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This is Random?

This is Random? - Sat Nov 24, 2012, 09:24 AM
Jcrondps's Avatar
Since: Jun 2010
Posts: 147
Here are 2 hands from a MicroMillions Satellite I was playing. They are 7 hands apart.

Hand 1:

Hand 2:

Anyone care to calculate the odds of an overpair being beaten by and underpair improving to quads twice in 8 hands? No wonder there are so many conspiracy theorists. If this happened live, there would be a riot.

Last edited by Jcrondps; Sat Nov 24, 2012 at 09:28 AM..
Sat Nov 24, 2012, 11:38 AM
bearxing's Avatar
Since: Jun 2010
Posts: 499
Let us start by calculating the approximate odds of getting quads in this way. 1 1ne in 17 times you get dealt a pair. Once every 8 times you improve to a set. Once in 47 times your set improves to quads on the turn. Odds to make quads are one in 17*8*47=6392. There are 9 players on a fullring table, so the odds of somebody having quads in this way is 6382/9=710. The eight other players each have a one in 17 chance of having a pair. So a little less than half the time there are quads, there will be another pair, or about 1 in 1450. Half the time it will be smaller or one in 2900. To have it happen again, within eight hands is 2900*2900/8=1051250.

So it is about a million to one chance. PokerStars has dealt nearly 90 billion hands. A million to one shot has happened many times. You just happened to see one of them.

Good luck

3 Time Bracelet Winner

Sat Nov 24, 2012, 11:49 AM
Ovalman's Avatar
Since: Feb 2011
Posts: 1,778
It's just as we're human we try and identify patterns, I'm sure if I looked over my 300,000 hands stored on my PC I could see similar odd hands.

Nicely worked out Bear, I'd have imagined the odds to be higher but just goes to show that any card combo will happen if you get a big enough sample.
Sat Nov 24, 2012, 01:45 PM
Jcrondps's Avatar
Since: Jun 2010
Posts: 147
I didn't check your math but, assuming it's correct, if you correct from a full ring to a 4 handed table, the odds change to 1 in 40.7 million.

I guess I should buy a lotto ticket because my odds of winning are better than that.
Sat Nov 24, 2012, 02:14 PM
Jcrondps's Avatar
Since: Jun 2010
Posts: 147
A little further consideration on the 4 handed table takes the odds closer to 1/178,321,612

I believe your initial math to be correct but you have to account for the 3/17 chance someone else has a PP and the 24% of the time someone has a higher PP at a 4-handed table.


6382/4 = 1595.5

ans/.176 = 9065

ans/.24 = 37770


Odds are approximately equal to the above number, 1/178 million.

I'm going to ride my winged pig to get that lotto ticket.
Sat Nov 24, 2012, 02:31 PM
EdinFreeMan's Avatar
Since: Feb 2010
Posts: 4,540
I have no idea about the maths here - but to me the fact that you saw this happen epitomises randomness. Just like my getting AA two hands in a row in the last half-hour. It doesn't happen often, when it does we notice.

If these things never happened then I would really worry about the randomness.

If anyone watches QI, in a recent episode the host Stephen Fry shuffled a pack of cards and claimed, backed up by statistics, that no pack of cards had ever been in the same exact order before in the history of the world.

Now that did my head in...


4 Time Bracelet Winner

Sat Nov 24, 2012, 03:50 PM
Jcrondps's Avatar
Since: Jun 2010
Posts: 147
Sure these things happen but everyone has the defense of "90 Billion hands". No one player has seen all 90 billion hands so the stats should still reflect the number of hands that player has seen and not the full 90 billion.

The 90 billion hand logic would mean that I could have seen this roughly 450 times (about 5 times per billion hands) and it would still be acceptable. However, if this happened even more than once in the few hundred thousand hands I've seen, it would be a statistical anomaly.

On a side note, I guess if you factor in a Russian's chance to suck out and a Canadian's chance to be sucked out on, the odds work out to approximately 1/8.
Mon Nov 26, 2012, 05:39 PM
Grade b's Avatar
Since: Jun 2010
Posts: 3,607
Hi Jcrondps,

A truly random event does not take into account any of the events that go before it.

The "classic" proof or explanation of this is found in the follow.

If you spin a perfectly normal coin 100 times and it comes up heads every time what is the chance 101st spin will be heads.

Grade b

I am always ready to learn although I do not always like being taught. ~Winston Churchill

13 Time Bracelet Winner

Last edited by Grade b; Mon Nov 26, 2012 at 11:36 PM.. Reason: added word "chance"

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