Ghostlords

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The Ghost of Graymarrow is a Skeleton Lord who is the final boss of The Fort of the Damned Raid in Sea of Thieves. Once killed, the Ghost of Graymarrow drops the Fort of the Damned Key that opens the locked Fortress Vault.

Backstory[edit | edit source]

Ghost of Graymarrow is, as his title suggests, a ghostly apparition of the Skeleton LordGraymarrow who appears as a boss during the Revenge of the MorningstarTall Tale. With the Fort of the Damned Content Update, the FortressOld Boot Fort enveloped in thick fog and transformed into the Fort of the Damned as a part of a dark Ritual, supposedly orchestrated by Stitcher Jim and the Masked Stranger, who had previously dabbled with Dark Relics, Reaper's Chests, Rag & Bone Crates to plan for a resurrection ritual at Shipwreck Bay to bring back the Ghost of Sir Arthur Pendragon, which they later succeeded in during The Seabound Soul Content Update and Tall Tale. As of now, it is unknown whether the summoning of Graymarrow's Ghost was intended as a practice Ritual, or whether there was a larger reason behind it. The summoning ritual could not have been a coincidence, for Graymarrow was the one to seal Sir Arthur Pendragon in his painting. None-the-less, Duke and Stitcher Jim tasked adventurous Pirates with completing the Ritual and disposing of the Ghost of Graymarrow and his ghostly Shadow of Fate Skeletons.

During the October 2020 Fate of the Damned Content Update, Larinna sent Bilge Rats to hunt for Flames of Fate to combat Shadows of Fate that appear during the Festival of the Damned, but all the Bilge Rats went missing. As such, she sent Player Pirates to determine their fates. It turned out that Skeletons had been performing rituals all across the Seas to resummon the Ghost of Graymarrow so that they could stop the rise of Captain Flameheart and fight him.

Location & Raid[edit | edit source]

The Ghost of Graymarrow can only be summoned as a part of a Ritual at the Fort of the Damned Skeleton Fortress. The Fog surrounded Fort is the base for a Ritual that requires Pirates to gather all 6 Flames of Fate, light Ferryman Statues with the appropriate Flames and place a Ritual Skull on the Headless Skeleton in the Ritual Cage to begin the Raid. The Raid is signified by a massive Skeleton Skull cloud with Red eyes above the Fort that stays there for the remainder of the Raid.

Half-life download free. The Raid consists of 12 waves of Shadow of Fate Skeletons, ending with a 13th wave that summons the Ghost of Graymarrow. Unlike other Skeleton Lord fights within Tall Tales, the Ghost of Graymarrow always has a set amount of Health that does not scale with crew sizes. After defeating the Ghost of Graymarrow, the Skull cloud will disappear and he will drop a Fort of the Damned Key that can be used to open up the Fortress Vault, hiding away valuable Treasure.

Abilities[edit | edit source]

The Ghost of Graymarrow has a mostly similar move-set to the living Graymarrow:

• He can switch between the Pistol, Blunderbuss and Cutlass depending on the player's range.
• He has a high-damage blast attack, raising two Chests from the ground and slamming them together, causing a shockwave that sends all nearby Players backwards into the air, dealing increasing damage depending on their proximity to the boss. This attack may cause additional fall damage.
• He can Summon minions by taking out one chest and throwing around coins. Unlike Graymarrow who summons regular Skeletons, the Ghost summons Shadow of Fate Skeletons to aid him.
• He can eat a Coconut to supposedly regenerate lost heath. The amount of health regenerated (if any) is currently unknown. It may be that the purpose of this action is to show him getting low on health.

Notes and Tips[edit | edit source]

• The Ghost of Graymarrow does not have the ability to Teleport like the other Skeleton Lords.
• Unlike Tall Tale Skeleton Lords, the Ghost of Graymarrow always has a set amount of Health that doesn't scale with the size of the Crew fighting him.
• Gunpowder Barrels are an effective tool to deal large amounts of damage to the Ghost of Graymarrow, as he cannot Teleport away from them. 100 Gunpowder Barrels has been confirmed to kill the Ghost in one blast.
• If it is your second time fighting the Ghost during one session, you can save up the Stronghold Gunpowder Barrels from the Vault for the next boss fight. It is unknown whether Stronghold Barrels do more damage than regular Gunpowder Barrels though.
• When Ghost of Graymarrow summons reinforcements, larger Crews should dedicate one member to eliminate the firearm Skeletons, or retrieve or use the Gunpowder Barrels that some of the summons carry while the rest work on killing the boss.
• A good strategy with the Ghost of Graymarrow is to lure him down to the pier in range of the Ship's Cannons to kill him faster. It should take around 100 direct Cannonball hits to kill the Ghost of Graymarrow.
• If choosing to kill the Ghost at the pier, one of the Crew's Pirates can use the Harpoon to stun the boss in place for easier Cannoning. Each Harpoon shot also does 15 Damage, making it more effective than a Cutlass.
• Graymarrow's shockwave attack pushes back any adjacent ships. Anchoring the ship guarantees that the Ship doesn't move.
• Firebombs work against Ghost of Graymarrow.

The miniatures game Infinity has some interesting and unique mechanics. The first is that the player who is not currently taking their turn gets to have their models react to the actions of the active player. The second mechanic is that if the action and reaction are directly opposed (for example, the two models are firing at one another), both players roll dice at the same time (called a Face to Face roll). The player who scores 'better' wins the contest and their models performs the action.

Let's take a very simple case of two basic infantry troops shooting each other. The active model is he Fusilier Angus, firing his Combi Rifle with Ballistic Skill (BS) of 12. This weapon lets him roll 3 20-sided dice, which will succeed on a roll of his BS of 12 or less on each die. His opponent is the Zhanshi Wen Liu, firing his Combi Rifle with BS 11. As he is reacting, he only gets a single die, and his BS is lower, so he is looking to roll an 11 or less. They both roll their dice at the same time, and then compare results. First, any dice that missed (rolled above the firer's BS) are discarded. Then, any successes that rolled lower than the opponent's highest die are discarded. This leaves at most one player with any successful hits, which are then applied to the target. There are a few more complexities, but this outlines the basic flow. To make it concrete – Angus rolls a 15, 10, and 7, and Wen Liu rolls a 9. Angus's 15 is discarded as a miss (since he rolled greater than 12), and his 7 is discarded since it is lower than Wen Liu's 9. Meanwhile, Wen Liu's 9 is discarded since Angus rolled a 10. The only die left is Angus's 10, meaning he scored one hit on Wen Liu.

In this basic case, the probabilities are relatively easy to calculate. For each of the active player's dice, it is easy to calculate the chance that they rolled less than or equal to their target, minus the chance that their opponent rolled higher without going over their own target value. And in fact, there has long been an online tool called Infinity Math to help calculate probabilities where the reactive player is limited to one die.

The calculations get much more complicated when the reactive model is allowed to roll multiple dice. I attempted for some time to come up with a reasonably simple numerical way of calculating these chances, but kept on coming up short. Eventually, I remembered that my personal strengths are not in numerical analysis, but rather in computational and algorithmic optimization. Therefore, I decided to make a program which implements a really simple and straightforward means of calculating these probabilities, and then optimize it until it was acceptably efficient.

Basic Design Overview

The basic design of my dice rolling engine is to enumerate every possible permutation of dice that could be rolled, evaluate the results, and then calculate how likely each possible result is. Since the number of dice required can change for every scenario, my program implements this step using recursion. This allowed me to produce accurate results, but very slowly. Even a moderately complex calculation could easily take several minutes to complete. As such, looked for ways to optimize the algorithm to reduce the time taken.

Optimization – Matrix Symmetries

The first and biggest optimization that I implemented that decreased my running time by several orders of magnitude was to take advantage of symmetries in the matrix of all dice rolls I was generating. In other words, I made sure I never calculated results that varied only by the order of the numbers rolled.

Take this matrix showing all possible combinations of two four-sided dice as a simplified example:

Because a player doesn't care what order they rolled their dice in (since all dice are rolled simultaneously), we can cut the number of dice rolled approximately in half, by including only those rolls where the second number is greater than or equal to the first. Rising world download free.

As you can see, the second matrix doesn't have any duplicate entries, but does mark the ones that need to be double-counted. As the number of dimensions increases, the multiplicative factor can become much larger than 2, based on the number of repeated values.

As the number of dice increases, so do the number of dimensions of the matrix. In these higher-dimension matrices, the savings from matrix symmetries increase exponentially.

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And so forth.

Optimization – Miss Consolidation

The great thing about that optimization is that it always works, no matter what the scenario. The next one I did, however, helps in most common cases, but will occasionally offer little to no benefit.

Since all dice that roll higher than the target number are discarded without being used, it is unnecessary to roll all of them. I let the first failing die through in order to count it in the statistics for failures and misses, and I simply multiply the number of results by how many other failure states I rolled up. From the initial example of Fusilier Angus trying to roll a 12 or less, this:

Becomes this:

Obviously, the lower the target numbers involved, the greater the value of this optimization. Due to the way that this optimization stacks with the prior one, it frequently reduces the number of rolls calculated by well more than half.

Optimization – Multithreading

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The final optimization I implemented was to make the tabulating of dice rolls multi-threaded. I start one thread for each of the 20 possible values of the first die, and then tabulate the results when all threads have completed. My hosting company gives me access to 2 CPU cores, so the calculation takes approximately half as long to complete. Due to the various optimizations in the prior sections, different threads will take different amounts of time to complete, but how the operating system balances them between the cores evens everything out.

Web App

With that done, I had the time consuming part of the calculations taken care of. The next step was to create a web frontend that allows you to select what sort of scenario you would like to run, and then hands the data off to the back end utility. This has been another significant challenge, but has overall been pretty straightforward. My tool is available here, for you to play around with if such things interest you. I periodically update it with new features and to keep it up-to-date with the latest releases for the game.

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Prologue – Numerical Analysis

After I had already mostly completed work on this part of my tool, one of my fellow Infinity players from Maryland took the time to find a solution to this that is as close to closed-form as possible, using Mathematica and my tool to check his results. His description of his method is available in HTML or PDF, if you are interested.