Results from 37k Hands Dealt

So far we've reviewed the conceptual issues which should illustrate that major online poker sites are dealing from a random "deck of cards."

And we've learned that third-party certification sites have reviewed actual hands dealt and come to the conclusion that they qualify as the results of a random, unpredictable, unbiased shuffle.

But all those certifications are based on data we can't see.

Fortunately, a player kept a log of over 37,000 hands he was dealt and reviewed all the hole cards and board cards to determine if there was any noticeable bias in the cards dealt.

You can read all the details for yourself in his Usenet post:
TonyH Cards Dealt Analysis for Paradise Poker


I'll cover some of the basics. First, let's look at pocket pairs:

Paired starters dealt: 2264 (5.979%)
Paired starters expected: 2227 (5.88%)

Each pair expected: 171 (0.452%)
A's dealt: 157 (0.415%)
K's dealt: 140 (0.370%)
Q's dealt: 184 (0.486%)
J's dealt: 168 (0.444%)
T's dealt: 183 (0.483%)
9's dealt: 167 (0.441%)
8's dealt: 185 (0.489%)
7's dealt: 182 (0.481%)
6's dealt: 192 (0.507%)
5's dealt: 178 (0.470%)
4's dealt: 186 (0.491%)
3's dealt: 162 (0.428%)
2's dealt: 180 (0.475%)

All this looks pretty good, and what you'd expect. There's a lot of room within only 37,000 hands for this to vary a good amount. But the numbers are all "in the ballpark" for being dealt from a random deck. Poor Tony ran pretty dry on AA and KK, but had more than expected QQ, TT, and others. We've all gone on rushes of cards and dry spells of cards.

Several Party Poker is Rigged theorists claim that the board creates flushes too often. I plan to address these theories later, but at first glance, the data compiled contradicts such speculation

Three cards on the flop make up a:
3 straight:293 (3.43%) expected: 272 (3.18%)
2 flush:4698 (54.97%) expected: 4710 (55.1%)
3 flush:463 (5.42%) expected: 446 (05.22%)

He also compiled data on how often he flopped a flush draw and then how often that flush made it home on the turn or river:

USER HAS ANY TWO SUITED CARDS (dealt 6293 times):
Four flushes flopped: 729 (11.58%)
expected: 689 (10.9%)
When flop four flush, got flush:251 (34.43%)
expected: 255 (35.0%)

The entire post is worth a read. Many people who play frequently on the Internet have tallied many more than 37,000 hands. But none have been nice enough to compile the data and make it available to the public. Thanks, Tony.

You can find prior entries on this topic here:

Do Online Poker Site Shuffle Certifications Mean Anything?


How Poker Site Shuffles are Different than Planet Poker ‘99

Online Poker Room Cracked (not a hoax)

Basics of Online Shuffling

Live Cardroom Deck Shuffles

Online Shuffling - Setting Expectations