odds of having two sets with 6 or 7 spoils

[Smokey McBandit]

Fellow CCers,

I apologize if this question has been answered somewhere; I searched but didn't find it.

I know the odds of having a set with 3 cards is 33% and of having a set with 4 cards is roughly 80%, but what are the odds of having two sets with 6 cards? For 7 cards?

I haven't seen this anywhere and would love to know. Thanks!

[Georgerx7di]

I think I worked this out on paper once. I believe it was 38% with 6 cards and 78 or 79% with 7 cards. Obviously with 8 cards its 100%.

When I have some time I'll try to do this again, I'm not sure about those numbers.

[chapcrap]

I think I worked this out on paper once. I believe it was 38% with 6 cards and 78 or 79% with 7 cards. Obviously with 8 cards its 100%.

When I have some time I'll try to do this again, I'm not sure about those numbers.

7 cards has to be higher than 78%. If you have 7 and trade a set, then you have 4, that's an 80% chance by itself.

I wonder what the answer is to this... I will think about it and get back to this thread, if I come up with an answer.

[Geger]

Hm... have a question : if we have 2 set of spoils (6 or more spoils) after eliminating someone, can we play 2 sets?

[sherkaner]

Hm... have a question : if we have 2 set of spoils (6 or more spoils) after eliminating someone, can we play 2 sets?

Yes, you can

[Tin Trumpet]

Unless I'm being thick, the chance of a trade with 3 cards is 40%, not 33%.
But I'm prepared to be proved otherwise!
TT

[betiko]

Unless I'm being thick, the chance of a trade with 3 cards is 40%, not 33%.
But I'm prepared to be proved otherwise!
TT

i think you're being thick!

kidding aside, whatever 2 first cards you start with, there will always be 1 and only 1/3 colours that will give you a set on your third card, so obviously 33%

[Metsfanmax]

Unless I'm being thick, the chance of a trade with 3 cards is 40%, not 33%.
But I'm prepared to be proved otherwise!
TT

i think you're being thick!

kidding aside, whatever 2 first cards you start with, there will always be 1 and only 1/3 colours that will give you a set on your third card, so obviously 33%

The 40% number comes from writing down the possible combinations of three colors one can obtain, of which there are 10, and noticing that 4 of them are valid sets. However, the 33% number comes from recognizing that not all of those color combinations are equally likely. betiko's claim is correct; if you write down the first two cards and then consider the third cards that can come after, you can explicitly verify that exactly 6 of the 18 possibilities are valid sets.

[Tin Trumpet]

Bravo. Makes perfect sense. Maths teacher...?

[elbitjusticiero]

The 40% number comes from writing down the possible combinations of three colors one can obtain, of which there are 10, and noticing that 4 of them are valid sets. However, the 33% number comes from recognizing that not all of those color combinations are equally likely. betiko's claim is correct; if you write down the first two cards and then consider the third cards that can come after, you can explicitly verify that exactly 6 of the 18 possibilities are valid sets.

Huh?

EDIT: I understand now. You talk about combinations as opposed to permutations, so "two blues and a red" is one combination but corresponds to three possible permutations. Thanks.