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#1
10-04-2006, 03:01 AM
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KK ran into AA 4 times in a row - NOT a bad beat post
In the last 5 days I have been dealt KK 4 times. Each time I have ran into AA. Now I've been playing long enough not to be worried about this sort of thing (anyway, I sucked out the fourth time [img]/images/graemlins/smile.gif[/img]) but it got me thinking about how unlikely it is, and I realised I was not sure how to calculate the probability of this happening.
Is my simple method correct?... It is approximately 20 to 1 to run into AA when you have KK at a full handed table, so I simply multiplied the 20 to 1s together. So the odds of having KK run into AA the last 4 times I had KK would be (20x20x20x20) to 1. This is 160,000 to 1. Is this the correct method? 160,000 to 1 is rather a long shot, and I wouldn't believe anyone who told me it had happened to them, but there you go... 
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#2
10-04-2006, 09:13 AM
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Re: KK ran into AA 4 times in a row - NOT a bad beat post
Yes for a given run of 4 KKs this is mathematically correct (taking your word on the 1/20 stat).
However, there are some deeper problems with the general procedure of noticing something unusual and then afterwards calculating the odds for that event only. The problem is that there may be quite a few "surprising events" that you would have found highly unusual and which might have made you post at 2 plus 2. For example, what if the 4KKs vs. the AAs had been last month and not in the past 5 days? What if you had had 4QQs and faced KKs each time? Or what if you had flopped boats vs. quads four times? Etc? And then after one of the remarkable events happens, you calculate the probability only for that particular event, and find that it is very low. A better measure of "unlikeliness" is to *first* write down *all* the events that you would consider unlikely, and the measurement period, and then afterwards calculate the odds.
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#3
10-04-2006, 09:42 AM
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Re: KK ran into AA 4 times in a row - NOT a bad beat post
[ QUOTE ]
In the last 5 days I have been dealt KK 4 times. Each time I have ran into AA. Now I've been playing long enough not to be worried about this sort of thing (anyway, I sucked out the fourth time [img]/images/graemlins/smile.gif[/img]) but it got me thinking about how unlikely it is, and I realised I was not sure how to calculate the probability of this happening. Is my simple method correct?... It is approximately 20 to 1 to run into AA when you have KK at a full handed table, so I simply multiplied the 20 to 1s together. So the odds of having KK run into AA the last 4 times I had KK would be (20x20x20x20) to 1. This is 160,000 to 1. Is this the correct method? [/ QUOTE ] Not quite. If it were 20-to-1, that would be a probability of 1 in 21, and you would multiply 21*21*21*21 to get the probability, and then subtract 1 to get odds, since you multiply probabilities not odds. The actual number for a 10-handed table is 21.8-to-1 as shown here, so you would take 22.8*22.8*22.8*22.8 - 1 =~ 270,233-to-1. [ QUOTE ] 160,000 to 1 is rather a long shot, and I wouldn't believe anyone who told me it had happened to them, but there you go... [/ QUOTE ] While this is very unlikely for any 4 specific hands, it is almost guaranteed to happen over enough hands. Remember, extremely rare events happen all the time.
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#4
10-04-2006, 10:03 AM
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Re: KK ran into AA 4 times in a row - NOT a bad beat post
it appears you guys are working out the chances of this happening the next 4 times, not the last 4 times.
the last 4 times = 100%
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#5
10-05-2006, 09:16 PM
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Re: KK ran into AA 4 times in a row - NOT a bad beat post
One other question. You say you were dealt KK four times, is that exactly correct? Or are you neglecting hands where you were dealt KK and you didn't see any other hands? That would raise the probabilities considerably since AA is certain to stay in preflop and likely to stay until showdown; while hands in which no one has AA are more likely to be folded to you. It's not a night-and-day difference but it would change the probabilities some.
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#6
10-06-2006, 12:39 AM
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Re: KK ran into AA 4 times in a row - NOT a bad beat post
I saw something more rate last week at Hustler 4/8.
A single player got AA 3 times in succession (and they held up all 3 times). If I'm not mistaken that is 10,793,860 to 1 221*221*221 - 1 to 1 Though since they did hold up each time, and AA holds up approx 33% of the time in a limit game, would that mean that it was 221*221*221*3*3*3 - 1 to 1 =~ 291,434,246 to 1 ? ? AB
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#7
10-06-2006, 02:43 AM
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Re: KK ran into AA 4 times in a row - NOT a bad beat post
Eliminate the first set of aces, the first 221. You would have started the count if ANYONE at the table had gotten the aces three times in a row.
So what are the odds that anyone would have been dealt aces (how many players were at the table) then continue with the 221 etc. (response to alien boy)
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#8
10-06-2006, 03:01 AM
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Re: KK ran into AA 4 times in a row - NOT a bad beat post
[ QUOTE ]
I saw something more rate last week at Hustler 4/8. A single player got AA 3 times in succession (and they held up all 3 times). If I'm not mistaken that is 10,793,860 to 1 221*221*221 - 1 to 1 Though since they did hold up each time, and AA holds up approx 33% of the time in a limit game, would that mean that it was 221*221*221*3*3*3 - 1 to 1 =~ 291,434,246 to 1 ? ? AB [/ QUOTE ] There were 10 people to the flop every hand?
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