The game with the dollar bills between Marlowe and Lennox

I don't know about the game, but I'm more intrigued about your rating system.

It's called Liar's Poker. Players try to bluff one another about the numbers in a bill's serial number.

Here are the rules of Liar's Poker from the Wiki page:

Liar's poker is a bar game that combines statistical reasoning with bluffing, and is played with the eight-digit serial number on a U.S. dollar bill. Normally the game is played with a stack of random bills obtained from the cash register. The objective is to make the highest bid of a number that does not exceed the combined total held by all the players. The numbers are usually ranked in the following order: 2,3,4,5,6,7,8,9,0 (10) and 1 (Ace). If the first player bids three 6s, he is predicting there are at least three 6s among all the players, including himself. The next player can bid a higher number at that level (three 7s), any number at a higher level (four 5s) or challenge. The end of the game is reached when a player makes a bid that is challenged all around. If the bid is successful, he wins a dollar from each of the other players, but if the bid is unsuccessful, he loses a dollar to each of the other players.

Nice touch by Altman or Brackett providing background to Marlowe's and Lennox's friendship by having them engage in a round of Liar's Poker