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As far as I'm concerned, you only roll initiative at the beginning of combat and keep those rolls for the rest of the encounter.

If that's the case (if it isn't, why?), what happens when the initiative value of a player changes during the combat? For example, a Druid polymorphing into a creature. Should he/she reroll? Simply add the new modifier to the roll? Or keep the first rolled value regardless of any change in Initiative?

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Standard rules: after being established once at the start, initiative order does not change during combat.

It's not the rolls that you keep, but the initiative order as a whole. Further, the rules state that a Dexterity check to establish the initiative order occurs at the start of combat, and that this order remains the same throughout combat and is not updated.

Thus initiative values ( = results of the Dexterity check) do not change even if Dex modifiers change mid-combat. To be more precise: they do not even formally exist any more during combat. They're used for establishing the initiative order, and then discarded.

From the 5E Basic Rules section on initiative (emphases mine):

Initiative determines the order of turns during combat. When combat starts, every participant makes a Dexterity check to determine their place in the initiative order. [...]

The DM ranks the combatants in order from the one with the highest Dexterity check total to the one with the lowest. This is the order (called the initiative order) in which they act during each round. The initiative order remains the same from round to round.

[...]

However, there is a variant presented in the DMG that changes this.

The "Speed Factor Initiative" variant rule, presented on DMG pp. 270-271, requires a new initiative roll each round, and so would be responsive to changes in modifiers. AngryGM writes about it a bit here (warning: profane and vulgar language punctuates excellent analysis and description). You should also be aware of some of the issues raised in these questions:

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  • \$\begingroup\$ There are also certain things (features and/or spells I cant recall atm ) that may alter / bump the initiative of an ally. Other groups may also enter initiative mid combat. So the initiative roll may not ever change once made, but the order of combat can sometimes be effected. \$\endgroup\$
    – Airatome
    Apr 21, 2017 at 13:11
  • \$\begingroup\$ @Airatome Other groups entering doesn't change anyone's initiative value or relative place on the list but just adds entries, so that's not really what is asked here, but a rather good argument to not discard initiative values in practice after setting up the initial order. Regarding spells: I'm no expert, but scrolling through the SRD and looking at likely candidates (selected by looking at their names) yielded nothing. If you or anyone can name such exceptions, I'll gladly add them. \$\endgroup\$ Apr 21, 2017 at 13:31
  • \$\begingroup\$ @xNGTMx any effect that boosts your ability checks, specifically dexterity checks, will boost your initiative roll. The Guidance cantrip for example adds 1d4 to any ability check: dexterity included. Also, Bardic Inspiration can be used on an ability check, so an initiative check counts. Finally, the Enhance Ability spell has the Cat’s Grace enhancement, which gives you advantage on all dexterity checks, which would include initiative rolls. I don't know of anything that can change the initiative order itself though; just the bonuses on the initiative roll. \$\endgroup\$
    – Adam
    Apr 21, 2017 at 14:29
  • \$\begingroup\$ @Adam Indeed. But these cannot be applied during combat to alter the already rolled initiative and manipulate the order after its initial setup - which, as I understood it, was what Airatome meant. \$\endgroup\$ Apr 21, 2017 at 14:44
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    \$\begingroup\$ There's one instance where initiative can change mid-combat: a controlled mount's initiative changes to match the rider's. \$\endgroup\$
    – Doval
    Apr 21, 2017 at 15:57
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NickOfTime's answer provides the general rule. Under usual circumstances, the initiative order remains fixed once it is set. However, there are a few exceptions.

Sphinxes can force initiative rerolls.

One of the Sphinx's Lair Actions (e.g. the androsphinx or gynosphinx):

On initiative count 20 (losing initiative ties), the sphinx can take a lair action to cause one of the following magical effects; the sphinx can’t use an effect again until it finishes a short or long rest:

  • The flow of time is altered such that every creature in the lair must reroll initiative. The sphinx can choose not to reroll.
  • [...]

A mount's initiative can change mid-combat.

If you mount a horse or other controlled mount after initiative has been set, the mount's initiative changes to match the rider's:

The initiative of a controlled mount changes to match yours when you mount it.

A likely ill-advised use of the wish spell.

One of the listed uses of the wish spell may allow you to force an initiative reroll:

You undo a single recent event by forcing a reroll of any roll made within the last round (including your last turn). Reality reshapes itself to accommodate the new result. For example, a wish spell could undo an opponent's successful save, a foe's critical hit, or a friend's failed save. You can force the reroll to be made with advantage or disadvantage, and you can choose whether to use the reroll or the original roll.

I say that it may allow you to use wish on an initiative reroll because it says "last round" and technically initiative rolls happened before the round structure was put into place.

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  • \$\begingroup\$ So... what happens to the initiative of a controlled mount when you unmount them? After all, you can use feeblemind to make your fellow party members not count as "intelligent", if need be. The only real trick would be figuring out how to train them to accept a rider. \$\endgroup\$
    – Ben Barden
    Mar 6 at 15:38

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