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N Medium humanoids have gathered on an arbitrarily long field, standing in a line with each creature 120 feet away from each of its neighbors. The creature at one end of the line is mounted on a horse with a speed of 60. The creatures are arranged in initiative order, such that all N creatures will act in the order of their position in a single melee round. The mounted creature acts first.

Each creature other than the mounted creature is holding a pike and has readied an action to Shove the next mounted creature that moves adjacent to it.

On its turn, the mounted creature commands its mount to move 60 feet towards the next creature, then drops prone (which is not stated as a condition for dismounting in the Mounted Combat section of the 5e PHB) and orders the horse to Dash and move 60 feet more, closing the distance. At this time, the next creature's readied Shove triggers, and it makes an attack on the rider. Assuming the attack hits (which is likely, given that the rider is prone, thus granting advantage, and for the sake of the example has no armor or dexterity bonus to AC) the rider will be pushed off of his mount and the mount leaves his control. At this time he has used his actions and the second creature's turn begins.

Creature 2 starts by mounting the now-adjacent horse, whose initiative changes to match his. However, the horse's turn ended when its first rider's turn did, and thus it is taking a new turn when its second rider mounts it. The second rider orders it to move 60 feet towards the third creature, drops prone, and orders it to Dash another 60 feet, triggering the third creature's readied Shove. This procedure continues until one of the Shove attacks fails, allowing the horse to move a theoretically infinite distance in a single 6-second round.

I am absolutely certain there is a flaw in this logic, but I can't find it – what error breaks this strategy?

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    \$\begingroup\$ This is notably similar to a popular exploit in the Heroes of Might and Magic series, in which you'd create "hero trains" of mounted leaders in long succession on the map, and each would pass off their army from one to another in order to move the forces across the world in a single turn. \$\endgroup\$ – Southpaw Hare Dec 1 '17 at 18:37
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No. The Amazing Light Speed Horse™ cannot move an infinite distance
(And what distance it does move without taking the dash action is at a speed of at most movement per round, and with the dash action is 2×movement per round.)

Per the definition of movement from the Basic Rules v 0.3, page 63, and also from the Player's Handbook, page 181:

Every character and monster has a speed, which is the distance in feet that the character or monster can walk in 1 round.

(Note that the riding horse is stated as a monster in the Player's Handbook on page 310, and the warhorse on page 311.)

Your exploit only works if you incorrectly substitute turn for round under an assumption along the lines of somehow the horse receives one turn for each humanoid rider's turn, rather than one turn per round. While the second individual could attempt to mount the horse on their turn in your scenario, the horse will already have used all its movement for the round.

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    \$\begingroup\$ Holy crap, never even noticed that, no matter how many times your initiative might change or turns you get in a round, your movement is per round no matter what. \$\endgroup\$ – Airatome Nov 5 '16 at 20:57
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    \$\begingroup\$ That was true in the Basic Rules, but I'm seeing things in the PHB that seem to contradict it; "On your turn, you can move a distance up to your speed." PHB page 190. If you can find a source for your response in a published book or errata, I'll accept this answer. \$\endgroup\$ – Passage Nov 5 '16 at 21:20
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    \$\begingroup\$ Despite the p. 190 language, PHB, p. 181 defines Speed thus: “Every character and monster has a speed, which is the distance in feet that the character or monster can walk in 1 round.” This is actually consistent, because p. 190 also says that turns are 1 per creature per round: “During a round, each participant in a battle takes a turn.” It should take only a small edit to fix up this answer's argument. \$\endgroup\$ – SevenSidedDie Nov 5 '16 at 23:53
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    \$\begingroup\$ @Passage It is also true in the PHB: see my revised answer. :) \$\endgroup\$ – Lexible Nov 6 '16 at 2:43
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    \$\begingroup\$ Note that Jeremy Crawford disagrees with you. \$\endgroup\$ – GreySage Jan 26 '18 at 22:28
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Summary
The answers to date already say "no", but I wanted to point out some other issues with your logic. The final result is that RAW would allow you to do everything except let the horse take multiple turns in a round to move unlimited distances, but not quite the way you stated it.

That said, you should be able to move the horse indefinitely by just shoving it, though you will need high-level NPCs (around level 24), since they need a Strength (Athletics) skill of at least 15. And your rider will need a Dexterity modifier of at least +9 if you want to move horse and rider.

Of course, the biggest flaw in this whole thing is that you'd need to get a bazillion NPCs standing around waiting for you and your horse. A level 24 player or NPC could easily afford to just hire a level 13 wizard to teleport them to their destination in much less time than it would take all your NPCs to hike to their destinations.

Attack rolls won't get you anywhere near light speed, let alone infinity
If you were relying on attack rolls, you'd fail every 20th time, on average, even with +200 attack rolls vs an unarmored target.

If the d20 roll for an attack is a 1, the attack misses regardless of any modifiers or the target’s AC. (D&D basic rules, page 73)

To hit the speed of light, you'd have to make it through about 49 million npcs in one round. The odds of that are right at zero. (About 1 in 10^million ish. That's googol^(10000), or a 1 followed by a million zeros.)

Doing it with shove actions
However, the "shove" action isn't really an attack. It uses an attack action, and is considered "a special melee attack", but you actually make a contested Strength (Athletics) check against the target's Strength (Athletics) or Dexterity (Acrobatics), with the target choosing which.

The target of your shove must be no more than one size larger than you, and it must be within your reach. You make a Strength (Athletics) check contested by the target’s Strength (Athletics) or Dexterity (Acrobatics) check (the target chooses the ability to use). If you win the contest, you either knock the target prone or push it 5 feet away from you. (D&D basic rules, page 74)

I'm not seeing anything that says it automatically knocks the person off the mount in the basic rules, even if the shove succeeds. Assuming there's something in the full PHB that makes this clear, you could modify the question to work better.

If each NPC has +20 Strength (Athletics) and +0 Dexterity (Acrobatics), then the NPC currently on the horse chooses to contest the shove with Acrobatics rather than Athletics, and the best roll they could get is natural 20 + 0 = 20. The NPC on the ground would have a worse case roll of natural 1 + 20 = 21, which always succeeds, since opposing skill checks have no automatic failure.

Problems with falling off via a shove
Now, if the full PHB doesn't say the mounted guy automatically falls off if he's been successfully shoved, there are three ways I can think of to shove someone off a mount.

First, the shove action can push a target 5 feet away from you. Since horses are generally not 5 feet wide, that means you're no longer on the mount. Since there's no explicit saving throw when the rider is moved against their will, it seems logical this an automatic dismount. However, it's not explicitly stated this way, at least in the basic rules.

Second, the shove action could be used against either the horse or the rider to knock it prone. Knocking the horse prone would screw with its movement (from D&D basic rules page 70, it requires half your movement speed to stand up), so we'd want to knock the rider prone. At this point, the rider needs to make a Dexterity check at DC 10 to avoid falling off. Since the lowest modifier you can get is -5 for an ability score of 1 (D&D basic rules page 57), the rider would succeed with a roll of 15 or higher, or 30% of the time. This is even worse than the attack roll scenario.

Third, the shove action could be used against the horse to move it 5 feet, which would trigger the same Dexterity check at DC 10. The cool part of this is you can hypothetical get an extra 5 feet per round if you shove the horse as it's passing you, moving it 5 feet in front of you, then mounting it since it's within 5 feet of you. But it's still not a good scenario.

Once during your move, you can mount a creature that is within 5 feet of you or dismount.

....

If an effect moves your mount against its will while you’re on it, you must succeed on a DC 10 Dexterity saving throw or fall off the mount, landing prone in a space within 5 feet of it. If you’re knocked prone while mounted, you must make the same saving throw.

If your mount is knocked prone, you can use your reaction to dismount it as it falls and land on your feet. Otherwise, you are dismounted and fall prone in a space within 5 feet it. (D&D basic rules, page 76)

Deliberately falling prone
Your intent to deliberately fall prone while on the mount might be construed as being "knocked prone", requiring each NPC to pass their subsequent Dexterity check at DC 10 to stay on. You could either just not do this, since the skill check can be guaranteed anyways, or you could ensure your riders have at least a +9 Dexterity modifier (28-29 score).

If each NPC has a +9 Dexterity modifier, it's Dexterity (Acrobatics) is necessarily at least 9, so they'd need a Strength (Athletics) of 29 or more.

Doing away with all the shoving
I'm not sure this is the intended interpretation. However, it seems that you can mount once per turn and dismount once per turn (the wording could also be interpreted as saying you can either mount or dismount in a turn, but not both). Since each action takes half your movement speed, each of your NPCs could simply mount the horse at the start of their turn, then dismount the horse at the end of their turn, allowing the next NPC to mount without shoving anyone.

A better way to move the horse indefinitely.
Ok, so the other answers noted that the horse can't take multiple turns and keep running. But nothing says we can't keep shoving the horse.

Instead of NPCs 120 feet apart, put them 5 feet apart. Assume the NPCs and the horse all allow each other to invade their protected area.

Next, assume the NPCs have a Strength (Athletics) skill that's at least 20 higher than one or both of the horse's Strength (Athletics) or Dexterity (Acrobatics) skills.

Now, the first NPC is directly behind the horse and shoves the horse forward 5 feet, just past the second NPC. The second NPC shoves the horse another 5 feet, etc. If we rule that you can't literally shove the horse through the other NPC, you could have each NPC stand to the side of the horse's path, then step behind the horse on their turn before shoving. Regardless, the horse moves 5 feet per NPC turn.

If you want, you can have a rider with a Dexterity modifier of +9 or more (to avoid falling off each time the horse is shoved). Then both horse and rider can move indefinitely by being shoved across the planes.

(You can shove something up to one size larger than you. I'm assuming horses are Large size. If not, your NPCs would need to be scaled accordingly.)

A note on skill levels
I've been playing through Icewind Dale and Knights of the Old Republic, which are based on earlier editions of D&D where you increment your skills each level. I'd forgotten that 5e has a baked-in proficiency bonus that's related to your character level rather than something you advance manually, which makes it much harder to get numbers like +20 on your checks.

That said, it should still be possible. First, assume the horse has a Dexterity of 1, giving it a -5 modifier. Now, the NPC "only" needs a +15 modifier to always beat it. At level 20, there's a +6 proficiency bonus. A Strength score of 28-29 gives an ability modifier of +9, for a total of +15.

I know you can get a Strength of 20 through leveling. I'm guessing there's some magic item or another that grants +8 to Strength. If not, find a race that does have 28 Strength for your NPCs. Additionally, my understanding is you can earn 2 Strength per level past 20 if your DM allows it. Even without extended proficiency bonuses, a level 24 NPC could have the required 28 Strength naturally.

Similarly, the rider needs a +9 Dexterity modifier to always beat the DC 10 check to avoid falling off the horse, which requires the same kind of solution as getting a +9 Strength modifier.

The problem of practicality
Sure, RAW might allow a bazillion and one NPCs to dutifully line up so we can move our horse (and/or rider) a million miles in 6 seconds flat.

But it's rather doubtful your DM is actually going to allow that. Since RAW allow the DM to govern the NPCs in a manner that makes sense, RAW allows the DM to automatically prevent your solution from ever starting to take place, let alone work.

The reason it doesn't matter
Ok, so we have a bazillion and one NPCs dutifully lined up to move our horse (and/or rider) a million miles in 6 seconds flat. We broke the game!

Not really.

This is D&D, which is a fantasy game. In this fantasy world, is a cool little thing called the "Teleport" spell.

Teleport
7th-level conjuration
Casting Time: 1 action
Range: 10 feet
Components: V
Duration: Instantaneous

This spell instantly transports you and up to eight willing creatures of your choice that you can see within range, or a single object that you can see within range, to a destination you select. If you target an object, it must be able to fit entirely inside a 10-foot cube, and it can’t be held or carried by an unwilling creature.

The destination you choose must be known to you, and it must be on the same plane of existence as you. Your familiarity with the destination determines whether you arrive there successfully. The DM rolls d100 and consults the table. (D&D basic rules, page 102)

Teleport is a 7th level spell with only a verbal component. The only thing you need is a 13th level Wizard and you can move as far as you like within the same 6-second round. Consulting "the table", we can guarantee exact teleportation with no mishaps as long as you either have a sigil sequence to a permanent teleportation circle, or just an object from the destination taken from there within the last six months.

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When you mount a creature it switches to your initiative. The RAW says that the initiative is the order of turns; not that your turn starts on your initiative. It also states that each participant acts once in each round. Therefore, your horse only receives one turn during the round, regardless of how many times its initiative order changes. So the supposition that mounting the horse allows the horse to move again because it has a new turn is invalid.

Additionally you state that you are assuming the attacker hits. However each attacker has a minimum 5% chance of failure (by rolling a 1). This means that in the best case scenario, your system will break down with a probability of 1-.95^(#pikers). A chain of only 14 pikers will break before completion at least half the time. A chain of 90 or more pikers will break before completion in excess of 99% of the time. Clearly there is a statistical limit on how far this mechanism is functional.

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    \$\begingroup\$ "When you mount a creature it switches to your initiative. The RAW says that the initiative is the order of turns; not that your turn starts on your initiative." I think you should remove these two sentences or clarify where you're going with them. You appear to be trying to make a point about turn economy, but you don't go anywhere with that point and it's ultimately tangential to the parts that actually talk about the horse and peasants. \$\endgroup\$ – doppelgreener Nov 6 '16 at 11:58
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    \$\begingroup\$ @doppelgreener "However, the horse's turn ended when its first rider's turn did, and thus it is taking a new turn when its second rider mounts it." So I'm not sure why you've said this. The whole thing is predicated on the idea that the horse starts a new turn every time it changes initiative, so the statement doesn't need to "go anywhere". It is already a counter to one of the predicates, which makes it a flaw. \$\endgroup\$ – Wesley Obenshain Nov 6 '16 at 15:26
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    \$\begingroup\$ That additional sentence neatly puts a bow on the reasoning and makes its conclusion explicit to every reader. Nicely improved. +1 \$\endgroup\$ – SevenSidedDie Nov 6 '16 at 18:47
  • \$\begingroup\$ Jeremy Crawford says that the mounted creature gains an additional turn. \$\endgroup\$ – GreySage Jan 26 '18 at 22:30
  • \$\begingroup\$ @GreySage Primary source? \$\endgroup\$ – Wesley Obenshain Jan 28 '18 at 7:16
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Yes, I believe it does, with a few caveats

First, PHB pg 190. "Combatants often find themselves... on the ground . You can drop prone without using any of your speed...to move while prone you must crawl..."

Next, PHB pg 195. "...you can make a special attack to shove a creature, either to knock it prone or push it away from you..."

Lastly, PHB pg 198. "...if you're ... prone while mounted, you must make a saving throw or fall off the mount..."

At first glance we find that you can not mount a creature and then 'drop prone' , as you are now on a creature and not on solid ground TO drop prone on as per the rules on page 190, and if you were to afflict yourself with the 'Prone' status while mounted you would be subject to the saving throw or else fall off your mount before you even had a chance to try and command it to move.

As per the readied action shove attack, this seems fine though I'm not sure how you plan on attempting to remove the rider from its horse by trying to shove it prone or away from you as that would count as attempting to move the rider or mount against its will while mounted, resulting in the same saving throw (not a guarantee of knocking the rider off).

Everything else seems to be sound, unless I have missed something or misinterpreted any of the above rules or PHB quotes. In closing, however, it is very important that you try not to rationalize or put into real world context the combat mechancis and rules of a fictional fantasy game such as D&D ; logic will always fail. A round is 6 seconds, were these events to come to pass by following the rules the horse would, indeed, move an impossible distance in only 6 seconds which; if rationalized into real world context, would move incredibly fast.

I'm absolutely certain you can see why we don't apply such realism or rationale to a fantasy game, yes? As many have said, this is not a simulator, and the rules were not meant to simulate such things realistically. When we do...events like your question happen and make it really hard to explain; RAW or otherwise.

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  • \$\begingroup\$ don't forget you can choose to fail your saving throw to stay mounted.... \$\endgroup\$ – nitsua60 Nov 5 '16 at 20:46
  • \$\begingroup\$ @nitsua60 you mean can not right? because clearly: mobile.twitter.com/JeremyECrawford/status/708009718757720064 no rule exists that let you choose to fail a saving throw; but many exist the say you must make them when the text of an ability or spell tells you to. \$\endgroup\$ – Airatome Nov 5 '16 at 21:01
  • \$\begingroup\$ I don't mean that. Until Jeremy actually publishes that in Sage Advice, I'm with the reading of the PHB rules that GMNoob provides in the highest-voted answer, not in the terse non-explanation that Jeremy gives (and which forms the basis of a later answer on that question). Jeremy's tweets mean very little to me. \$\endgroup\$ – nitsua60 Nov 5 '16 at 21:11
  • \$\begingroup\$ As you've pointed out, I may have had the ordering wrong. It should still work if the rider instead drops prone after the attack is made, which leaves the attacker without advantage. This leaves an average of ~1.5 chances to fall off the horse, assuming the attackers have a +0 attack bonus and the universe's DM allows for dropping prone while mounted. (I wouldn't rule it impossible, given that the referenced text merely states that being prone is the state of lying on the ground, rather than that you must be on the ground to drop prone.) \$\endgroup\$ – Passage Nov 5 '16 at 21:25
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    \$\begingroup\$ @Meta4ic that's because each creature in the initiative is only readying the shove action to go off outside of thier turn and then it is thier turn and THEN they move and mount the horse during thier initiative, not off of it. \$\endgroup\$ – Airatome Nov 7 '16 at 14:54

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