Playing war with cards

[BMAD]

I saw a teacher mistakenly describe the rules to war as follows: each player receives five cards from the set of 1-10.  They randomly pick a card to show the other opponent.  The highest card turned over is the winner.  The winner takes both cards and adds them to their collection to be used after shuffling their deck.  She forgot the added rule that the highest card can be beat by the smallest card, the implications of this mistake should be obvious.  Between two players what is the expected number of 'shows' needed before one player beats the other?

 

 

also, note that in general i enjoyed the lesson by the teacher as the intent was to improve the students subitizing of number.

Edited July 31, 2015 by BMAD

[bonanova]

 She forgot the added rule that the highest card can be beat by the smallest card, the implications of this mistake should be obvious.  Between two players what is the expected number of 'shows' needed before one player beats the other?

The omitted rule is the smallest card beats (only) the highest card. Should we assume the students are now playing without that rule in effect?

[BMAD]

 She forgot the added rule that the highest card can be beat by the smallest card, the implications of this mistake should be obvious.  Between two players what is the expected number of 'shows' needed before one player beats the other?

The omitted rule is the smallest card beats (only) the highest card. Should we assume the students are now playing without that rule in effect?

yes.