Quote:
Originally Posted by spadebidder
I think what you are referring to might be this:
http://www.spadebidder.com/flop-analysis/part2/
There are some charts there of how ranks are distributed on the flop, and the amount of card removal effect that is expected due to players tending to hold higher cards when seeing flops.
Here's a sample:
(EXCERPT FROM PART 7)
Conclusions
I predicted 50 extra paired flops per 100K, and the result came up a little less but still very significant, and is the largest single effect measured.
Rank Bias was already quantified empirically in Part 2 and broken down further to specific patterns in Part 4, resulting in the 3 predictions below.
I predicted a shortage of “Connector & 1-gap” and “Connector & 2-gap” due to Rank Bias, and it was significantly short in every dataset, averaging more than -3 SD.
I predicted a surplus of “Connector & 3-gap” due to Rank Bias, and this was true in every pattern but the average confidence was less than 98%, so the effect is small if it exists.
I predicted extra 3-straights and that turned out to be weak, showing in only two datasets.
I said that monotone flops would have a surplus if players tended to fold unsuited hands more than 3x as often as suited hands since they naturally occur at a 3:1 ratio. The surplus averaged over 3 SD, so players do favor suited hands to see the flop.
The Rank Bias and Pair Bias effects are consistent and predictable. The Suitedness Bias is smaller and a little more inconsistent, but in some game structures it is significant (relatively speaking). The only effect that may be useful to understand in actual game play seems to be the general Rank Bias effect, but probably not specific patterns. An example of utilizing the general effect is described in the post Testing Barry Greenstein’s claim. The other effects are so small that it takes a huge sample to even recognize them.
Why do poker sites not routinely summarize their statistics like this and publish them? I think the major sites probably already know a lot of what I’ve written about here. They have probably run the stats and found that community cards are not 100% random. But it took me 30 pages of explanation to describe why that happens honestly with a random deal. Unless everything came out nice and neat and evenly distributed, it may just be too much trouble to convince users why Aces will come up less than 1/13 of the flopped cards in the long run, and why pairs show up on the flop 7 standard deviations more often than they “should” in 200 million flops. Publishing such counter-intuitive stats might not be the confidence builder that some people would like to see, it might in fact just create more controversy.
Another reason is summed up nicely by one of the 2+2 mods in this post.
“Because this is nearly impossible. Let’s say I own a poker site, and I publish the hole card distribution. Rigtard A then claims that he flops sets too often, so I show post-flop results. Rigtard B claims there is a new-deposit boomswitch and a cashout boomswitch, so I produce data about players winning and losing when they do each of these things. Rigtard C claims that shortstacks win too much in tournaments. And on and on and on and on it goes.
You’re basically asking them to prove a negative, that poker isn’t rigged. There are just way too many possibilities to make that realistic IMO.”
Fortunately I don’t have to worry about any demands to “prove it” or “I don’t believe the data”. Anyone who truly wants to do the work themselves can reproduce my results. I have no agenda other than showing objectively that flops are not 100% random and there are quantifiable card removal effects. But the data also shows that the deal is random and player behavior is what alters the flop distribution. I’ll be happy to provide methods and source code and save you a few hundred hours.
In future posts we’ll be examining Turn & River cards and the patterns they form, and whether suck-outs happen at the expected frequencies, and if not then why not. I’m also already working on an All-In Analysis with more detail than anyone has ever published before.
Please point out any errors I’ve made in this post or anywhere else. Comments are open and welcome.