View Full Version : Multiple pairs in the hole

11-30-2004, 10:54 AM
Not sure about all the rules here, so I will refrain from mentiontioning names.

Over the past 3 months, I observed that multiple players are dealt big-card pairs in the hole in an online poker site. For example if one player is dealth TT, there would be two other players with pairs higher than TT. This happens about 20%-25% of the time a large pair is dealt in the hole. Have seen this occur atleast a dozen times in 3 months.

What are the probabilities of that, and do all online poker random-generators have this problem?


11-30-2004, 01:04 PM

First of all, it is highly unlikely that there is a "problem" with one of the larger site's random number generators. I don't know how often you play, but seeing 2 or more big pairs dealt in a single hand a dozen times over a few months is not very strange at all.

Here's how you calculate the chance that two players will both be dealt a big pair (TT or above) in a full ring game:

There are nCr(52,2) = 1326 possible holdem hands. Of those, 30 are big pairs. So, the chance of exactly two big pairs is:

nCr(10,2)*(30/1326)*(29/1325)*(1297/1324)*(1296/1323)*(1295/1322)*(1294/1321)*(1293/1320)*(1292/1319)*(1291/1318)*(1290/1317)= 1.83%, or about 1 hand in 54

Similary, the chance of exactly 3 big pairs is:

nCr(10,3)*(30/1326)*(29/1325)*(28/1324)*(1297/1323)*(1296/1322)*(1295/1321)*(1294/1320)*(1293/1319)*(1292/1318)*(1291/1317)=.0005, or 1 in 2000 hands.


11-30-2004, 09:29 PM
In your calcs I think the number of non high pair starting hands would start at 1296 (1326 - 30) not 1297, so it is a little less likely then your calculations end up with. But your point is well taken - it's not too unlikely to see 2 or more high pairs in a single hand at a full table. I see it in live play often enough.

Sorry for snapping in another thread.

11-30-2004, 10:53 PM
In your calcs I think the number of non high pair starting hands would start at 1296 (1326 - 30) not 1297,

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You're right, though it affects the calculation only by 1/100 of a percent: 1.83% becomes 1.82%.


12-01-2004, 01:28 AM
Happened just the other day at Foxwoods KK vs QQ vs JJ. Everyone went all in and KK held.

12-01-2004, 03:30 AM
Thanksgiving w/e . . . QQ vs. QQ -- board shows AKT by the end, but neither of us had the cajones to bet and drop the other.