Odds questions for you experts

[djoyce003]

Hey guys. I have a couple of questions for you based on some extremely weird happenings in my games last night.

Question 1: what are the odds of three different people having pocket pairs and flopping trips. Trip Kings, Jacks, and 5's on the flop, everyone having pocket pairs of the above.

Question 2: What are the odds of someone having the exact same pocket pair as you.

Question 3: What are the odds of flopping a straight flush. A-5 straight flush after the flop.

[TheHip41]

Not good. Set over set over set is exceedingly rare, and painful unless you have top set /images/graemlins/grin.gif

[Bez]

Same pocket pair: 50 other cards for any other player so 1/50*1/49 = 1 in 2450 per player therefore 9 times out of 2450 at full table I reckon.

[Slick Al]

I am by no means an expert, but let's see if I can get close here for you:

1. Flopping trips x 3. There are 6 cards (remaining 2 of each value) out of 46 cards (since we know 3 pairs). So with those assumptions, the odds would be:

6/46 * 4/45 * 2/44 = .000527, or approx 1 in 1897.5

(1 out of the 3 hits trips, 1 out of the 2 remaining hits trips, last person hits trips)

2. This one I'm not positive about, but here's my thoughts. We know you have a pocket pair, and let's assume it's a full game (9 other people, this matters). So that gives 9/50 for one of these people to hit one of your cards, then 1/49 for that person to hit your other card.

9/50 * 1/49 = .003673 or 1 in 272.22

I'm really not sure about that calculation.

3 - Well, the odds of a A-5 straight flush coming would be (assuming you have no cards in the A-5 range nor do you know about any of them):

20 cards for the first one (A-5 x 4 suits)
4, 3, 2, 1 card respectively (remaining A-5 of that suit)
so, if you are in the hand, and know your two cards, it's:

20/50 * 4/49 * 3/48 * 2/47 * 1/46 = .0000018879 or 1 in 529690

if you don't know any of the cards (spectator, or just dealing 5 cards off the deck for example, it's

20/52 * 4/51 * 3/50 * 2/49 * 1/48 = 1 in 649740

Hopefully I did that right.

Al