov 16, 2009
• Posts: 1246
June 22nd, 2015 at 6:44:13 PM permalink
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.
Wisdom is the quality that keeps you out of situations where you would otherwise need it
charliepatrick
Joined: Jun 17, 2011
• Posts: 2338
June 23rd, 2015 at 12:37:07 AM permalink
^ 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.
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...
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
MangoJ
Joined: Mar 12, 2011
• Posts: 905
June 23rd, 2015 at 12:56:25 AM permalink
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.
mustangsally
Joined: Mar 29, 2011
• Posts: 2463
June 23rd, 2015 at 3:00:36 AM permalink
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,
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
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champ724
Joined: May 13, 2015
• Posts: 64
June 23rd, 2015 at 8:45:33 AM permalink
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.
teliot
Joined: Oct 19, 2009
• Posts: 2159
June 23rd, 2015 at 9:04:10 AM permalink
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.
Poetry website: www.totallydisconnected.com
dwheatley
Joined: Nov 16, 2009