Conquer Club

Today, I decided to do some research in dice/cards statistics
1. What is the chance of getting a set with three cards? (1/3)
2. What is the chance of getting a set with four cards? (15/19)
Statistics:

1. What is the chance of getting a set with three cards?
R=Red B=Blue G=Green

Possibilities:
RRR
RBR
RRB
RBB

RGR
RRG
RGG
RGB
RBG

BBB
BRB
BBR
BRR
BGB
BBG
BGG
BGR
BRG

GGG
GRG
GGR
GRR
GBG
GGB
GBB
GBR
GRB
Result: 9 in 27 or 3 in 9 or 1 in 3 chance

2. I had some more time... so
What are the chances of getting a set with 4 cards?
RRRR
RRRG
RRRB
RRGR
RRBR
RGRR
RBRR
RRGG
RRBB
RGGR
RBBR
RGGG
RBBB
RGGB
RBBG
RGBB
RBGG
RBGB
RGBG
*And so on, just switch the letters, this sequence repeats three times with different colours*

Result: 15 of 19 possibilies are sets (multiply that by three and the total is) 45 out of 57 individual sets

(last updated April 13, 2008 by Splash_x)

2. I had some more time... so
What are the chances of getting a set with 4 cards?
RRRR
RRRG
RRRB
RRGR
RRBR
RGRR
RBRR
RRGG
RRBB
RGGR
RBBR
RGGG
RBBB
RGGB
RBBG
RGBB
RBGG
RBGB
RGBG
*And so on, just switch the letters, this sequence repeats three times with different colours*

Result: 15 of 19 possibilies are sets (multiply that by three and the total is) 45 out of 57 individual sets

What is interesting is that I always assumed the odds of making a set with 4 cards is 2 in 3 but that is merely the chances of making a set with your 4th card if you don't already have one. Of course, that is only worth knowing with respect to your own cards, not when trying to predict whether your opponent has one.

In that case, you do need to take into account the likelihood they already had a set with 3, which makes the chances of "making a set" with the 4th 100%. That would explain why your odds on 4 cards are higher than 66%.

some people do not cash in with three cards to manipulate others to think they don't have a set. So when choosing which player to eliminate during an escalating game (early on), one might survive longer and when the set is cashed, be able to eliminate others and win the game

Splash_x wrote:some people do not cash in with three cards to manipulate others to think they don't have a set. So when choosing which player to eliminate during an escalating game (early on), one might survive longer and when the set is cashed, be able to eliminate others and win the game

That was sort of my point.