A Drink In The Ol' Saloon.

[Joan]

Happy July, everybody. (We had it here first).

I'm not really one for oneupmanship, Peepmaster, but Malc and I had it a couple of hours before you!

[The Peepmaster]

Happy July, everybody. (We had it here first).

I'm not really one for oneupmanship, Peepmaster, but Malc and I had it a couple of hours before you!

That thought had occurred to me, Joan!

[Mince]

That thought had occurred to me, Joan!

Next time it occurs to you to think, perhaps you might try it out.

[Fyodor]

When Wild Bill Hickok was killed in a Deadwood bar, he was playing poker. He was holding two aces, two eights and a queen----now known, unsurprisingly, as "Dead Man's Hand".

But the chance of having that particular hand (assuming that all hands have equal probability) is:

ACE + ACE + EIGHT + EIGHT + QUEEN

4/52 * 3/51 * 4/50 * 3/49 * 4/48 * (13C4) = 0.0023

So 0.2% of all hands will be a Dead Man's Hand. So if he played at least 1000 games of poker, he would have obtained a Dead Man's Hand at least twice, and so the "unsurprisingly" loses some of its irony.

I don't think so. I can see where you're coming from, but the (13C4)
term doesn't make sense to me. The bit before that is the probability
of getting the 5 cards dealt in the order AA88Q, and it looks like the
 (13C4) is an attempt to adjust for the different possible orders, but
it doesn't make sense.

What you need to do for the last term is to multiply the probabilities
by the number of different orders you could get AA88Q in. It doesn't
matter which suits they are, as you've already allowed for that in the
earlier calculation (4/52 refers to any ace).

The actual number of ways you can arrange AA88Q is 30. This comes from
the number of ways to arrange 5 cards = 5! = 5*4*3*2*1=120. Then since
you have 2 aces you have to divide this by 2! (which equals 2), to get
60, and then by 2! again for the eights to get 30.

So the actual probability is 4/52 * 3/51 * 4/50 * 3/49 * 4/48 * 30 =
0.0000554 , or approximately a one in eighteen thousand chance.

We can confirm this by thinking about it slightly differently. We can
calculate how many different poker hands there are, i.e. the number of
ways to choose 5 cards from 52. This is the calculation (52 C 5) which
can be calculated as 2598960. Then we need to work out how many of
these are the dead man's hand. There are 6 possible ways to choose two
aces, 6 possible ways to choose two eights, and 4 possible queens.
Multiply these together 6x6x4 = 144 possible dead man's hands.

So the probability of a dead man's hand is 144/2598960 = 0.0000554,
the same as above.

Yes, I know, but Roger would not have known the difference.

The answer would have been better if you had stuck either to permutations or to combinations.

I gave 2 methods of arriving at the correct answer. You gave one method
of arriving at the wrong answer. I think we may be able to agree which
is better.

[Tarquin Thunderthighs lll]

COMING SOON - a mathematical explanation of The Offside Law.

[Mince]

I gave 2 methods of arriving at the correct answer. You gave one method
of arriving at the wrong answer. I think we may be able to agree which
is better.

How are you defining "better"? My only purpose was to convince Roger of something mathematical, and quite frankly I could have written the solution to a quadratic equation and he would have been none the wiser. Your method, on the other hand, was rather overkill. I just could not be bothered to look up the equation for combinations and permutations.

Or are you proposing maths duels at dawn? 

[The Peepmaster]

I gave 2 methods of arriving at the correct answer. You gave one method
of arriving at the wrong answer. I think we may be able to agree which
is better.

Or are you proposing maths duels at dawn? 

If it involves terminating your existence, I'm all for it. 

[Fyodor]

I gave 2 methods of arriving at the correct answer. You gave one method
of arriving at the wrong answer. I think we may be able to agree which
is better.

How are you defining "better"? My only purpose was to convince Roger of something mathematical, and quite frankly I could have written the solution to a quadratic equation and he would have been none the wiser. Your method, on the other hand, was rather overkill. I just could not be bothered to look up the equation for combinations and permutations.

Or are you proposing maths duels at dawn? 

Last word. Word.

[Roger Kettle]

He don't like it when you stick it up him, Fido!

[Tom]

Does this mean we're heading for a high noon showdown?

[Malc]

I'm not really one for oneupmanship, Peepmaster, but Malc and I had it a couple of hours before you!

Joan, kindly stop blabbing to people every time you and I have it.

Are you back yet? I thought we might have it again. I brought the stuff.

[Joan]

Not back yet, Malc - three more weeks to go.  Thought it was my turn to bring the stuff.

[Malc]

Oh, ok. Could you get it in tubes this time? Fourteen should do it. It rots through the paper cups. I don't know how you women manage to keep it all in. My eyes water after a couple of minutes.

[Joan]

We're made of stern stuff, Malc ... and what are you doing up at 3.10am?  Been indulging in the leftovers from last time?

[Joan]

Big tubes or little tubes?