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The warlock's Gift of the Ever-Living Ones (XGtE p. 57) eldritch invocation is described as follows:

Whenever you regain hit points while your familiar is within 100 feet of you, treat any dice rolled to determine the hit points you regain as having rolled their maximum value for you.

The description of the Vampiric Touch (PHB p. 285) spell states:

On a hit, the target takes 3d6 necrotic damage, and you regain hit points equal to half the amount of necrotic damage dealt.

How do these two interact? Do I roll for damage, and then gain 9 hit points?

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The invocation doesn't change how vampiric touch works.

The description of the warlock's Gift of the Ever-Living Ones eldritch invocation says (XGtE, p. 57; emphasis mine):

Whenever you regain hit points while your familiar is within 100 feet of you, treat any dice rolled to determine the hit points you regain as having rolled their maximum value for you.

Note that this only applies to dice whose purpose is to determine the HP you regain.

The vampiric touch spell description states, in part (PHB, p. 285; emphasis mine):

Make a melee spell attack against a creature within your reach. On a hit, the target takes 3d6 necrotic damage, and you regain hit points equal to half the amount of necrotic damage dealt.

Here, the dice rolled simply determine the damage you do to the target; the resulting healing is simply derived from that value. Thus, Gift of the Ever-Living Ones doesn't interact with it.

Rules designer Jeremy Crawford supports this ruling in his answer to a similar question about the invocation's interaction with the enervation spell (XGtE, p. 155) - which similarly deals necrotic damage and heals half the damage dealt - in an unofficial February 2018 tweet:

Gift of the Ever-Living Ones (lock invocation) states: treat any dice rolled to determine the hit points you regain as having rolled their maximum value. Would this effect make an Enervation cast max roll every time because of it's healing effects?

If you cast the enervation spell, you regain a number of hit points equal to half the amount of necrotic damage the target takes. In other words, you're not being healed directly by a die roll; you check to see how much damage the target took, halve that amount, then heal.

The vampiric touch spell's "healing" works the same way: you make a damage roll, and then halve that amount and heal. As such, vampiric touch's "healing" would be unaffected by the warlock's Gift of the Ever-Living Ones eldritch invocation, as the actual roll being made is for damage, not healing - you just regain HP worth half of the amount of the damage roll.

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The die of life draining effects are determining how many hit points you regain.

Example 5d6 = 30/2 15 life restored. 30 value max value for the die.

Treat the damage roll as a separate roll, and restore effects as a separate maximum value.

30/2 15 would always be restored

Once again, treat any dice rolled to determine the hit points you restore as having rolled their maximum value. These die are determining hit points restored so you always restore 15. The damage can be rolled as normal even if you roll 5 damage 15 will always be restored. These dice are determining value

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    \$\begingroup\$ Can you explain the reasoning behind this answer? What lead you to this kind of logic? How did you extrapolate this from what the rules say? It's an interesting answer but it needs some support behind it. \$\endgroup\$ – Purple Monkey Dec 9 '18 at 6:34

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