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Kolrami was quite skilled at the game of Strategema, reaching the rank of third level grand master. While aboard the Enterprise-D, he easily defeated Commander Riker at the game, causing him to have a low opinion of Riker's ability as a strategist. During the simulation, however, Kolrami was impressed by Riker's highly unorthodox style which saw the heavily outmatched Hathaway score several simulated hits on the Enterprise-D.
Once the battle simulation was underway, the Ferengi marauder Kreechta interrupted in the false belief that the Hathaway held some secret value. Offering his strategic advice, Kolrami insisted that the Enterprise-D abandon Riker and his crew as acceptable losses; Captain Picard refused, and Riker was able to fool the Ferengi into believing his ship had been destroyed. Further impressed by Riker's strategic machinations, Kolrami filed a favorable report on Riker's performance to Starfleet.
After witnessing Riker's earlier defeat at Strategema, Doctor Pulaski encouraged Lieutenant Commander Data to challenge Kolrami to a game of Strategema, in the belief that Data was infallible and could not be defeated by an organic person. Kolrami easily triumphed, causing Data to question his own abilities and to even request to be relieved of duty, believing that his advice could be flawed and that Captain Picard should not rely on it. Data later realized that his own strategy was flawed and challenged Kolrami to a second game; this time passing up obvious avenues of opportunity to gain an advantage. This stalling defensive tactic so frustrated Kolrami that he quit the game, handing victory to Data by default. (TNG: "Peak Performance")