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This might be hard to code, but before each of the rounds, let the player designate up 2 two spots that are guaranteed a position be offered.
Now, the card that comes is only guaranteed to be eligible for that position. It may be sub-optimal, but when you go into round 10+ needing a catcher, and none show up the rest of the way, at least you can get a warm body.
And, if you choose a position, there may be other cards that come out and fill that position, as well, meaning you wasted a chance at a possibly useful player in that guaranteed spot.
And make it so you can only designate a position 1 time per draft, after round 3 (start with gold cards).
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When you let your 10 year old name the team
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