Arguably, this isn't your problem. In most circumstances, you don't give loot to specific characters - you give it to the party, and let them sort out how it gets distributed.

Yes, this could theoretically lead to one player hogging all the magic items, but that's a solved problem; As long as your players are aware that they can negotiate how stuff gets shared around, they'll generally spot unfair situations, renegotiate as necessary, and generally agree on equitable solutions on their own.

If one player's lack of magic items is dragging the party down, that's the whole party's problem, and most players will realise that pretty quickly; Even the most selfish of players will agree it's a good idea to share the wealth if it improves their own survivability.

If magic items have already made one player much more powerful than the others - Well, it's not like magic items are bound to the first person who picks them up; Your players can always just redistribute them where they'll be more useful.

If your players don't find an uneven distribution of loot to be inequitable - Well, then there's no problem to solve; Everyone's already having fun, and that's what the game is all about.

So, to repeat myself, this isn't your problem: Working out how to distribute loot is just another part of the game. Heck, some players find it one of the most fun parts of the game: Working out how to effectively use available resources is core gameplay, and deciding how magic items should be distributed for best effect is part of that.

There's no perfect way to assign rarities to all the tables.

I made a spreadsheet counting the percentage of items of each rarity¹ contained in each of tables A through I. These results are as follows.

\$ \begin{array} {c|r|r|r|r|r} \textbf{Table} & \text{Common} & \text{Uncommon} & \text{Rare} & \text{Very Rare} & \text{Legendary} \\ \hline \textbf{A} & 50\% & 50\% & & & \\ \hline \textbf{B} & & 100\% & & & \\ \hline \textbf{C} & & 14.3\% & 85.7\% & & \\ \hline \textbf{D} & & & 6.3\% & 93.8\% & \\ \hline \textbf{E} & & & & 42.9\% & 57.1\% \\ \hline \textbf{F} & & 100\% & & & \\ \hline \textbf{G} & & 2.1\% & 96.8\% & 1.1\% & \\ \hline \textbf{H} & & 2.9\% & 8.7\% & 88.4\% & \\ \hline \textbf{I} & & & 7.8\% & 23.4\% & 68.8\% \\ \end{array} \$

As can be seen, only tables B and F are completely consistent in their rarity, so it's not possible to assign a rarity to every lettered table perfectly.

But there's a better way to solve the problem.

The problem isn't really what rarity to assign each lettered table. It's how to preserve which rarities become available to a character when they reach a specific tier and at a particular point cost (according to the Shared Campaign rules being used). For example, it doesn't matter that table I contains a mix of very rares and legendaries. What matters is that major legendaries only become available at tier 3 for 12 points, and only table I has them, so for all practical purposes when a character becomes eligible for table I then they become eligible for major legendaries.

So, how to solve that version of the problem...

1. Observe when each minor and major rarity becomes available to a character for the first time based on tier requirements, grouping any rarities that share a tier requirement and point cost.

2. Observe which lettered tables cover each minor and major rarity most precisely, grouping any tables that share a tier requirement and point cost.

3. See if we can find an obvious mapping from the table groups in step 2 to the rarity groups in step 1. If so, we can refactor the purchase options.

My observations for the minor items are as follows.

• Commons, uncommons, and rares start at tier 1 for 4 points. Tables A, B, and C (plus the minor commons in Xanathar's) almost perfectly² cover these rarities.
• Very rares start at tier 2 for 8 points. Table D almost perfectly² covers this rarity.
• Legendaries start at tier 3 for 8 points. This rarity is exclusive to table E.

My observations for the major items are as follows.

• There are no commons.
• Uncommons start at tier 1 for 8 points. Table F almost perfectly² covers this rarity.
• Rares start at tier 2 for 10 points. Table G almost perfectly² covers this rarity.
• Very rares start at 3 for 10 points. Table H almost perfectly² covers this rarity.
• Legendaries start at tier 3 for 12 points. This rarity is exclusive to table I.

I think an obvious mapping has emerged: in the table of magic item purchase options in Xanathar's (p. 174), replace each of the lettered tables with the following minor/major rarities and then ignore tables A to I in favor of the minor/major rarity tables in Xanathar's.

• A, B, and C (as a group): minor common, minor uncommon, and minor rare.
• D: minor very rare.
• E: minor legendary.
• F: major uncommon.
• G: major rare.
• H: major very rare.
• I: major legendary.

Although this mapping is not exactly equivalent to the way the purchase options were originally presented, the scenarios where a player could buy an item earlier or later than the original options allowed are essentially edge cases that balance each other out.

This mapping ought to allow the players to use the tables in Xanathar's instead of the DMG's tables A through I easily without deviating greatly from the balance apparently intended in the original options, which was the real problem to begin with.

Footnotes on My Methods

1. These percentages are according to the rarity of the item names listed in the table, not the probability of randomly generating an item of each rarity using the table's d100 column, since we're not trying to generate random treasure. Data entry errors should be insignificant.

2. When I say "almost perfectly" I mean there are on the order of 5 outliers out of just under 400 entries, which is insignificant. Note that by "entries" I mean the number of item names listed in the tables preserving duplicates across tables, not the number of unique items described in the book, which is far fewer.