Home → Help → GamingPeak Card Distribution
GamingPeak Card Distribution
Throughout GamingPeak’s lifetime, we’ve received concerns that our distribution hasn’t been proper - that somehow it has been skewed, incorrect, or otherwise statistically incorrect. After hearing your concerns and consulting a number of mathematical sources, we have done careful analysis and created this report.
GamingPeak card distribution is completely and mathematically correct.
Still unsure? Read on for our theory, analysis, and the cold, hard facts:
The Technology
We’re using the Mersenne Twister for our random number generation. It is a proven, mathematically sound, pseudo-random number generator which produces very good results. We have consulted experts on our seeding process and distribution technique, and we have all concluded that we are using the Mersenne Twister properly.
First and foremost, this means that the numbers we use to generate the card shuffling are correct.
Why does the Distribution feel different?
1. Real-life isn’t completely random
When you’ve just finished a hand of cards and re-shuffle, the cards don’t get completely reshuffled. Think of this: After each hand, there are four like-suited cards next to each other in the deck - the odds are greater that you won’t completely shuffle the deck, and those cards will tend to be grouped together. In the same way, unless you do a lot of shuffling each time, the cards aren’t going to be completely random. Thus the cards will “feel” differently distributed in real life, and that’s probably why.
2. The mind doesn’t remember the good hands as well as the bad
Studies have shown that the human mind tends to only remember the unexpected situations - in Spades, when you get a distribution that you consider to be out-of-whack, you’re going to remember that situation much more than the seven-or-so hands you just played which had an unremarkable distribution.
The mental vision you have of a random card distribution are affected by your own experience as a player. But even if you could sense whether or not a distribution was completely random, the number of hands you’ve played recently is much smaller, so a sampling of your own hands might not be large enough to accurately represent the distribution.
The Proof
Still uncertain? Here’s the proof.
In the update on Sunday, January 26th, 2008, we began tracking statistics for every hand which was dealt at GamingPeak. We recorded every hand which was actually dealt to the players here, and we have proof that our distribution is spot-on.
While we just recently implemented this logging feature, our statistics prove without a doubt that our card distribution is mathematically correct.
Here is a sampling of data that we collected in our testing so far. Even though we haven’t had a long time to gather data, already our distribution lines up very closely with the “perfect” random distribution:
===============================================================
| TOTAL HANDS: 9,564,348 |
===============================================================
| DISTRIBUTION | HANDS | ACTUAL | IDEAL | DIFF | % ERROR |
|--------------|--------|--------|--------|--------|----------|
(4, 4, 3, 2) 2059967 21.54% 21.55% 0.01% 0.000612
(5, 3, 3, 2) 1485192 15.53% 15.52% 0.01% 0.000746
(5, 4, 3, 1) 1238756 12.95% 12.93% 0.02% 0.001632
(5, 4, 2, 2) 1012624 10.59% 10.58% 0.01% 0.000739
(4, 3, 3, 3) 1007629 10.54% 10.54% 0.00% 0.000083
(6, 3, 2, 2) 539474 5.64% 5.64% 0.00% 0.000358
(6, 4, 2, 1) 448009 4.68% 4.70% 0.02% 0.003811
(6, 3, 3, 1) 329755 3.45% 3.45% 0.00% 0.000126
(5, 5, 2, 1) 303427 3.17% 3.17% 0.00% 0.000448
(4, 4, 4, 1) 286827 3.00% 2.99% 0.01% 0.001904
(7, 3, 2, 1) 179974 1.88% 1.88% 0.00% 0.000472
(6, 4, 3, 0) 126117 1.32% 1.33% 0.01% 0.005738
(5, 4, 4, 0) 119708 1.25% 1.24% 0.01% 0.006651
(5, 5, 3, 0) 84616 0.88% 0.90% 0.01% 0.011730
(6, 5, 1, 1) 67207 0.70% 0.71% 0.00% 0.003727
(6, 5, 2, 0) 62307 0.65% 0.65% 0.00% 0.000605
(7, 2, 2, 2) 49092 0.51% 0.51% 0.00% 0.000639
(7, 4, 1, 1) 37525 0.39% 0.39% 0.00% 0.001283
(7, 4, 2, 0) 34591 0.36% 0.36% 0.00% 0.000088
(7, 3, 3, 0) 25259 0.26% 0.27% 0.00% 0.004335
(8, 2, 2, 1) 18569 0.19% 0.19% 0.00% 0.009308
(8, 3, 1, 1) 11237 0.12% 0.12% 0.00% 0.000540
(8, 3, 2, 0) 10409 0.11% 0.11% 0.00% 0.002966
(7, 5, 1, 0) 10338 0.11% 0.11% 0.00% 0.003875
(6, 6, 1, 0) 6878 0.07% 0.07% 0.00% 0.005899
(8, 4, 1, 0) 4372 0.05% 0.05% 0.00% 0.011041
(9, 2, 1, 1) 1626 0.02% 0.02% 0.00% 0.045492
(9, 3, 1, 0) 948 0.01% 0.01% 0.00% 0.013472
(9, 2, 2, 0) 793 0.01% 0.01% 0.00% 0.008612
(7, 6, 0, 0) 556 0.01% 0.01% 0.00% 0.044688
(8, 5, 0, 0) 324 0.00% 0.00% 0.00% 0.082267
(10, 2, 1, 0) 105 0.00% 0.00% 0.00% 0.001617
(9, 4, 0, 0) 86 0.00% 0.00% 0.00% 0.069251
(10, 1, 1, 1) 39 0.00% 0.00% 0.00% 0.030233
(10, 3, 0, 0) 8 0.00% 0.00% 0.00% 0.458867
(11, 2, 0, 0) 2 0.00% 0.00% 0.00% 0.818822
(11, 1, 1, 0) 2 0.00% 0.00% 0.00% 0.160538
That data is a result of compiling the suit distribution from real hands dealt at GamingPeak. Not a test, not a sample - this is an analysis of actual hands which players here have received.
This statistical analysis shows that our distribution is random and correct. And since we’re using real-life hands to analyze the data, this is a true representation of our distribution’s correctness.
Moving Forward
We will continually monitor our data to ensure our distribution remains statistically accurate. But as we mentioned before, our readings are accurate already and will only grow more accurate as the sample size increases, not less.
The conclusion? Our distribution is indeed correct, and represents random dealing, which is exactly what we want it to represent. While the human mind may perceive our distribution in different ways, depending on its own experience, we have run the numbers, done the calculations, consulted experts, and have found that our distribution works great.
Good luck!