1. 


A negative payoff indicates a loss to the row player. 
2. 


The row [1 1 2] dominates the row [1 0 0]. 
3. 


The column [1 2 3]^{T} dominates the column [1 1 0]^{T}. 
4. 


If the payoff matrix of a game reduces to a 11 matrix, then the row and column that are left give each player's optimal pure strategy. 
5. 


If a game has no saddle points, it may still be possible to reduce the game to a 11 game using dominance. 
6. 


Some strictly determined games do not have saddle points. 
7. 


The game 

is not strictly determined. 

8. 


The game 

is not strictly determined. 

9. 


In a strictly determined game, the row and column corresponding to optimal pure strategies always intersect in a saddle point. 
10. 


When analyzing a game, it pays to first check for saddle points. 
11. 


Different saddle points in the same payoff matrix may have different payoffs. 
12. 


If a game is not strictly determined, there is a mixed strategy for the row player that is better for the row player than any pure strategy. 
13. 


For every mixed row strategy, there is a pure strategy for the column player that maximizes his or her outcome. 
14. 


If you fail to use an optimal strategy, then there is a counter strategy your opponent can use that is worse for you than anything he or she might do if you use an optimal strategy. 
15. 


It is necessary to first reduce a game by dominance when solving it by the simplex method. 
16. 


If you use the simplex method to solve a strictly determined game, then the value of the game may differ from the value of a saddle point. 
17. 


If both players' optimal mixed strategies for a game happen to be pure strategies, then the game is strictly determined. 
18. 


If a game is strictly determined, it may still be necessary to use the simplex method to solve it. 
19. 


Every game can be solved by the simplex method. 
20. 


If you know your opponent's strategy, it is still always best to use your optimal mixed strategy. 