Pocket Pairs

Last night I wrote about the statistical anomaly that was getting dealt pocket 10's 5 times in 84 hands.

Tonight I've played 309 hands, and these are the pairs that I have had:

AA x 1
KK x 1
QQ x 1
JJ x 1
TT x 2
99 x 1
88 x 2
66 x 2
55 x 1
44 x 4
33 x 1
22 x 4

That's a total of 21 sets of pocket pairs. Given that a pocket pair is dealt every 17 hands, I should have expected to see 18 pairs in my hole cards - so this is only slightly above average.

However, once you have been dealt a pair, you expect to improve to a set, on the flop, one in every 9 times you have a pocket pair (actual odds are 77/10). So, for my 21 sets of pocket pairs I could have easily expected to hit twice, and optimistically have expected to catch three-times.
Not a sniff, in the 21 times I have had a pocket pair I saw 18 flops (folded Deuces twice, and got a walk with Kings) and didn't hit a single set.

Also, you would expect a reasonably even spread of the pairs hit, but 17 out of the 21 pairs were 10's or below. I only had AA, KK, QQ or JJ once each and was dealt Deuces and Fours 4 times each and Sixes, Eights and Tens twice each - a bit lop-sided.

Maybe 309 hands is not a big enough sample, but you have to feel pretty aggrieved to be defying the odds so badly.

*FINAL UPDATE*

I played a total of 610 hands:

AA x 3
KK x 1
QQ x 4
JJ x 1
TT x 4
99 x 2
88 x 3
77 x 3
66 x 6
55 x 2
44 x 4
33 x 2
22 x 4

I saw a total of 39 pocket pairs (and additional 18) - when statistics say 36 is about right, so still just above average.

I saw the flop with 16 of the 18 recent pairs (got a walk with QQ and folded 66 pre), making a total of 34 flops with a pocket pair and I finally hit a set with pocket 6's on hand 515.
That's 1 set on 34 flops with a pocket pair - almost 4 x the average.

Realistically, I should have expected to see a set a minimum of 4 times from 34 flops - so just 1 is an atrocious return; no wonder I couldn't make any money this evening.

I did get Aces 3 times, and won every pot I was in with them - I also won the pot with the 6's where I eventually made a set. I got a walk with Kings and once with Queens, but lost every other pot I was in with a pair. That's 33 flops, probably 13 of them I flatted and the other 20 were calls, so that's approximately $0.65 in limps and at least $3.00 in calls - so my action with pocket pairs cost me in the region of $3.65 (probably more, as I can remember continuing after the flop with a couple).

I ended the session $3.06 down - so if I had not bothered calling with anything less than QQ, I would probably have made a small profit. Something to think about!