Starting hand odds at PP

I have a question about the odds of being dealt certain starting hands in Hold Em. I tracked 50 consecutive tournaments ($5, $10 and $20), 2680 hands, at Paradise Poker and here is what I was dealt:


114 pairs (23.5-1 odds)

432 aces (6.2-1)

583 suited (4.6-1)

81 suited & connected (33.1-1)


Now, according to Warren's book (Winner's Guide To Texas Hold Em) these are the actual number of hands I should have been dealt:


167 pairs (16-1)

470 aces (5.7-1)

825 suited (3.25-1)

101 suited & connected (26.6-1)


Warren doesn't list odds for the following types of hands I was dealt, but I'll include them hoping someone can provide me with the expected odds:


173 two face cards, A-J (15.5-1)

432 connected (6.2-1)


First of all, are Warren's numbers correct? I'm not concerned with the numbers not adding up exactly, but I am wondering why I am being dealt fewer hands than expected in every category.


Second, I'm not asking this because I'm looking for a place to vent about losing. I'm actually doing pretty well, but I could obviously be doing better if I was getting better starting hands.


Third, I know this is not a scientific study, but I would certainly think that over the course of 2680 hands I would have been dealt more than the average number of starting hands in at least one category. Am I leaving out any important categories? If so, let me know and I can provide the numbers for them.

I'm trying to do this right now actually with my own hands! How did you count? Maybe you missed some hands, if not, I have some other ideas of what might be wrong...


- Tony

Wow! Aren't you supposed to be dealt MORE hands in those kind of categories at PP? That's what Doug Duke has always assured me.


Here's an idea from the crazy, but it just might work category: MAYBE YOUR SAMPLE SIZES ARE JUST NOT LARGE ENOUGH AND OVER THE LONG RUN EVERYTHING EVENS OUT.


Chris

Answering two questions from different people here...


How do I count? The old-fashioned way. I keep track of all the hands on paper. I just write them down as they're dealt to me. I have about 30,000 hands from tournaments and regular raked games going back several months. I also keep notes on things like being re-raised pre-flop with AKs by a guy with 72o and seeing the board hit A-K-7-7-2. In the long run I'd love to keep playing that guy, but that was a painful loss.


As far as the sample size, yes it's pretty small. But it's a small sample out of a much larger pile of written data that I just haven't had the time to add up yet. I do have one done: The total number of pairs dealt to me in 9650 tournament hands (about 200 tourneys) is 437. That's 22-1. At the expected odds of 16-1 I should have had 603 pairs. That's quite a shortcoming. I am expecting a windfall of pairs any day now. /images/smile.gif


But like I said originally, I'm not posting this as a complaint. I'm just posting my observation that it's strange that I'm seeing a deficit in every starting hand category.

You need to do some more math to convert your data into worthwhile standard deviation (SD) stats. Math always looks ugly through a keyboard but here it is starting with the pairs:


Actual = 114 Expected = 167 16-1 needs to be turned into a decimal of 1/17 = .059


Sample SD = SQRT(2680) x SQRT(.059 x (1 - .059))


= 12.2


Now calculate the number of SDs by which your sample varies:


167 expected - 114 observed = 53

53 / 12.2 = 4.3 SDs below expectation.


What this means:


1 SD - shouldn't raise an eyebrow

2 SD - I would be curious, would check another batch of data

3 SD - highly suspect, something is not right.

4+SD - Experiment or hypothesis is way wrong.


Now you go do the others and report back here.

You have odd's and probability confused.


For example, 16-1 against getting a pair means you have a 1/17 chance of having one, which means you should have expected to see 1/17*2680 pairs, which is about 158. So Warren's numbers are right, but your application of them isn't.


Further, the odds you should have calculated for seeing your pairs are (1 - 114/2680)/(114/2680) = 22.5-1 against. You did 2680/114 and called that your odds.


Still, I did the math with these corrections, and you received many fewer pairs than you should have (I'd double check my counting methods to make sure I really am marking down every pair). However, you received more Aces than you should have. Warren says you should receive about 400 aces (1/6.7 * 2680). You received 432.

Wow! Are you and Tony oblivious to how transparent your motives are? My goodness, but can it be you’re both immune from embarrassment? Can it be that your obsessively vigilant monitoring of this forum only appears to be damage control duty, but isn’t? How quickly you pounce. No time for a cup of coffee and a cigarette, I guess, when your ship has a whole in it.


However, it doesn’t matter where you’re coming from; your posts can be considered on their merit. Unfortunately, they don’t have any. Tony says, “Maybe you missed some hands, if not, I have some other ideas of what might be wrong...” I infer that he means something is wrong with TW’s numbers, his method, or him, but not possibly Paradise. Not exactly an open-minded approach.


Your response, ChrisVWH, has even less merit, which can only mean it has negative merit. You simply shouted in Tw’s face, as well as other readers’ faces and mine. It’s like you don’t have anything to say, but you’re going to shout it out anyway because you gotta plug those leaks. That’s a good job?


One more thing: Please don’t respond with another whiney “poor Chrissy” post about how you’re so tired of reading about paradise’s integrity. It’s insulting that you could think anyone buys that.


Tom D

I calculated 52!/2!(52-2)!= 1,326 ways to choose 2 cards from 52. I calculated 48!/2!(48-2)! = 1,104 ways to choose 2 card from 52, leaving 222 ways to choose 2 cards from 52 that contain 1 or more Aces.


222/1326 = 0.1674

0.1674*2,680 hands = 448.69 two card hands with at least 1 Ace.


I did something wrong?


Tom D

48!/(2!(48-2)!) = 1128, not 1104. I suspect you actually got 1104.5, but you let it slide instead of trying to find your mistake.


That gives 198 hands with AT LEAST one ace.


Odds : (1-198/1326)/(198/1326) = 5.7:1 against it happening.


Prob : 198/1326


E(number) = 198/1326*2680 ~= 400. If you want to compare your numbers to Warren's numbers, don't forget to count AA as a pair, AND as a hand with an ace.

I didn't read the entire thread. However C(48,2) or "48 choose 2" (The number of combinations of 2 taken from 48) is 1128, not 1104.

About 1 billion more sample hands and you can make an accurate comparison. I have written blackjack simulation engines numerous times and recorded all the data. It is common to still be 5% off in some areas after several hundred million hands and then begin to drift into what the math says it should be.

Are you sure you're not missing any pairs?


Or overcounting the number of hands you've played and were DEALT CARDS in?


Just some things to double check. Both would account for the lack of pairs! /images/smile.gif


- Tony

Ah, thank you for the informative response. I now realize my mathmatical mistake so I'll make sure to do it right when I complete my analysis. I'll post the results hopefully in a few weeks.


So, how many hands would you folks consider sufficient for a fairly accurate statistical analysis? If I play at PP for 5 years at the speedy rate of 60 hands/hour 10 hours a day 365 days a year (whew!), that would bring me about 1 million hands. Enough? Remember, I want real world stats here, not numbers from simulations.


I knew I would draw some fire (this place is no different than Usenet), but man, I need to get my asbestos suit back out of mothballs if I'm going to continue to post here. /images/smile.gif

The asbestos suit is only needed if you dare to besmirch Paradise. A lot of posters have a ton of capital (monetary, time-wise and psychic) tied to Paradise and will defend it blindly to the death.


Re sample size, if you use my calculations any sample size can provide information. Bigger is, of course, better but the value goes up with the square root of the size. A 10,000 item sample is only ten times as valuable as a 100 item sample.

It wasn't that long ago that PP posted here under the Paradise name to defend themselves. My guess is that they still do.

Wow! Are you and Tony oblivious to how transparent your motives are? My goodness, but can it be you’re both immune from embarrassment? Can it be that your obsessively vigilant monitoring of this forum only appears to be damage control duty, but isn’t? How quickly you pounce. No time for a cup of coffee and a cigarette, I guess, when your ship has a whole in it.

---------


I had to read that paragraph 3 times before it made any sense, but eventually I figured you must think I'm employed by Paradise in some kind of damage control capacity. Well, I live in Australia, as you could tell by having a look at my IP back when 2+2 published IP's with the messages. But then, I guess nowhere is safe from the long arm of Paradise, right?


------

Your response, ChrisVWH, has even less merit, which can only mean it has negative merit. You simply shouted in Tw’s face, as well as other readers’ faces and mine. It’s like you don’t have anything to say, but you’re going to shout it out anyway because you gotta plug those leaks. That’s a good job?

------


I didn't intend to shout in his face at all, although it might have come out looking like that. It just amused me how well this post complemented Doug Duke's ramblings. Both small sample sizes and with completely opposite results. Meanwhile, I still haven't seen any posts with large sample sizes from people running programs like Pokerstat. Why?


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One more thing: Please don’t respond with another whiney “poor Chrissy” post about how you’re so tired of reading about paradise’s integrity. It’s insulting that you could think anyone buys that.

-----


I don't expect you to buy anything of what I say. I remember you arguing that even though the 1 million flops published by Paradise showed random DISTRIBUTION, that didn't mean they were random. It just meant that Paradise had rigged all of the one million flops not only to meet their nefarious deck-stacking plans, but also so that the million flops would still have random distribution. It's clear you don't have any interest in what the most likely explanation is. It's impossible to convince anyone of ANYTHING when they take a position like that.


Chris

Lemme help, I think I've got a handle on this thing....


I've taken a sample of 10 hands from PP and two of them were pairs.


Sqr(10)*Sqr(.059*(1-.059)) = 0.176


Expected 0.588 - 2.0 = -1.411 = 8.02 SD's.


Wow. Ugly! Something is obviously crazy wrong here. It must be totally impossible to be dealt 2 pairs in ten hands.


Standard deviation does NOT tell the whole story here. Much larger deviations are possible over smaller samples. You need to do a significance test, which I once knew how to do but have forgotten.


Chris

I must agree with you Doug, once again.


For those (like myself) who are analyzing the Paradise BOARDS for "juiced flop" conditions, ie too many big pairs, big co-ordinated cards, trips, straight and flush combos, etc. on the boards, it makes sense that lesser co-ordinated starting hands would be going to players, in order to increase the juice of the flops. However, not to the extent indicated in the original example.


Hmmm, maybe the theorists who postulate that "winners" are getting penalized with crappier cards after good runs up are on to something after all??


In any case, I agree with Doug. The "Cultist" closed minded, rigidly dogmatic, mindset here is not coming from conspiracy theorists. It is the knee jerk defenders of PP.


Since Paradise extended a phony offer to have their software algorythyms, servers, etc. examined by an interested expert, and then retracted their offer when he called their bluff, (check archives, some know what I am talking about), then why does the ancient history PP "million boards" give anyone comfort about what is happening now?


And who ever did the number crunching on those millions boards anyway, and now has the analysis of percentage boards that came 4 of one suit, trips, fulls, quads, straight combos, etc for us to compare to expected stats on those boards? I'd love to see THAT data.


Do YOU have that analysis info ChrisVHW? You DON'T have it? Gee, what a shock..... And here you seem so certain and all.


If Enron can cook books as they did under the noses of legislators, auditers, Justice departments, Boards of directors, share holders, etc etc etc...


Then pray tell what is to stop an offshore, unregulated, unaccountable, handful of website owners from doing whatever the hell they want to increase their "take" from a site that see millions in play "transactions" flowing through it daily?


Geez PP vested interest types, must laugh their asses off, when they see how well controlled their littl band of mindless monkey "defenders" behaves.


Let's see the consecutive boards from 2001 on a few tables, analyzed for co-ordinated cards, straight and flush combo frequency, big pair vs. small pair ratio, 5 big board card vs. random expected, etc etc. Get that info in valid form, open the software to a truly independent audit by a genuinely unbiased thrid party. Yeah, Abbadon freezes over.

"Let's see the consecutive boards from 2001 on a few tables, analyzed for co-ordinated cards, straight and flush combo frequency, big pair vs. small pair ratio, 5 big board card vs. random expected, etc etc. Get that info in valid form, open the software to a truly independent audit by a genuinely unbiased thrid party. Yeah, Abbadon freezes over."


I'm working on the board analysis. Starting card analysis is done, and has been done by others. But I agree, there's no way to get 100% proof without an independent audit by an unbiased third party.


People who believe it's not rigged, will still believe it's not rigged, after a flop and board analysis, irregardless of the outcome of that analysis, and vice versa.


- Tony

I couldn't agree more. If Paradise is so sensitive about bad-press chat (I'm not saying they're wrong, btw) that they ban subversive players, I can't see them silently ignoring the discussions on this forum.


If you think about it, it's amusing. Since Paradise doesn't have the ability to ban people from this forum like they can on their site, they're left to find other ways to quash the turbulence here. One method they could have thought of would be to try to abuse and ridicule anyone and everyone who even hints that there could be something wrong.


Tom D

A man convinced against his will is of the same opinion still!