src/RaidGeld.sol

@@ -107,7 +107,7 @@ contract RaidGeld is ERC20, Ownable, Constants {
             champion: Raider({level: 0}),
             profit_per_second: 0
         });
-        bosses[addr] = Boss({level: 0, boss_variants: RaidGeldUtils.generate_boss_variants(block.prevrandao)});
+        bosses[addr] = Boss({level: 0, variants: RaidGeldUtils.generate_boss_variants(block.prevrandao)});
     }
 
     // New player want to register with ETH
@@ -164,16 +164,21 @@ contract RaidGeld is ERC20, Ownable, Constants {
         emit RaidPerformed(player, players[player].total_minted, balanceOf(player));
     }
 
-    // Function to get Player struct
+    // Function to get the Player struct
     function getPlayer(address addr) public view returns (Player memory) {
         return players[addr];
     }
 
-    // Function to get Army struct
+    // Function to get the Army struct
     function getArmy(address addr) public view returns (Army memory) {
         return armies[addr];
     }
 
+    // Function to get the Boss struct
+    function getBoss(address addr) public view returns (Boss memory) {
+        return bosses[addr];
+    }
+
     // Quick fn to check if user is registered
     function isRegistered(address addr) public view returns (bool) {
         return players[addr].created_at != 0;
@@ -245,7 +250,7 @@ contract RaidGeld is ERC20, Ownable, Constants {
         );
     }
 
-    function battle_with_boss() external onlyActiveSession {
+    function battle_with_boss() external onlyActiveSession returns (bool[2] memory hasWonOrAscended) {
         // first perform raid
         performRaid(msg.sender);
         Boss memory boss_to_attack = bosses[msg.sender];
@@ -255,15 +260,16 @@ contract RaidGeld is ERC20, Ownable, Constants {
             : balanceOf(msg.sender);
         bool hasWonBattle = RaidGeldUtils.calculateBossFight(boss_to_attack.level, geld_to_burn, block.prevrandao);
         if (hasWonBattle) {
-            // Burn geld, get some sweet DAO Token and continue
+            // Burn geld, send some sweet DAO Token and continue
             _burn(msg.sender, geld_to_burn);
-            uint256 reward = RaidGeldUtils.calculateBossReward(boss_to_attack.level);
+            uint256 reward = RaidGeldUtils.calculateBossReward(boss_to_attack.level, BUY_IN_DAO_TOKEN_AMOUNT);
             players[msg.sender].total_rewards += reward;
             daoToken.transferFrom(address(this), msg.sender, reward);
             if (boss_to_attack.level == 6) {
-                // User ascends! Moloch is defeated
+                // User ascends! Moloch is defeated, user can start a new run
                 players[msg.sender].prestige_level += 1;
                 player_dies(msg.sender);
+                return [hasWonBattle, true /* New prestige level! */ ];
             } else {
                 // else go to next boss
                 bosses[msg.sender].level += 1;
@@ -272,6 +278,7 @@ contract RaidGeld is ERC20, Ownable, Constants {
             // Whoops u died, boss defeated you
             player_dies(msg.sender);
         }
+        return [hasWonBattle, false /* hasnt gotten prestige level */ ];
     }
 
     function player_dies(address player) private {

src/RaidGeldStructs.sol

@@ -26,5 +26,5 @@ struct Player {
 
 struct Boss {
     uint8 level;
-    uint8[7] boss_variants;
+    uint8[7] variants;
 }

src/RaidGeldUtils.sol

@@ -2,6 +2,7 @@
 pragma solidity ^0.8.13;
 
 import {Army} from "../src/RaidGeldStructs.sol";
+import {console} from "forge-std/Test.sol";
 
 library RaidGeldUtils {
     uint256 public constant PRECISION = 10000;
@@ -30,6 +31,7 @@ library RaidGeldUtils {
         else if (level == 4) return 90000000000;
         else if (level == 5) return 900000000000;
         else if (level == 6) return 9000000000000;
+        else return 0;
     }
 
     function getBossCumulativeChance(uint8 level) internal pure returns (uint256 chance) {
@@ -38,11 +40,26 @@ library RaidGeldUtils {
         require(level <= 7, "Bosses only go to level 7");
         if (level == 0) return 99e16;
         else if (level == 1) return 8811e14;
-        else if (level == 2) return 7048e14;
+        else if (level == 2) return 70488e13;
         else if (level == 3) return 493416e12;
         else if (level == 4) return 30591792e10;
         else if (level == 5) return 1560181392e8;
         else if (level == 6) return 6240725568e7;
+        else return 0;
+    }
+
+    function getBossChance(uint8 level) internal pure returns (uint256 chance) {
+        // for boss chances (percent) [99, 89, 80, 70, 62, 51, 40]
+        // where cumulative chance is in the form of 18 precision related to 1e18
+        require(level <= 7, "Bosses only go to level 7");
+        if (level == 0) return 99;
+        else if (level == 1) return 89;
+        else if (level == 2) return 80;
+        else if (level == 3) return 70;
+        else if (level == 4) return 62;
+        else if (level == 5) return 51;
+        else if (level == 6) return 40;
+        else return 0;
     }
 
     function calculateUnitPrice(uint8 unit, uint16 currentLevel, uint16 units) internal pure returns (uint256) {
@@ -77,20 +94,24 @@ library RaidGeldUtils {
     }
 
     // Returns how much Dao Token player is due for winning
-    function calculateBossReward(uint8 bossLevel) internal pure returns (uint256) {
+    function calculateBossReward(uint8 bossLevel, uint256 baseReward) internal pure returns (uint256) {
-        return getBossPower(bossLevel) * (getBossCumulativeChance(bossLevel) * 10 / 5) ** 2;
+        // TODO: This could as well just be pre-calculated
+        uint256 cumulativeChance = getBossCumulativeChance(bossLevel); // 0 - 1e18 range
+        uint256 rewardMultiplier = ((2 * (1e18 - cumulativeChance)) ** 2) / 1e18;
+        return (baseReward * rewardMultiplier);
     }
 
     // Calculates whether user survives the fight
     function calculateBossFight(uint8 bossLevel, uint256 geldBurnt, uint256 prevrandao) internal pure returns (bool) {
         uint256 bossPower = getBossPower(bossLevel);
+        uint256 bossRoll = getBossChance(bossLevel);
         require(geldBurnt <= bossPower, "Cant try to defeat boss with more than what boss power is");
         uint256 random_n = random(prevrandao, 1, 100);
         // Relative power as in, you can only put in 800 geld to defeat 900 geld boss,
         // but you will get exponentially worse chances
         uint256 relativePower = ((geldBurnt ** 2) * 100) / bossPower ** 2;
-        uint256 roll = (random_n * relativePower * PRECISION) / (100 * PRECISION);
+        uint256 roll = random_n * relativePower / 1e2;
-        return roll >= bossPower;
+        return roll < bossRoll;
     }
 
     function generate_boss_variants(uint256 prevrandao) internal pure returns (uint8[7] memory boss_variants) {

test/RaidGeld.t.sol

@@ -3,7 +3,7 @@ pragma solidity ^0.8.13;
 
 import {Test, console} from "forge-std/Test.sol";
 import {stdStorage, StdStorage} from "forge-std/Test.sol";
-import {RaidGeld, Army, Player} from "../src/RaidGeld.sol";
+import {RaidGeld, Army, Player, Boss} from "../src/RaidGeld.sol";
 import "../src/RaidGeldUtils.sol";
 import {Constants} from "../src/Constants.sol";
 
@@ -285,4 +285,32 @@ contract raid_geldTest is Test, Constants {
         assertLt(newBalance, newestBalance);
         assertLt(last_raided_at, last_raided_at_2);
     }
+
+    function test_08_attack_boss() public {
+        // Let some time pass so we dont start at block timestamp 0
+        vm.warp(120);
+
+        // Register player 1
+        vm.startPrank(player1);
+        registerPlayer();
+        raid_geld.addUnit(0, 1);
+
+        Boss memory boss = raid_geld.getBoss(player1);
+        // assert boss is initialized
+        assertEq(boss.level, 0);
+        // make sure variants shuffled
+        assertNotEq(boss.variants[1], boss.variants[2]);
+
+        // Make a lot of time pass so user deffo has GELD to attack the boss
+        vm.warp(1200000);
+
+        bool[2] memory results = raid_geld.battle_with_boss();
+        console.log(results[0]);
+        console.log(results[1]);
+
+        // Should almost always defeat first boss
+        assertEq(results[0], true);
+        // First boss doesnt grant a new prestige level (ascension)
+        assertEq(results[1], false);
+    }
 }

test/RaidGeldUtils.t.sol

@@ -4,6 +4,7 @@ pragma solidity ^0.8.13;
 import {Test, console} from "forge-std/Test.sol";
 import {Army, Raider} from "../src/RaidGeldStructs.sol";
 import "../src/RaidGeldUtils.sol";
+import "@openzeppelin/contracts/utils/math/Math.sol";
 
 contract raid_geldTest is Test {
     function test_0_unit_price() public pure {
@@ -51,4 +52,64 @@ contract raid_geldTest is Test {
             + _anLvl * RaidGeldUtils.ANOINTED_PROFIT + _cLvl * RaidGeldUtils.CHAMPION_PROFIT;
         assertEq(profits_per_second, expected);
     }
+
+    function getConfidenceInterval(uint8 bossLevel)
+        internal
+        pure
+        returns (uint256 lower, uint256 upper)
+    {
+        /*
+            man i struggled getting this math with just integers so its 
+            easier to just do it like this (precalculated):
+            z = 1.96 (95%)
+            Probability | Expected | Variance | Margin | Lower Bound | Upper Bound
+            99%	990	0.00099	62	928	1052
+            89%	890	0.000979	61	829	951
+            80%	800	0.00016	49	751	849
+            70%	700	0.00021	45	655	745
+            62%	620	0.0002356	48	572	668
+            51%	510	0.0002499	49	461	559
+            40%	400	0.00024	48	352	448
+        */
+        if (bossLevel == 0) {
+            return (928, 1000);
+        } else if (bossLevel == 1) {
+            return (829, 951);
+        } else if (bossLevel == 2) {
+            return (751, 849);
+        } else if (bossLevel == 3) {
+            return (655, 745);
+        } else if (bossLevel == 4) {
+            return (572, 668);
+        } else if (bossLevel == 5) {
+            return (461, 559);
+        } else if (bossLevel == 6) {
+            return (352, 448);
+        }
+    }
+
+    function test_2_calculateBossFight_probabilities() public {
+        uint256[7] memory probabilities =
+            [uint256(99), uint256(89), uint256(80), uint256(70), uint256(62), uint256(51), uint256(40)];
+        uint256 totalRuns = 1000;
+        console.log("Checking boss rolls (1000 times)");
+        for (uint8 bossLevel = 0; bossLevel < 7; bossLevel++) {
+            console.log("Boss level: ", bossLevel);
+            uint256 bossPower = RaidGeldUtils.getBossPower(bossLevel);
+            uint256 geldBurnt = bossPower;
+            uint256 successCount = 0;
+            for (uint256 testRun = 0; testRun < totalRuns; testRun++) {
+                uint256 prevrandao = uint256(keccak256(abi.encodePacked(block.prevrandao, testRun * 1e9))); // Unique seed each time
+                if (RaidGeldUtils.calculateBossFight(bossLevel, geldBurnt, prevrandao)) {
+                    successCount++;
+                }
+            }
+            (uint256 lowerProb, uint256 upperProb) = getConfidenceInterval(bossLevel);
+            console.log("expected at least wins", lowerProb);
+            console.log("expected at most wins", upperProb);
+            console.log("actual wins", successCount);
+            console.log("----------");
+            vm.assertTrue(successCount >= lowerProb && successCount <= upperProb, "Success rate not within expected range");
+        }
+    }
 }