apparently many derive pleasure from losing around here…

# Dr. Sun's Poker Lab

Getting your opponents to fold absolutely reduces variance. You can’t win a pot if you fold. There are never bad beats. You may not get full value if you’re overbetting, but does it make up for it in terms of the chips you don’t lose in showdowns? I’m inclined to think so.

you are not getting value at all

You will get whatever value you have managed to extract preflop and on any streets that came before. In tournaments, it can be better to win a modest pot with no risk rather than try to squeeze out a little extra and end up losing a big pot or being forced to fold on the river.

No, you will get whatever chips your opposition has put in the pot…the object in poker is to get the value of your hand and overbetting (topic of conversation) defeats getting value

So I have decided to collect some data in order to test the accuracy of the pRNG. This has nothing to do with “fairness” because fairness means that everyone has the same chances and one person or group isn’t given special treatment.

Anyway, I wanted to pick something easy to track, so I am looking at how many times I flop a set when starting with a pocket pair. Obviously, if I don’t see the flop, that pocket pair is not counted. I am also only using my own cards, not those of other people.

First, we have to know how often we should flop a set. This can be calculated by figuring out how often we WON’T flop a set, then subtracting this from 100%.

So we have seen 2 cards, leaving 50 unseen. Of these, 48 will not make a set. We can do this with each card and get…

100% - ((48/50 X 47/49 X 46/48) X 100) = 11.75%

So far, I have only collected 36 instances, and 5 of these flopped sets. This is 13.9%, which seems to be well within the margin of error for such a small sample size. I will keep collecting data until I get at least 1,000 instances, which could take awhile.

Set Flopping Update:

I’m still collecting data on flopping a set. So far, I have seen 136 flops when I was dealt a pocket pair, and 16 of these flopped or would have flopped a set.

That’s: (16/136) X 100 = 11.76%

Since we were expecting 11.75%, that’s pretty close. I’ll keep collecting numbers until I get 1,000 instances and see what happens.

Another Set Flopping Update:

I haven’t been playing much, but am still collecting data about set flopping. Here’s what i have so far.

Flops seen when holding a pocket pair: 218

Sets flopped: 25

So (25/218) X 100 = 11.5%

And we should expect to see 11.75%

So far, it seems to be running pretty close to what would be expected.

One thing I have noticed is that I flop less sets when holding big pocket pairs. Since I almost always raise big preflop with these hands, I am guessing that people call with bigger cards than they would if I limp. So it might be that I have less outs to a set than I would have with smaller pairs.

I am tracking which specific pairs I see, and will post the whole data set once I reach 1,000 instances.

If you have Aces you are more likely to be called by someone with A9 than you with 22 are to be called by someone with 2 9, but then again your opponent with an unmatched A against your AA has his outs severely reduced.

The ideal is what happened to me tonight, which is that I got into a pot with 22 and flopped something like A Q 2 and was able to eliminate or cripple the stack of two opponents on the hand. When you have AA and A comes on the flop, you are less likely to get any action post flop unless an opponent also flops a set or two pairs, which is very good for you.

If I understand you, you are agreeing that raised big pairs are less likely to flop a set because their preflop calling ranges will contain more big cards. Yes, that was what I was trying to say.

All I’m trying to do with this experiment is collect some actual data to sort of test the pRNG. OK, one small aspect of the pRNG anyway. I picked set flopping because pocket pairs are fairly common, but not so common that the data collection will be a pain in the butt.

Big pairs should flop sets at the exact same rate as small pairs.

Big preflop raises can make it appear otherwise by causing the table to fold before the flop when they are weak and call when they are strong.

Human behavior that removes data(flops not seen) lessens the accuracy of the experiment.

Also, if one calls minimum bets with 22 but folds that hand to large raises, the experiment is also being compromised.

For a good study all flops should be seen.

I agree with this and with all you said. “Big preflop raises can make it appear otherwise,” and this was my point. I’m saying that it’s quite possible that my data is being skewed to some degree by the number of flops I am seeing with big pairs, and by the hands that can call big raises against those hands.

Keep in mind, however, that I am not limiting my data collection to hands I am still in. If I fold 22 preflop, but get to see the flop, I count it as a set if a 2 comes on the flop, whether I’m in the hand or not.

This isn’t perfect, but I can’t see every flop, so it’s as good as I can manage.

The basic question then is whether pre-flop action effects your odds of flopping a set. Remember that I’m looking at this from a tournament perspective, and the answer is “yes.”

I found an article asking professional players, “Are you calling a blind shove first hand of the WSOP Main Event?” As one might expect, their calling ranges were heavily weighted towards big pairs and bigger cards in general. This would be even more apparent with a non-blind shove.

Many pros said they would only call with AA. If I shove AA preflop and only get called by AA, there is NO chance of a set, right? Clearly then, preflop action does have some effect.

I’m not saying that preflop action will influence the distribution of cards. Theoretically, you always have the same chance. But here in reality land, preflop action not only influences the number of flops you will see, but also influences the cards you will be facing when you do see the flop.

So yes, preflop action is skewing my results to some extent.

Ref: Ask the Pros: Are You Calling a Blind Shove First Hand of the WSOP Main Event?

Well said SPG.

I almost used the AA example as it most clearly shows how preflop action can alter our perceptions.

If I always go all-in with AA I will not see a big percentage of flops because the table often folds. But when I do see the flops it is more likely someone is holding a hand with an ace(AA, AK, AQ). So my percentage of sets flopped with AA will probably be smaller than the math suggests.

Yet another set flopping update…

So far, I have seen 498 flops while holding a pocket pair. I have made (or would have made) 61 sets. This gives us (61/498) X 100 = 12.25%. Statistically, it should be 11.75%, for a difference of 0.5%.

The percentage is swinging back and forth around the statistical expectation. Sometimes it’s a little under, sometimes a little over. So far, I haven’t seen it off by more than would be expected with this sample size.

I’ll keep collecting the data until I get to 1,000 instances. I’m about half way there!

Last set flopping update before final results…

So far I have had 741 pocket pairs where I have seen the flop. I made (or would have made) 87 sets. Note that i say (would have made) because there were times I folded my pair, but got to see the flop anyway.

So (87/741) X 100 = 11.74%. Statistically, it should be 11.75%, for a difference of 0.01%.

I’m tempted to call it here and say that, for this aspect of the game, the pRNG is spot on, but I guess I might as well motor on to the finish.

3/4 of the way there!

Set Flopping: Final Report

I have now had 1023 pocket pairs where I have seen the flop. I flopped or would have flopped 120 sets. This gives: (120/1023) X 100 = 11.73%. (I also flopped quads once, which I didn’t count)

Statistically, you will flop a set when holding a pocket pair 11.75% of the time, for a difference of 0.02%. Here’s the raw data…

It’d be interesting to calculate how well distributed your sets are by rank. That is, you should see 11.75% of your pairs make a set regardless of the rank of the pair. It seems 33 hits a set more much more frequently than AA, though.

The sample sizes are way too small to draw any meaningful inference. In general, you need to take the square root of the number of trials to get a ballpark estimate of the standard deviation; since almost all of these “mini-experiments” have fewer than 100 trials, your standard deviation is going to be in the same realm as your expected value.

You could as easily comment on the relative rarity of being dealt 22-44 compared to TT+. It’s far likely to be a quirk of the data than anything meaningful.

Of course. I’m just trying to encourage SPG to continue collecting data until he has 1000 pocket pairs of every rank. That will keep him busy a while