What are the odds ?

[EvilPie]

636763050:1

If i was on my pc I'd show some kind of working.

Seeing as I'm on my phone I won't bother....

Basically you can remove one random card so we're dealing with the remaining 51.

We then need to hit 8 specific cards so 8/51 * 7/50 * 6/49

You get the idea.....

Seems a ridiculously high number but I can't figure how it can any different?

[Tal]

The aces and the jacks can be in any order, so the odds are better than that.

Still haven't been bothered to do all the maths, so sorry!

[EvilPie]

Thought I'd covered that by saying we've got 8/51 to hit then 7/50 etc......

Might be wrong obviously but can't see how right now.

[Tal]

I'll get a fag packet and a BetFred pen and work out you're right later.

[cambridgealex]

im doing some simple maths for open face chinese and my brain is being painfully tiresome with things that are very basic i'm sure.

If someone could answer this, with working, I'd be very grateful.

There are 8 cards dealt to 4 players A,B,C and D, so two each. Two of the 8 cards are picture cards. What are the odds that player A gets AT LEAST one picture card?

[edgascoigne]

im doing some simple maths for open face chinese and my brain is being painfully tiresome with things that are very basic i'm sure.

If someone could answer this, with working, I'd be very grateful.

There are 8 cards dealt to 4 players A,B,C and D, so two each. Two of the 8 cards are picture cards. What are the odds that player A gets AT LEAST one picture card?

Well player A's first draw sees him have a chance of 2/8.

If he hits (which happens 25% of the time) he is then 14.2857% or whatever it is to hit the next one). As such the chance of Player A scooping the two picture cards is x*y= 3.6%

He gets a couple of goes at getting one of the two. Calculated as:

 .75 (6/8 to brick)*.286 (2/7 to hit)= 21.43%
.25 (2/8 to hit) * .857 (6/7 to brick) = 21.43%

Sum them up and you get 46.46% chance of getting at least one picture.

[Karabiner]

In the old days at Gala Nottingham of self-dealt tourneys I once witnessed a hand where the flop was 9, 7, 3 and after much raising and shoving I folded my pocket 66 and the cards went on their backs.

Player A had 99, player B had 77, and player C had 33.

The turn was the case 3 and the river was a 6 !!!

Player C was none other than tikay and I would have thought that the coup was crooked except for one thing, I was the dealer.

[cambridgealex]

im doing some simple maths for open face chinese and my brain is being painfully tiresome with things that are very basic i'm sure.

If someone could answer this, with working, I'd be very grateful.

There are 8 cards dealt to 4 players A,B,C and D, so two each. Two of the 8 cards are picture cards. What are the odds that player A gets AT LEAST one picture card?

Well player A's first draw sees him have a chance of 2/8.

If he hits (which happens 25% of the time) he is then 14.2857% or whatever it is to hit the next one). As such the chance of Player A scooping the two picture cards is x*y= 3.6%

He gets a couple of goes at getting one of the two. Calculated as:

 .75 (6/8 to brick)*.286 (2/7 to hit)= 21.43%
.25 (2/8 to hit) * .857 (6/7 to brick) = 21.43%

Sum them up and you get 46.46% chance of getting at least one picture.

Cheers Ed. Was doing all sorts of permutation and factorial calculations and obviously making it much more complicated than it is.

[edgascoigne]

im doing some simple maths for open face chinese and my brain is being painfully tiresome with things that are very basic i'm sure.

If someone could answer this, with working, I'd be very grateful.

There are 8 cards dealt to 4 players A,B,C and D, so two each. Two of the 8 cards are picture cards. What are the odds that player A gets AT LEAST one picture card?

Well player A's first draw sees him have a chance of 2/8.

If he hits (which happens 25% of the time) he is then 14.2857% or whatever it is to hit the next one). As such the chance of Player A scooping the two picture cards is x*y= 3.6%

He gets a couple of goes at getting one of the two. Calculated as:

 .75 (6/8 to brick)*.286 (2/7 to hit)= 21.43%
.25 (2/8 to hit) * .857 (6/7 to brick) = 21.43%

Sum them up and you get 46.46% chance of getting at least one picture.

Cheers Ed. Was doing all sorts of permutation and factorial calculations and obviously making it much more complicated than it is.

A bit like when I used to 6-bet jam A2 and stuff like that?

[Bertpup]

Right then,

The odds of being dealt a pocket pair is 17:1

I can't quite decide what the calculation should be for the odds of two players being dealt a pocket pair, but have found a calculation for a 6 handed table (this was 7 handed), so am going to use that.

0 players dealt a pair is simply:
(16/17)^6 = 0.6951 for 6-handed
and
(16/17)^9 = 0.5795 for 9-handed

1 player dealt a pair is:
6*(1/17)*(16/17)^5 = 0.2606 for 6-handed
and
9*(1/17)*(16/17)^8 = 0.3296 for 9-handed

So 2 or more people being dealt a pair will roughly be:
1 - 0.6951 - 0.2606 = 0.0443 for 6-handed (1 in every 22.6 deals)
and
1 - 0.5795 - 0.3296 = 0.0909 for 9-handed (1 in every 11.0 deals)



So, the odds of two players getting dealt a pocket pair is 22:1

The odds of a third player then being dealt one each of those pocket pair cards is 564:1 (2/48 x 2/47)

And finally, the odds of the remaining case pocket pair cards being flopped is 15,180:1 (91,080 combinations of 46 cards being flopped, with 6 combinations of the two case cards being flopped)

Which would make the total odds 22 x 564 x 15,180 : 1 or 188,353,440 : 1


Seems a big number.  Have I missed something obvious ?  (Should I be ignoring the first odds, as the probabilty of the second and third part are already based on the first bit having happened ?)

My head is hurting here trying to work it out and i don't think i'm capable of doing the maths. However I think there are lots of permutations that bring the odds down of it happening.

Things like
 
Fiive players are dealt pocket pairs then that gives x number of 2 card combinations which could then show up on the flop.

so AA,KK,QQ,JJ,1010 would give ak aq aj a10 kq kj k10 qj q10 j10 then flops containing 2 of AKQJ10

I could just be sprouting shite for all i know though