# Guides/Quarry Prospecting/Spiral Search

**Below is a copy of Yendor's T6 Spiral Search Example.**

I follow Marvl's Dead T3 link method for marble quarrying. It is a very efficient search strategy. Unfortunately, Marvl's guide combines the search method, an explanation of its efficiency, and a probabilistic analysis of the slate cost into one massive document.

This page gives a much simpler explanation of spiral search, and a few specific example searches from Tale 6.

## Spiral Search (The basics)

We start with the two people (30, 30) units away from each other. For maximum efficiency, both can look for different types of marble, but the explanation here assumes that player 1 is the only one prospecting. Initially, players alternate moving 60 coordinates at a time (so each time player 1 and player 2 are (30, 30) coordinates away). Once there is an initial spot with a two-slate break, then the spiral search comes into play. The key idea is that player 2 moves only when there is a two-slate break; player 2 will move 1/2 way to player 1. Player 1 will move at a right angle to whichever direction player 2 moved and try again—so if Player 2 moves SE, Player 1 should move NE. In this way, players alternate between being diagonally away from each other and being in a straight line from each other. The search ends when players are standing directly next to each other on a (1,1) coordinate boundary.

There is one small quirk: 32 coordinates is too far away to prospect. Players are initially 30 units away, and the first move is 14 coordinates instead of 15. This gives a nice power-of-2 distance.

The table below shows the correct distances between players at each step:

Start | Step 1 | Step 2 | Step 3 | Step 4 | Step 5 | Step 6 | Step 7 | Step 8 | Step 9 | Step 10 |

(30, 30) | (0, 30) | (16, 16) | (0, 16) | (8, 8) | (0, 8) | (4, 4) | (0, 4) | (2, 2) | (0, 2) | (1, 1) |

The explanation can be hard to see in abstract, so here are a few example prospecting runs. Note that if there is only one slate break, player 1 is the only person to move; if there is a two-slate break, player 2 moves 1/2 way to player 1, and player 1 then moves at right-angles to the next step size.

## Example Quarry 1

Initial break happens with P1 at 1800, 3300, and P2 at 1770, 3330 P2 moves 1/2 way, to 1784, 3316 (SE). Player 1 moves NE to 1814, 3316 No break, so try 1784, 3346 P2 moves 1/2 way to 1784, 3330 (N). Player 1 moves E to 1800, 3346 No break, so try 1800, 3314. Then 1768, 3314 P2 moves 1/2 way to 1776, 3322 (SW). Player 1 moves NW to 1768, 3322 P2 moves 1/2 way to 1772, 3322 (W). Player 1 moves S to 1768, 3318 No break, so try 1768, 3326, then 1776, 3326. P2 moves 1/2 way to 1774,2224 (NE). Player 1 moves SE to 1778, 3324 P2 moves 1/2 way to 1776, 2224 (E). Player 1 moves S to 1778, 3322 P2 moves 1/2 way to 1777, 3323 (SE). Player 1 moves SW to 1777, 3321 P2 moves 1/2 way to 1777, 3322 (S). Player 1 moves W to 1776, 3321 No break so try 1776, 3323 Plant quarry! (24 slate used)

## Example Quarry 2

Initial two-break at 2030, 3340 & 2000, 3370 P2 moves NW to 2016, 3354. P1 moves NE to 2016, 3384 No break so try 2046, 3354, then 2016, 3324 and 1986, 3354 P2 moves W to 2002, 3354. P1 moves N to 1986, 3370 P2 moves NW to 1994, 3362. P1 moves NE to 1994, 3374 P2 moves N to 1994, 3370. P1 moves E to 2002, 3378 No break, so try 1986, 3378 then 1986, 3362 and 2002, 3362 P2 moves SE to 1998, 3366. P1 moves SW to 1998, 3358 No break so try 1990, 3366 then 1998, 3374 P2 moves N to 1998, 3370. P1 moves E to 2002, 3374 No break so try 2002, 3366 P2 moves SE to 2000, 3368. P1 moves SW to 2000, 3364 P2 moves S to 2000, 3366. P1 moves E to 2002, 3364 No break so try 2002, 3368 P2 moves to 2001, 3367 (NE). P1 moves SE to 2003, 3367 No break so try 2001, 3365 then 1999, 3367 P2 moves to 2000, 3367 (W). P1 moves N to 1999, 3368 Plant Quarry! (34 slate used)