nturley / halite

Neil and Bob Halite Bot

New Features

Game Visualizer

Now you can highlight cells in yellow!

def draw_game(boards: Board[], highlights: Point[][])

It also displays board coordinates along the outside edges as well as the player score on the right hand side.

Strategies

Behaviors

Our theory is that ships will have a behavior assigned to them by some higher level strategy engine. The behaviors will probably be things like

• Mine
• Harrass/Raid
• Border Patrol

The most important one to begin with is mining.

Djikstra Path Planning

I think this one is the winner. Given a set of target points it will find the best paths to all points on the board of length t. We use the result from t-1 to calculate t. So this algorithm should be linear complexity with respect to t. We use some objective function to evaluate the relative merits of different paths.

The objective function can be mining halite, increasing board control, avoiding hazards or a mixture of all three.

See here for more details.

Oracles

Oracles are functions that can answer questions like

• what is the most likely next N moves that my opponents will make?
• If I generate a miner at this point in the game, am I likely to make a positive return on the investment?
• What is the path for my miner that will harvest the most halite?

Board Control

We have a theory that board control is advantageous. The theory is that it is much easier to herd enemy ships than it is to capture them (similar to two kings on a chess board). Effective herding may be able to push enemy miners away from the high value mining locations and secure them for our own miners.

My theory is that board control is trying to maximize the amount of the board where the closest empty ship is owned by us. The larger area that is, the more area our miners will have to safely mine. Territory with large amounts of halite is especially valuable. The border patrol behavior is to make moves that will herd enemy ships away from our territory, move toward vulnerable edges of our perimeter, while expanding our territory into valuable areas of the map.

The other part of board control is harrassment. Which is to send empty ships behind enemy lines to disrupt the area of control of our opponents. Harrassment behavior most likely involves chasing around enemy miners to prevent them from mining high value halite and returning their cargo. Because we have three opponents, investing in harrassment is probably only useful against opponents that are close to us in rank (sabotaging the opponent that is just above us in rank to take his place or just below us to prevent them from taking our place).

Herding

The two kings theory of herding is that rather than pursing enemy ships around the board, we establish a boundary and prevent enemy ships from crossing it.

For instance in the below image, suppose B wants to prevent A from reaching X. B should not move directly onto A. It should stay where it is.

If A goes left to B4, B should go to B5

B can prevent A from ever getting to X, by simply guarding row 5. Its obviously more complicated when there are more ships and halite involved, but the overall concept is that it is easier to block enemy ships from crossing boundaries than it is to chase them down and destroy them.

Useful Utilities

precomputing things like distance for every point to every point will be a bit large. 21 x 21 x 21 x 21 x 4 = 760kB. Manhattan distance is pretty cheap anyways so it may not be worth it.

Vector Distance

Vector distance gives the shortest distance to a point as a vector (dx, dy). Positive dx means EAST. Positive dy means SOUTH (for some reason).

center = Point(board_size // 2, board_size // 2)
def vector_distance(origin: Point, dest: Point, board_size: int):
       return (dest - origin + center) % board_size - center

Manhattan Distance

I think this is the cheapest way to do a Manhattan distance.

def manhattan_distance(p1: Point, p2: Point, board_size: int):
    dp = abs(vector_distance)
    return dp.x + dp.y

Bot Analysis

Optimus

• Optimus gives each ship a collection of action options, Eliminates options that are unacceptable, and adds options that automatically will fire
  • always move to an adjacent position with a vulnerable enemy ship.
  • Unacceptable targets seem to be positions that are adjacent to enemy ships with lower halite
• Optimus assigns each ship a target.
• The target will add one or more actions to the action collection of the ship.
• All possible directions are at the back of the list of the action collection.

Mining Strategy

Optimus rates each possible destination with a score and sets that max score as the destination as the target for that ship. the score for mining is based on the expected halite per turn assuming a path that goes directly to the target and then directly to the nearest shipyard. This means that we mine cells that are

• close to us
• close to a shipyard
• have a lot of halite

I'm still trying to understand the equation for number of turns to mine. something about logarithm of carried/remaining ratio and then a lookup table.

All of this seems like a lot of work that doesn't take into account the possibility of simply not returning the halite back to the shipyard. You can ignore the travel cost to the shipyard if you don't need the money right now to buy more ships. I think this would ignore the value in mining two medium cells that are adjacent.

This will miss optimal solutions that involve mining clusters of medium halite especially clusters that are far away.

The score for returning the halite is carried_halite/distance. This is logical because a ship should return home if it is very close (the cost for returning is low), or if is very full (the cost of losing the cargo is high).

I'm guessing scipy.optimize tries to find a unique target for each ship.

Shipyard Conversion

Only creates a shipyard if

• There are no shipyards. Chooses the ship with the most halite.
• danger without escape
• last turn and we need to return our halite

Doesn't seem to be any planning about where to place the shipyard besides not using a ship that is in danger.

Combat

• Vulnerable ships present a better destination target (adds on top of halite)
• Do not choose a lower halite ship as a destination
  • This prevents us from trying to mine a square that an enemy ship is already mining.

Enemy ships that are on less than 50 halite seem to be invisible as far as selecting destinations but they do contribute to attack and avoid matrix.

Ship Production

Always tries to maintain a fleet of 20 ships, near end of game only tries to maintain 15. Why would you ever create a ship after turn 375?

Vulnerabilities

1. Mining isn't optimal. Doesn't try to mine near clusters. Doesn't try to mine too far from shipyards.
2. If it experiences significant ship loss near the end of game, it will waste tremendous resources to replace ships that will never pay themselves off.
3. Even if there is a giant crowd of enemy ships two squares away, it will happy run toward it until it comes right up to them.
4. No hazard path planning. It just beelines to the target until it notices a hazard. Then it will just move back and forth until it's path clears. It won't even try to choose a different target.
5. No defensive moves to clear hazards or offensive moves to harrass opponents. It pretty much just mines.
6. Prone to distraction. A heavy halite ship could be chased for eternity.

Swarm

Mining

This mining algorithm is much greedier. It only considers neighboring cells and if it can't find any with a non-neglible amount of halite, then it just patrols around the map.

I can't even find where it returns the halite to the shipyard.

Shipyard Conversion

If there are no shipyards and the ship can afford it or enemy forces us into a position with no escape.

Ship Production

maintain a fleet of 9 or 3 depending on how close to the end of the game we are

Combat

Avoid hostile ships always

Vulnerabilities

This is much more primitive than Optimus

1. Mining is nowhere near optimal.
2. Each ship only ever considers neighboring cells
3. No defensive moves or even opportunistic attacks.

Replay Analysis

The factors that seem to indicate the game outcome are

1. What is the mining efficiency? (halite/ship/turn)
   • additional shipyards, how do you choose mining paths? How often do you return?
2. How many and when were ships lost due to collisions?
   • expected total game loss = mining efficiency * decrease in ship lifetime
3. When was ship production halted?
   • We will be riding zero halite prior to this point, and then investing nearly zero halite in ships after this point
   • when marginal ship benefit goes below zero

• 2 and 3 involve estimating what the value of a ship is over it's lifetime.
• 1 and 2 involve path planning.

We are blue and win in this game.

We took an early lead because of our second shipyard which made our mining more efficient and allowed us to increase our fleet size faster than our opponents. The third shipyard and additional ships pushed us even further to the top.

---

We are green and lose this game.

This game we lost is particularly instructive. The map cannot support more than about 40 ships simultaneously mining. None of the players realize this and continue to invest in ships for most of the game. The halite starts to deplete and income starts dropping for all players. Halfway through the game, our average harvest per turn drops to about 40 while we have 25 ships mining so each ship is averaging about 1.6 halite per turn which means that it takes 312 turns to get a positive return on investment for a ship. So every single ship built at this point is a loss. The winner is whoever buys the fewest ships at this point. Orange builds the fewest ships and wins.

The amount of money wasted on buying ships was really tragic. We bought 4 ships after turn 250. We lost by about 2000 halite.