The majority of game mathematicians work on video slot machines. These games have somewhat complex payout structures, seeing that they may have 40 or 50 "lines" (directions in which identical symbols trigger a payout), one or more "scattered symbol" prizes (payouts based on the appearance of a minimum number of special symbols, regardless of lining up), wild symbols, multiple progressive jackpots (individual and shared), one or more bonus games, free spins (often at an increased payout multiple, with the possibility of triggering jackpots), and possibly more gameplay features.
Incorporating all of these features into a single games with an acceptable "hold percentage" (theoretical percentage of wagers that result in casino profit) that is still fun to play that gives players a feel that they have a good chance of winning and generates repeat play, is a difficult task that every slot machine vendor is trying to achieve, and the mathematicians are tasked with balancing frequency of payouts with amount of payouts to keep players playing.
Right now Aristocrat Gaming is the most successful, they have the most titles (and the top spots) on industry-wide slot performance surveys.
Incorporating all of these features into a single games with an acceptable "hold percentage" (theoretical percentage of wagers that result in casino profit) that is still fun to play that gives players a feel that they have a good chance of winning and generates repeat play, is a difficult task that every slot machine vendor is trying to achieve, and the mathematicians are tasked with balancing frequency of payouts with amount of payouts to keep players playing.
Right now Aristocrat Gaming is the most successful, they have the most titles (and the top spots) on industry-wide slot performance surveys.