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Mint set coins are usually struck on standard planchets but there have been a few specially prepared ones in the past and it's likely that they average slightly better otherwise. The big difference with mint set coins is that they are struck with new dies under increased pressure. Dies are retired after only about 30,000 strikes while the "business strike" coin dies go on to strike up to nearly a million more. The mint set coins are also mostly struck on the old single vertical presses rather than the hrizontal presses with four sets of dies. The mint set coin presses run a little slower so the coins are usually much better struck. The coins are then washed and dried before being placed in the mint sets.
Business strike dies are run at high speed at about 75 tons and are not retired until there is evidence of significant wear or the press has to be stopped for a broken die. This averaged around 400,000 strikes in those days but some dies might last as long as 950,000 strikes. Only a small percentage of such coins are struck by new dies and even when new there would be a higher probability of misalignment or lack of full strike due to insufficient pressure. These coins do not have a significantly higher probability of being marked up however.
Coins from several presses will be run together to fill bags so even if there are very well made coins going into a roll or bag there will always be mediocre and inferior coins going in with them. This makes it possible to look at an assortment of coins from mint sets or bags and state positively their source, but this is not possible except in context. An individual coin can be a dog right out of the mint set or it might be a superb gem from a bag. There are dates for which well made coins were avaialable only in rolls or only in mint sets. With experience you can get fairly good at telling the difference but you can't be certain even if you recognize a die pair since mint set dies are usually retired to strike regular issues.
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