I would start by doing a back run of 2 or maybe all 3 of the players you are considering. After 10 years, you may be to the point where you need a Drum of player x, an Uzit of player y, and a Lenox of player z. Now you have 3 options to finish off your back run. It may be another 10 years or more, but you have more options and are more likely to accomplish your goal. It would suck to need a Drum of player x, and after 10 years of waiting, that card appears at auction, it sells for 10 times more than you feel it is worth. It would suck even more if you needed a Drum of player x and that card never appears for sale.
You have more options of you start a run of more than 1 player. You can always sell or trade down the road. Maybe skip the easier backs for now, but start by collecting the tougher backs of 2 or 3 of the players.
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