Yes.

Unlike in previous editions of D&D, a creature's initiative in 5e is an ordinal (e.g "third turn in the round") rather than a numerical score (e.g. "Dexterity check total of eleven").

Because initiative is an ordinal, the "Controlling a Mount" rule works as follows:

A combat is in progress. Applejack the Warhorse's initiative is the sixth turn of every round. Bob the Battlemaster's initiative is the third turn of every round.

• On his turn, Bob spends half his movement to mount Applejack.
• Applejack's initiative is changed to match Bob's, becoming the third turn of every round.
• Bob selects Dash as Applejack's action, making Applejack's allowable movement for the turn 120'. Bob directs Applejack to move 70', bringing him within reach of an opponent.
• Bob takes his Attack action.
• Bob directs Applejack to move 50' away from the opponent. Applejack and Bob's shared turn is complete.

If Bob were to be unhorsed before the end of the combat, Applejack's initiative would revert to sixth again; the initiative order itself never changes.

What does "initiative" mean?

Since everything hinges on the phrase "the initiative of a controlled mount changes", let's comb through the rules text.

From page 189 of the Player's Handbook:

Initiative

Initiative determines the order of turns during combat.

Tells us what initiative does, but not what it is.

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.

There are two distinct concepts here:

1. The Dexterity check total. This is a numerical value in (roughly) the 1-20 range. There can be ties.

2. The rank in the initiative order. This is an ordinal value (first, second, third,...last). There are never ties, since they're always resolved according to the following rule:

If a tie occurs, the DM decides the order among tied DM-controlled creatures, and the players decide the order among their tied characters. The DM can decide the order if the tie is between a monster and a player character.

Taking (2) above as the definition of "initiative" gives the most satisfactory interpretation: initiative is a creature's rank in the initiative order. Creatures only share initiative in two cases:

• Multiple identical creatures under GM control
• Controlled mounts

Yes.

Unlike in previous editions of D&D, a creature's initiative in 5e is an ordinal (e.g "third turn in the round") rather than a numerical score (e.g. "Dexterity check total of eleven").

Because initiative is an ordinal, the "Controlling a Mount" rule works as follows:

A combat is in progress. Applejack the Warhorse's initiative is the sixth turn of every round. Bob the Battlemaster's initiative is the third turn of every round.

• On his turn, Bob spends half his movement to mount Applejack.
• Applejack's initiative is changed to match Bob's, becoming the third turn of every round.
• Bob selects Dash as Applejack's action, making Applejack's allowable movement for the turn 120'. Bob directs Applejack to move 70', bringing him within reach of an opponent.
• Bob takes his Attack action.
• Bob directs Applejack to move 50' away from the opponent. Applejack and Bob's shared turn is complete.

If Bob were to be unhorsed before the end of the combat, Applejack's initiative would revert to sixth again; the initiative order itself never changes.

What does "initiative" mean?

Since everything hinges on the phrase "the initiative of a controlled mount changes", let's comb through the rules text.

From page 189 of the Player's Handbook:

Initiative

Initiative determines the order of turns during combat.

Tells us what initiative does, but not what it is.

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.

There are two distinct concepts here:

1. The Dexterity check total. This is a numerical value in (roughly) the 1-20 range. There can be ties.

2. The rank in the initiative order. This is an ordinal value (first, second, third,...last). There are never ties, since they're always resolved according to the following rule:

If a tie occurs, the DM decides the order among tied DM-controlled creatures, and the players decide the order among their tied characters. The DM can decide the order if the tie is between a monster and a player character.

Taking (2) above as the definition of "initiative" gives the most satisfactory interpretation: initiative is a creature's rank in the initiative order. Creatures only share initiative in two cases:

• Multiple identical creatures under GM control
• Controlled mounts

Yes.

Unlike in previous editions of D&D, a creature's initiative in 5e is an ordinal (e.g "third turn in the round") rather than a numerical score (e.g. "Dexterity check total of eleven").

Because initiative is an ordinal, the "Controlling a Mount" rule works as follows:

A combat is in progress. Applejack the Warhorse's initiative is the sixth turn of every round. Bob the Battlemaster's initiative is the third turn of every round.

• On his turn, Bob spends half his movement to mount Applejack.
• Applejack's initiative is changed to match Bob's, becoming the third turn of every round.
• Bob selects Dash as Applejack's action, making Applejack's allowable movement for the turn 120'. Bob directs Applejack to move 70', bringing him within reach of an opponent.
• Bob takes his Attack action.
• Bob directs Applejack to move 50' away from the opponent. Applejack and Bob's shared turn is complete.

If Bob were to be unhorsed before the end of the combat, Applejack's initiative would revert to sixth again; the initiative order itself never changes.

Yes.

Unlike in previous editions of D&D, a creature's initiative in 5e is an ordinal (e.g "third turn in the round") rather than a numerical score (e.g. "Dexterity check total of eleven").

Because initiative is an ordinal, the "Controlling a Mount" rule works as follows:

A combat is in progress. Applejack the Warhorse's initiative is the sixth turn of every round. Bob the Battlemaster's initiative is the third turn of every round.

• On his turn, Bob spends half his movement to mount Applejack.
• Applejack's initiative is changed to match Bob's, becoming the third turn of every round.
• Bob selects Dash as Applejack's action, making Applejack's allowable movement for the turn 120'. Bob directs Applejack to move 70', bringing him within reach of an opponent.
• Bob takes his Attack action.
• Bob directs Applejack to move 50' away from the opponent. Applejack and Bob's shared turn is complete.

If Bob were to be unhorsed before the end of the combat, Applejack's initiative would revert to sixth again; the initiative order itself never changes.

What does "initiative" mean?

Since everything hinges on the phrase "the initiative of a controlled mount changes", let's comb through the rules text.

From page 189 of the Player's Handbook:

Initiative

Initiative determines the order of turns during combat.

Tells us what initiative does, but not what it is.

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.

There are two distinct concepts here:

1. The Dexterity check total. This is a numerical value in (roughly) the 1-20 range. There can be ties.

2. The rank in the initiative order. This is an ordinal value (first, second, third,...last). There are never ties, since they're always resolved according to the following rule:

If a tie occurs, the DM decides the order among tied DM-controlled creatures, and the players decide the order among their tied characters. The DM can decide the order if the tie is between a monster and a player character.

Taking (2) above as the definition of "initiative" gives the most satisfactory interpretation: initiative is a creature's rank in the initiative order. Creatures only share initiative in two cases:

• Multiple identical creatures under GM control
• Controlled mounts

Yes.

Unlike in previous editions of D&D, a creature's initiative in 5e is an ordinal (e.g "third turn in the round") rather than a numerical score (e.g. "Dexterity check total of eleven").

Because initiative is an ordinal, the "Controlling a Mount" rule works as follows:

A combat is in progress. Applejack the Warhorse's initiative is the sixth turn of every round. Bob the Battlemaster's initiative is the third turn of every round.

• On his turn, Bob spends half his movement to mount Applejack.
• Applejack's initiative is changed to match Bob's, becoming the third turn of every round.
• Bob selects Dash as Applejack's action, making Applejack's allowable movement for the turn 120'. Bob directs Applejack to move 70', bringing him within reach of an opponent.
• Bob takes his Attack action.
• Bob directs Applejack to move 50' away from the opponent. Applejack and Bob's shared turn is complete.

Yes.

Unlike in previous editions of D&D, a creature's initiative in 5e is an ordinal (e.g "third turn in the round") rather than a numerical score (e.g. "Dexterity check total of eleven").

Because initiative is an ordinal, the "Controlling a Mount" rule works as follows:

A combat is in progress. Applejack the Warhorse's initiative is the sixth turn of every round. Bob the Battlemaster's initiative is the third turn of every round.

• On his turn, Bob spends half his movement to mount Applejack.
• Applejack's initiative is changed to match Bob's, becoming the third turn of every round.
• Bob selects Dash as Applejack's action, making Applejack's allowable movement for the turn 120'. Bob directs Applejack to move 70', bringing him within reach of an opponent.
• Bob takes his Attack action.
• Bob directs Applejack to move 50' away from the opponent. Applejack and Bob's shared turn is complete.

If Bob were to be unhorsed before the end of the combat, Applejack's initiative would revert to sixth again; the initiative order itself never changes.