What tactics can you use to help determine what your opponent is looking for in two player 10 card Gin?
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In Gin, you don't get any hard information on what is in your opponent's hand until the hand is over.
This means you have to make use of whatever information you can get. The primary source of information is the discards. To be successful you need to keep track of both
Pay attention to both suits and the number of each card. For example, if your opponent discarded the 5 of clubs, he is most likely not interested in 5's or mid range clubs.
Observe your opponent, if he usually plays fast but pauses even briefly to consider the jack of diamonds you just tossed then he most likely has several cards around that. A couple examples of what he might have.
Perhaps from previous discards and pickups you could narrow down the options as to what he might have.