Shard Firebase RTDB by `userId` or any arbitrary string/identifier. Uses a 16 bit cyclic redundancy check to calculate the users shard number based on their user id string. This negates the need for a master instance that maps where users data is stored. See comment below code block for more details.

slotCalc.js

const lookup = [
  0x0000, 0x1021, 0x2042, 0x3063, 0x4084, 0x50a5, 0x60c6, 0x70e7,
  0x8108, 0x9129, 0xa14a, 0xb16b, 0xc18c, 0xd1ad, 0xe1ce, 0xf1ef,
  0x1231, 0x0210, 0x3273, 0x2252, 0x52b5, 0x4294, 0x72f7, 0x62d6,
  0x9339, 0x8318, 0xb37b, 0xa35a, 0xd3bd, 0xc39c, 0xf3ff, 0xe3de,
  0x2462, 0x3443, 0x0420, 0x1401, 0x64e6, 0x74c7, 0x44a4, 0x5485,
  0xa56a, 0xb54b, 0x8528, 0x9509, 0xe5ee, 0xf5cf, 0xc5ac, 0xd58d,
  0x3653, 0x2672, 0x1611, 0x0630, 0x76d7, 0x66f6, 0x5695, 0x46b4,
  0xb75b, 0xa77a, 0x9719, 0x8738, 0xf7df, 0xe7fe, 0xd79d, 0xc7bc,
  0x48c4, 0x58e5, 0x6886, 0x78a7, 0x0840, 0x1861, 0x2802, 0x3823,
  0xc9cc, 0xd9ed, 0xe98e, 0xf9af, 0x8948, 0x9969, 0xa90a, 0xb92b,
  0x5af5, 0x4ad4, 0x7ab7, 0x6a96, 0x1a71, 0x0a50, 0x3a33, 0x2a12,
  0xdbfd, 0xcbdc, 0xfbbf, 0xeb9e, 0x9b79, 0x8b58, 0xbb3b, 0xab1a,
  0x6ca6, 0x7c87, 0x4ce4, 0x5cc5, 0x2c22, 0x3c03, 0x0c60, 0x1c41,
  0xedae, 0xfd8f, 0xcdec, 0xddcd, 0xad2a, 0xbd0b, 0x8d68, 0x9d49,
  0x7e97, 0x6eb6, 0x5ed5, 0x4ef4, 0x3e13, 0x2e32, 0x1e51, 0x0e70,
  0xff9f, 0xefbe, 0xdfdd, 0xcffc, 0xbf1b, 0xaf3a, 0x9f59, 0x8f78,
  0x9188, 0x81a9, 0xb1ca, 0xa1eb, 0xd10c, 0xc12d, 0xf14e, 0xe16f,
  0x1080, 0x00a1, 0x30c2, 0x20e3, 0x5004, 0x4025, 0x7046, 0x6067,
  0x83b9, 0x9398, 0xa3fb, 0xb3da, 0xc33d, 0xd31c, 0xe37f, 0xf35e,
  0x02b1, 0x1290, 0x22f3, 0x32d2, 0x4235, 0x5214, 0x6277, 0x7256,
  0xb5ea, 0xa5cb, 0x95a8, 0x8589, 0xf56e, 0xe54f, 0xd52c, 0xc50d,
  0x34e2, 0x24c3, 0x14a0, 0x0481, 0x7466, 0x6447, 0x5424, 0x4405,
  0xa7db, 0xb7fa, 0x8799, 0x97b8, 0xe75f, 0xf77e, 0xc71d, 0xd73c,
  0x26d3, 0x36f2, 0x0691, 0x16b0, 0x6657, 0x7676, 0x4615, 0x5634,
  0xd94c, 0xc96d, 0xf90e, 0xe92f, 0x99c8, 0x89e9, 0xb98a, 0xa9ab,
  0x5844, 0x4865, 0x7806, 0x6827, 0x18c0, 0x08e1, 0x3882, 0x28a3,
  0xcb7d, 0xdb5c, 0xeb3f, 0xfb1e, 0x8bf9, 0x9bd8, 0xabbb, 0xbb9a,
  0x4a75, 0x5a54, 0x6a37, 0x7a16, 0x0af1, 0x1ad0, 0x2ab3, 0x3a92,
  0xfd2e, 0xed0f, 0xdd6c, 0xcd4d, 0xbdaa, 0xad8b, 0x9de8, 0x8dc9,
  0x7c26, 0x6c07, 0x5c64, 0x4c45, 0x3ca2, 0x2c83, 0x1ce0, 0x0cc1,
  0xef1f, 0xff3e, 0xcf5d, 0xdf7c, 0xaf9b, 0xbfba, 0x8fd9, 0x9ff8,
  0x6e17, 0x7e36, 0x4e55, 0x5e74, 0x2e93, 0x3eb2, 0x0ed1, 0x1ef0
];

/**
 * Convert a string to a UTF8 array - faster than via buffer / no buffer in RN
 * @param str
 * @returns {Array}
 */
function toUTF8Array(str) {
  let char;
  let i = 0;
  let p = 0;
  const utf8 = [];
  const len = str.length;

  for (; i < len; i++) {
    char = str.charCodeAt(i);
    if (char < 128) {
      utf8[p++] = char;
    } else if (char < 2048) {
      utf8[p++] = (char >> 6) | 192;
      utf8[p++] = (char & 63) | 128;
    } else if (
      ((char & 0xFC00) === 0xD800) && (i + 1) < str.length &&
      ((str.charCodeAt(i + 1) & 0xFC00) === 0xDC00)) {
      char = 0x10000 + ((char & 0x03FF) << 10) + (str.charCodeAt(++i) & 0x03FF);
      utf8[p++] = (char >> 18) | 240;
      utf8[p++] = ((char >> 12) & 63) | 128;
      utf8[p++] = ((char >> 6) & 63) | 128;
      utf8[p++] = (char & 63) | 128;
    } else {
      utf8[p++] = (char >> 12) | 224;
      utf8[p++] = ((char >> 6) & 63) | 128;
      utf8[p++] = (char & 63) | 128;
    }
  }

  return utf8;
}

/**
 * Convert a string into a CRC16 hash.
 * @param str
 * @returns {number}
 */
function generate(str) {
  let char;
  let i = 0;
  let start = -1;
  let result = 0;
  let resultHash = 0;
  const utf8 = toUTF8Array(str);
  const len = utf8.length;

  while (i < len) {
    char = utf8[i++];
    if (start === -1) {
      if (char === 0x7B) {
        start = i;
      }
    } else if (char !== 0x7D) {
      resultHash = lookup[(char ^ (resultHash >> 8)) & 0xFF] ^ (resultHash << 8);
    } else if (i - 1 !== start) {
      return resultHash & 0x3FFF;
    }

    result = lookup[(char ^ (result >> 8)) & 0xFF] ^ (result << 8);
  }

  return result & 0x3FFF;
}

/**
 * Get the shard number for a generated slot.
 *
 * @param slot
 * @param shards
 * @returns {number}
 */
function shardForSlot(slot, shards = 10) {
  const slotSize = Math.round(16383 / shards);
  return Math.ceil(slot / slotSize);
}

// testing using user ids
console.log(shardForSlot(generate('008ZlXmlSoR5JOUw9asn2uvfDnH2')));
console.log(shardForSlot(generate('00I0dU5eCjRsq5OsNEiR7F6Z81A3')));
console.log(shardForSlot(generate('010imbVXHJfmonoC0Mz6wGInsys1')));
console.log(shardForSlot(generate('016xRLmbTJhCLE8038hRQ6BzrlC2')));
console.log(shardForSlot(generate('01Ncn9PWMXXm6oc8uVNPZiFyJOE2')));
console.log(shardForSlot(generate('01T7yi9SJkMyjl5PmMMlqykwUd43')));
console.log(shardForSlot(generate('02771fjg81dCe9VwRyB9zEf5UMw2')));
console.log(shardForSlot(generate('02GtQG8tI9ORjadgVqQZ5POkotO2')));
console.log(shardForSlot(generate('zzpv0R09UnTgc5MjiMMMIQ1SHRF2')));
console.log(shardForSlot(generate('14ZxIeKAKHfdeW4LYkRYTJoRwPC2')));
console.log(shardForSlot(generate('zeEwnZaYYBP7XvEjrdEgMnB5J092')));
console.log(shardForSlot(generate('SIEntLUOUec5VsW7AuyV8hnOtVF2')));
console.log(shardForSlot(generate('tqJJIowPQgQx9TA2P1hqNI39Mnl1')));
console.log(shardForSlot(generate('MhBFF5R8XfdCPgoxaHaOzRP2KY33')));
console.log(shardForSlot(generate('47kKFge003VhEInw4YxJFkbPaiI3')));
console.log(shardForSlot(generate('JdaheYIX0IXGeVVwSl369uIUTCh2')));
console.log(shardForSlot(generate('kAn7T2EW0UaX88R1oFVoDBNHWnt1')));
console.log(shardForSlot(generate('FYNwIewg48aCSbEVRmImnhERgbG3')));
console.log(shardForSlot(generate('customUserId12byIFtTMURT')));
// these will all go to the same shard id
console.log(shardForSlot(generate('{foo}AoLwrQMawBfyCZ0Yp44y6h5I8nB2')));
console.log(shardForSlot(generate('{foo}mfipaYNDDyfJqzYSvy0TJYQDkN53')));
console.log(shardForSlot(generate('{foo}ZGxjo5cjLUQOI56kJyOiOm9aGDF3')));

// OUTPUT
/*
8
9
9
9
1
4
2
7
3
10
4
6
9
7
3
8
1
1
3

// same shard because of the tag 'foo':
8
8
8
*/
// e.g. my-rtdb-name${slot} - my-rtdb-name10

The same can be done for document ids etc.

Additionally, you can tag where specific data goes, for example, if you had a bunch of data relating to a chat group and wanted all the messages for that chat group on the same shard you can tag your string that you use to generate the shard instance number, e.g. {im-a-tag}message1234 & {im-a-tag}message5678 will both return the same shard number as its calculated based on the tag only (im-a-tag in this example, but it could also be the chat group id).

---

Code taken from my https://github.com/Salakar/cluster-key-slot npm package - which is used by both of the official Redis clients for Node.js - ioredis & redis packages on NPM.