Two Challenging Math Game Problems

(People say the wording is confusing. Fine.)

Problem 1

Alphonse and Beryl have decided to put on a mathemagical show one evening!

The audience shuffles a deck of 36 cards, containing 9 cards in each of the suits spades, hearts, diamonds and clubs. Alphonse predicts the suit of the cards, one at a time, starting with the uppermost one in the face-down deck. The design on the back of each card is an arrow. Beryl examines the deck without changing the order of the cards, and points the arrow on the back of each card either towards or away from Alphonse, according to some system agreed upon in advance. Is there such a system which enables Alphonse to guarantee the correct prediction of the suit of at least 19 cards?

Problem 2

Alphonse and Beryl have planned an exotic vacation in the Pacific. To pass the time on the plane ride, they decide to play a game. Alphonse and Beryl wish to divide 25 coins of denominations 1, 2, 3, . . . , 25 kopeks. In each move, one of them chooses a coin, and the other player decides who must take this coin. Alphonse makes the initial choice of a coin, and in subsequent moves, the choice is made by the player having more kopeks at the time. In the event that there is a tie, the choice is made by the same player in the preceding move. After all the coins have been taken, the player with more kopeks wins. Which player has a winning strategy?


(Source: Tournament of Towns Contest)