Cold Game-When there is no real advantage of making the first or second move.
Combinatorial Game-A game that involves a combination of moves and results to win.(see Conditions of Combinatorial Games).
Game Theory-a branch of math that deals with situations where people choose to do different actions or moves to maximize their chance of return or their chance of winning.
Game Tree-shows all possible scenarios in any game.
Grundy's Game-a combinatorial zero-sum game with one pile or more of anything where the only rule is you have to split the pieces up in 2 smaller unequal sizes of piles and the last person to move wins.
Hot Game-When there is a distinct advantage of making the first move.
Maximin Strategy-Method in decision making, a theory for minimizing the maximum possible loss.
Minimax Strategy-Method in decision making, a theory to maximize the minimum possible gain.
Prisoners Dilema-a type of zero-sum game where two people try to get out of jail by cooperating with each other or betraying each other. If both players betray each other then they both get an amount of time in jail which would be more than if both players stayed silent. If one player betrays and one player stays silent then the player who betrays goes free the other gets jailtime. What makes it hard is the players do not know what each other is going to do.
Wythoff's Game-A game of nim played with 2 piles of beans where you can take as much beans as you want from one pile or an equal number from both piles.
Zero Sum Game-When a player benefits it's at a players expense. Sum of loss + gain = 0.

Conditions of Combinatorial Games

1. Two players
2. Particular starting position
3. Clearly defined rules that specify what moves players can make
4. Players alternate turns
5. Normal play convention (player unable to move loses)
6. Games always end
7. Both players know what is going on
8. No chance moves