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Welcome to MoneyPot (https://moneypot.com)'s provably fair seeding event.

Our provably fair system is based on the first seeding event (https://bitcointalk.org/index.php?topic=922898.0), but with the addition of a third-party (https://www.provablyhonest.com) contribution. This preserves all provably fair guarantees while allowing external auditing. The high level of the scheme is:

1. Starting with a secret, we generate a chain of sha256 hashes by hashing the previous hash.
2. We play through that chain of hashes, in reverse order, and use the hashes to determine the crash point in a provably fair manner.
3. We mix in a “client seed” which we are hereby committing to, along with Provably Honest’s vxSignature (https://www.provablyhonest.com) to prove that we are committing to a sequence of game results from a fair distribution, without knowing the outcome.

Starting with a server secret, I have generated a chain of 100,000,000 sha256 hashes by recursively hashing the previous binary-encoded hash. The hash of the chain's last element is 3564a69ecd793515edefa28ae7440d5cdfefdfcb0b3f3cf840be6efb783c9891. This is also our commitment (https://www.provablyhonest.com/apps/moneypot/vx/summary/3564a69ecd793515edefa28ae7440d5cdfefdfcb0b3f3cf840be6efb783c9891) to Vx.

You can verify if a hash is part of the chain with a function like this:

Code:

import { sha256 } from "@noble/hashes/sha256";
import { bytesToHex, hexToBytes } from "@noble/hashes/utils";

const terminatinghash = hexToBytes("575faa089b45aea15ac51fa35d9e2cb085510b286c6b27ac5fa93235cdc30e6c");

function verifyInChain(hash: Uint8Array) {
  for (let gameId = 1; gameId < 10e6; gameId++) {
    hash = sha256(hash);
    if (hash === terminatinghash) {
      console.log("Hash is in the chain. It is game: ", gameId);
      return;
    }
  }
  console.error("hash is not in the chain");
}

Which could be used like:

Code:

verifyInChain(
  hexToBytes("85afc58736609dfe6f093ff15ba25ea6b48e39e01706780a20ebb04c83df5058")
);

If you also want to verify game results you can this use this open-source tool (https://stackblitz.com/edit/moneypot-verifier?file=index.js&view=editor).

Before calculating game results we need a house edge. Unlike normal casinos, instead of a fixed house edge (e.g. 1%) our house edge is only increased as little as necessary, in function of how much money the bankroll is risking and limited by the Kelly criterion.

Code:

// Note:
// casinoBankroll - the casino's bankroll
// playerBetting - the sum of money still in a game
// multiplier - at what multiplier the game is currently at (use the crash point for the final house edge)
function houseEdge(casinoBankroll, playerBetting, multiplier) {
  return expectedValue(casinoBankroll, playerBetting, multiplier) / playerBetting;
}

// From the casino's perspective, tells us how much money we will win or lose in the long run
function expectedValue(casinoBankroll, playerBetting, multiplier) {
  const winProbability = winProbabilityFromRisk(casinoBankroll, playerBetting, multiplier);
  const potentialProfit = winProbability * playerBetting;
  const howMuchToPay = playerBetting * (multiplier - 1);
  const potentialLoss = howMuchToPay * (1 - winProbability);
  return potentialProfit - potentialLoss;
}

// Returns the casino's probability (from 0 to 1) if players were betting at a given multiplier
function winProbabilityFromRisk(casinoBankroll, playerBetting, multiplier) {
  const potentialPlayerWin = (multiplier - 1) * playerBetting;
  return (potentialPlayerWin * (casinoBankroll + 2 * playerBetting)) / (casinoBankroll * (potentialPlayerWin + playerBetting));
}

The way we calculate the house edge could change in the future, without affecting our game generation algorithm. Have a look at our maths page (https://moneypot.com/maths) if you want to learn more.

Now we need a vxSignature. To prove that Provably Honest and MoneyPot are not collaborating, the message that is being signed will be mixed with the lowercase, hexadecimal representation of the hash of a Bitcoin block that has not been mined yet: Bitcoin block 798750.

Code:

import { concatBytes, utf8ToBytes} from "@noble/hashes/utils";

// Concatenate the previous game hash bytes with the client seed bytes
const message = concatBytes(prevGameHash, utf8ToBytes(clientSeed));

// Ask ProvablyHonest to sign the message using the public key 
// (VX_PUBKEY: 8be5ac83c91b3648d7b2c01d555dfbf60a0547c40524f495b656b6cfa9b69d5faf0967835257b30ac75fd80876c29c64)
const vxSignature = await vx.make_message(commitment, message, gameId, wager);

Once we have a vxSignature we can verify its authenticity:

Code:

import { bls12_381 as bls } from "@noble/curves/bls12-381";

// Note: the VX_PUBKEY is what is returned when the game server commits to Vx
const verified = bls.verify(vxSignature, message, VX_PUBKEY);
if (!verified) {
  throw new Error("Vx gave us something that didn't verify");
}

For more information on Provably Honest, see: https://www.provablyhonest.com (https://www.provablyhonest.com).

After we have our vxSignature and before each game begins, we take the next unused hash from the chain and use it to obtain a number ranging from 0 to 1. We call it scaledOutcome:

Code:

const crypto = require("crypto");

// The pure probability of the casino winning, before taking into account any edge
function scaledOutcome(gameHash, vxSignature) {
  const nBits = 52; // number of most significant bits to use

  // 1. HMAC_SHA256(key=vxSignature, message=gameHash)
  const hmac = crypto.createHmac("sha256", vxSignature);
  hmac.update(gameHash);
  seed = hmac.digest("hex");

  // 2. r = 52 most significant bits
  seed = seed.slice(0, nBits/4);
  const r = parseInt(seed, 16);

  // 3. X = r / 2^52
  return r / Math.pow(2, nBits); // uniformly distributed in [0; 1)
}

Now we can use the current game hash, house edge, and vxSignature to determine game results:

Code:

function gameResult(gameHash, vxSignature, houseEdge) {
  const X = scaledOutcome(gameHash, vxSignature);
  const result = (1 - houseEdge) / (1 - X);
  return Math.max(1, Math.floor(result * 100) / 100);
}

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