*"Ion,
*

*
Here is a problem for you to solve, axiomatic one.
*

*
I have 9 playing cards, Ace to nine... and 2 dice. I throw the dice and can choose to either; take to number showing from either dice, or the total of both dice added together. i.e. lowest possible number is 1, highest is 12 (although there are only 9 cards, remember). I can then eliminate the respective card from the Ace to nine. Example:
*

The object of the game is to eliminate all 9 cards.

*
ANY HELP APPRECIATED SO I CAN BEAT MY SISTER!!!!"*

Probability requires * number of favorable cases* and

1&1 = eliminates cards A or 2 1&2 = eliminates cards A or 2 or 3 1&3 = eliminates cards A or 3 or 4 1&4 = eliminates cards A or 4 or 5 1&5 = eliminates cards A or 5 or 6 1&6 = eliminates cards A or 6 or 7 2&1 = eliminates cards A or 2 or 3 2&2 = eliminates cards 2 or 4 2&3 = eliminates cards 2 or 3 or 5 2&4 = eliminates cards 2 or 4 or 6 2&5 = eliminates cards 2 or 5 or 7 2&6 = eliminates cards 2 or 6 or 8 3&1 = eliminates cards A or 3 or 4 3&2 = eliminates cards 2 or 3 or 5 3&3 = eliminates cards 3 or 6 3&4= eliminates cards 3 or 4 or 7 3&5= eliminates cards 3 or 5 or 8 3&6= eliminates cards 3 or 6 or 9 4&1 = eliminates cards A or 4 or 5 4&2 = eliminates cards 2 or 4 or 6 4&3= eliminates cards 3 or 4 or 7 4&4 = eliminates cards 4 or 8 4&5 = eliminates cards 4 or 5 or 9 4&6 = eliminates cards 4 or 6 5&1 = eliminates cards A or 5 or 6 5&2 = eliminates cards 2 or 5 or 7 5&3= eliminates cards 3 or 5 or 8 5&4 = eliminates cards 4 or 5 or 9 5&5 = eliminates card 5 5&6 = eliminates cards 5 or 6 6&1 = eliminates cards A or 6 or 7 6&2 = eliminates cards 2 or 6 or 8 6&3= eliminates cards 3 or 6 or 9 6&4 = eliminates cards 4 or 6 6&5 = eliminates cards 5 or 6 6&6 = eliminates card 6

A = 11 times; 2 = 11 times; 3 = 12 times; 4 = 14 times; 5 = 15 times; 6 = 16 times; 7 = 6 times; 8 = 5 times; 9 = 4 times.

Not all cards are equal! Number 6 is the favorite: It appears 16 times among the 36 possibilities (44%). Number 9 fares the worst: 4 occurrences (11%).

A quick strategy:

Good luck (to your sister, too)!

- Theory of Probability: Best Introduction, Formulae, Algorithms, Software.
- Fundamental Formula of Gambling: Theory of Probability, Mathematics, Degree of Certainty, Chance.
- Probability Caveats, Theory, Software: Life, Lottery, Gambling, Sports, Streaks.

Ion “Parpaluck” Saliu,

Founder of Mathematics of Card Games

· Facebook

· Google+

· Twitter