Moe and Joe had some time on their hands, so they played a simple game called "Dueling Cards."
In this game, each player has a deck of cards, shuffled and without jokers.
A hand consists of a single card taken from the top of each player's deck.
Suits and face values are both ranked. No two cards in a deck have the same rank.
A player wins the hand by holding a card that outranks the card of his opponent.
The bank pays 1 chip to the winner of a hand.
It's a simple game. No poker hands. No betting. Just high card wins.
After 52 hands the decks are re-shuffled, and play continues as long as desired.
Moe and Joe played through their decks 10 times, then stopped to see who won.
As they counted their chips Moe (a statistician) said, I wonder what the most likely winning score is.
Joe (a simpler person) replied, I wonder what the most likely combined score is.
I'm sure Bushindo can answer Moe's question.
I can't. So instead this puzzle asks Joe's question.