Is More Information Better?
 

The basic game is as follows:

Each player is given ten cards numbered 1 through 10.
In sequential rounds, each player selects one card to play,
with value unknown to the other player(s).
The player who plays the highest valued card wins that round
and collects points corresponding to the values on the cards
played in that round. Ties are ignored. Played cards are removed.
The player with the most points after 10 rounds wins.
The object is to win, and to win as many points as possible.

Is there any strategy that is an improvement on random selection?

Now suppose there are three players A, B, and C,
and a referee to look at the played cards.
"A" is told nothing after each round.
"B" is told who won after each round (or whether there was a tie).
"C" is given full information after each round, about who played what
and thus who won and how much.

Does player "C" derive any benefit from all that information?

[QUOTE=davar55;150823]... Does player "C" derive any benefit from all that information?[/QUOTE][spoiler]Yes. Example: C has the possibility to recognise some strategy from the previous plays of A and B. Once a strategy is recognised C can use the information to increase the chances of winning.[/spoiler]

[spoiler]Since playing a 1 is a guaranteed loss, it would be beneficial to play it against a 10. Since C knows the probabilities that A and/or B have a 10 on hand, then C can increase his chances of playing his 1 against a 10[/spoiler]

[quote=retina;150826][spoiler]Yes. Example: C has the possibility to recognise some strategy from the previous plays of A and B. Once a strategy is recognised C can use the information to increase the chances of winning.[/spoiler][/quote]

What about B?