This week the #puzzle is: Can You Win at Asymmetric Bingo? #probabilities #statistics

Can You Win at Asymmetric Bingo?

Solution, possibly incorrect:

Program

Result of running program:

Bingos on small vs large cards: 0.66518 0.33482

Some fun histograms:

Distribution, how many numbers necessary for bingo.

Only looking at small card, igonoring numbers on large card.

+---------+---------+---------+---------+---------+---------+---------+
               X                                                 
              XXX                                                
              XXX                                                
              XXX                                                
             XXXX                                                
             XXXX                                                
             XXXXX                                               
             XXXXX                                               
            XXXXXX                                               
            XXXXXX                                               
            XXXXXX                                               
            XXXXXX                                               
           XXXXXXXX                                              
           XXXXXXXX                                              
           XXXXXXXX                                              
          XXXXXXXXX                                              
          XXXXXXXXX                                              
         XXXXXXXXXXX                                             
         XXXXXXXXXXX                                             
        XXXXXXXXXXXX                                             
+---------+---------+---------+---------+---------+---------+---------+
Average: 14.29625

Same, for large card.

+---------+---------+---------+---------+---------+---------+---------+
                     XXXX                                        
                     XXXXX                                       
                    XXXXXX                                       
                    XXXXXX                                       
                   XXXXXXXX                                      
                   XXXXXXXX                                      
                  XXXXXXXXXX                                     
                  XXXXXXXXXX                                     
                  XXXXXXXXXX                                     
                 XXXXXXXXXXXX                                    
                 XXXXXXXXXXXX                                    
                XXXXXXXXXXXXX                                    
                XXXXXXXXXXXXXX                                   
               XXXXXXXXXXXXXXX                                   
               XXXXXXXXXXXXXXX                                   
              XXXXXXXXXXXXXXXXX                                  
              XXXXXXXXXXXXXXXXX                                  
             XXXXXXXXXXXXXXXXXXX                                 
            XXXXXXXXXXXXXXXXXXXXX                                
          XXXXXXXXXXXXXXXXXXXXXXXX                               
+---------+---------+---------+---------+---------+---------+---------+
Average: 22.07363

Looking at small card bingos, including numbers on large.

+---------+---------+---------+---------+---------+---------+---------+
                                  XXXX                           
                                 XXXXXX                          
                                XXXXXXXX                         
                               XXXXXXXXXX                        
                               XXXXXXXXXX                        
                              XXXXXXXXXXXX                       
                             XXXXXXXXXXXXX                       
                             XXXXXXXXXXXXXX                      
                            XXXXXXXXXXXXXXX                      
                           XXXXXXXXXXXXXXXXX                     
                          XXXXXXXXXXXXXXXXXX                     
                          XXXXXXXXXXXXXXXXXXX                    
                         XXXXXXXXXXXXXXXXXXXX                    
                        XXXXXXXXXXXXXXXXXXXXXX                   
                       XXXXXXXXXXXXXXXXXXXXXXX                   
                      XXXXXXXXXXXXXXXXXXXXXXXXX                  
                     XXXXXXXXXXXXXXXXXXXXXXXXXXX                 
                    XXXXXXXXXXXXXXXXXXXXXXXXXXXXX                
                  XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX               
                XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX              
+---------+---------+---------+---------+---------+---------+---------+
Average: 34.29726

Same, for large card.

+---------+---------+---------+---------+---------+---------+---------+
                                  XXXX                           
                                 XXXXXX                          
                                XXXXXXXX                         
                               XXXXXXXXXX                        
                              XXXXXXXXXXX                        
                              XXXXXXXXXXXX                       
                             XXXXXXXXXXXXX                       
                            XXXXXXXXXXXXXXX                      
                            XXXXXXXXXXXXXXX                      
                           XXXXXXXXXXXXXXXXX                     
                          XXXXXXXXXXXXXXXXXX                     
                          XXXXXXXXXXXXXXXXXXX                    
                         XXXXXXXXXXXXXXXXXXXX                    
                        XXXXXXXXXXXXXXXXXXXXX                    
                       XXXXXXXXXXXXXXXXXXXXXXX                   
                      XXXXXXXXXXXXXXXXXXXXXXXXX                  
                     XXXXXXXXXXXXXXXXXXXXXXXXXX                  
                    XXXXXXXXXXXXXXXXXXXXXXXXXXXX                 
                  XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX                
                XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX               
+---------+---------+---------+---------+---------+---------+---------+
Average: 34.00285

Fiddler: The small board (me) wins more than 50% of the time.

Extra credit: The small board (me) wins about 67% of the time.