This is a discussion on AA versus KK versus QQ within the online poker forums, in the General Poker section; I must apologise to Titan  after berating them for always coming up with this little confrontation, I ran into the same on Full Tilt 


#1




AA versus KK versus QQ
I must apologise to Titan  after berating them for always coming up with this little confrontation, I ran into the same on Full Tilt last night. I've now seen it twice in the last couple of weeks, and it happened in the last Cardschat Titan tournament (which I didn't play in). Anyone want to have a stab at the odds? Of course, it depends on the number of players playing (the lower the number of players, the less likely it is to occur), but here is my stab at the maths assuming an average 7 player table;
Likelihood of being dealt AA, or KK or QQ = 220/1 each. 220 x 220 x 220 = 10,648,000. Number of different 3 player permatations on a 7 player table = 35. So 10,648,000 / 35 = 304,228/1 Have I got this right? The 2 I saw in the last fortnight were on 5 player and 6 player tables, so the odds will be higher. Maybe I should start with the odds of being dealt either AA KK QQ, then times that by the odds of getting one of the remaining 2 pairs, and finally times by 220 for the last pair, but I cant reconcile this with the number of permatations of different players. Even doing it this was makes if over 80,000/1. I'm positive i've posted before about the occurance of these 3 hands at the same time before, so this seems to PROVE that Pokersites are juiced!? Is anyone else noticing these hands, or is it just me? 
#2




I've also begun to think some Poker sites have a problem with reality, but I'm trying not to bring myself to say "juiced" or "rigged". I subscribe to the less popular notion that many Random Number Generators that are used are either flawed or antiquated.
It is sort of like when you have your 10CD changer/player on "Random" mode and it plays 3 or 4 songs (maybe even consecutivelylisted songs) from the same disc before moving on to the others. I'm of the belief that it is currently not possible to duplicate the exact effect of a real card shuffle. Maybe in the future, but not now. I think they're workin' on it, though. 
#3




The first hand would be (12/52*3/51)=1.4% (any of AA, KK or QQ), then (8/50*3/49)=0.98%, and then finally (4/48*3/47)=0.53%, so then timed together and multiplied by the permutations would give slightly better odds than that of about 74000/1, which is still unlikely, since you'd then expect to see it on average once in over 10,000 hours of play.
I wouldn't be at all phased to see it happen on one site once, or another once... twice at the same site would be a more freak occurence, although you'd also have to bear in mind that with sites dealing sometimes 100,000's of hands a day, they could still be very uncommon and you just happen to be at the table where it hits the next time by some fluke and that would be a fluke but little evidence of site rigging. As an aside, some people hold up AA vs KK as evidence of site rigging, but following the same chance * chance * permutation calculation, that's (at a full table) 0.9%*0.49%*45, so you'd expect to see that about once in every 500 hands? So thats a couple of times a week or more for most of us on here? Using similar calculations, when you are holding KK, then you'll be up against AA in less than one in 20 hands... not often enough to count on it happening, but often enough that getting done in by it will probably happen to you sooner or later. 
#4




With regards doing a random shuffle, the standard random number generators which you get in standard development libraries like VB are very flawed, and nowhere near good enough for this kind of job. However, there are reasonable RNGs, and also some random number generators that are far more random than any card shuffler would manage with a real deck of cards  especially ones which use numbers generated from using atomic decay or other highly random sources as a seed value.
Some sites do not produce proof of the randomness of their cards  no independent auditors reports for public consumption, but while some sites do not verify their randomness, that doesn't mean that genuine random number generation is not possible. Additionally, over a long enough period of time, 'unlikely' occurrences are statistically likely to happen at some point  the longer you've played the more likely you are to see one of these unlikely events. One common misconception is that if it were truly random that a very unlikely event would not happen twice close together... if it is truly random, then if you take a sample of, say 100,000 hands and expect the event to happen twice, you'd look at those hands and expect to see around 2 occurrences, but you wouldn't expect them to be 50,000 hands apart  they're equally likely to have happened exactly 1 hand apart as 50,000 hands apart. 
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#8




yeah, a lot of people think the odds of getting aa then aa then aa then aa then aa all in a row will make it less likely to happen again the next hand.
hands are independent of eachother. and yes, RNG's for the most part are very flawed and not random at all. on a side note, my AJs once beat AA and JJ when we were all allin. 
#9




At a 7 player table I believe the calculation are as follows
(((52/4)*(51/3))/7) for the first pair multiplied by (((50/4)*(49/3))/6) for the second pair multiplied by (((48/4)*(47/3))/5) for the third pair for a total of roughly 1 out of every 40394 deals. But did the queens win both times? 
#10




re: Poker & AA versus KK versus QQ
It's been a while since I jacked around with the math, but here goes.
1st Ace 4/52 = .0769 2nd Ace 3/51 = .0588 1st King 4/50 = .0800 2nd King 3/49 = .0612 1st Queen 4/48 = .0833 2nd Queen 3/47 = .0638 Multiply the odds of each one of theses events to derive the odds of the combined event = .000000118 = 1/8,482,716.6666 This would be the odds of calling this shot beforehand for any three players, but at a full table of 9, and this is where I may need some help, I believe the odds of this event occuring are at least 3 times greater or 1/2,827,572.2222. Still a big number. But how unusual is it? To put it in perpective it is about 39 times less likely than being witness to a Royal Flush. I play about 2000 hands per month including tournaments or about 24000 hand per year, lets just call it 28,275. I should see this event occur about once every 100 years. I've already filled my quote for this century, but with 10,000 members, if everyone at cardschat played the same amount as me, this rare event should occur about twice per week. Funny, I've seen 3 or 4 royals in the last year. That's about 12 more than I should have seen. I'm sure I must have made a mistake somewhere. 
#11




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AAAAAARRRRRRGGGGG!!!!!! NOT THE AA TWICE IN A ROW THREAD AGAIN! 