🔢Mathematics

Complete mathematical breakdown of all game formulas and calculations.

Time Conversions

Slot-Based Time

Solana slots are the fundamental time unit:

1 slot = 400 milliseconds = 0.4 seconds

Conversions:
1 second = 2.5 slots
1 minute = 150 slots
1 hour = 9,000 slots
1 day = 216,000 slots
1 week = 1,512,000 slots

Duration Calculations

// Convert days to slots
days_to_slots(days) = days × 216,000

// Convert slots to days
slots_to_days(slots) = slots / 216,000

// Examples:
5 days = 5 × 216,000 = 1,008,000 slots
1,008,000 slots = 1,008,000 / 216,000 = 4.67 days

Token Calculations

Micro-Token Conversions

WATT uses 6 decimals:

1 WATT = 1,000,000 micro-WATT
1 micro-WATT = 0.000001 WATT

// Convert WATT to micro-WATT
watt_to_micro(tokens) = tokens × 1,000,000

// Convert micro-WATT to WATT
micro_to_watt(micro_tokens) = micro_tokens / 1,000,000

// Examples:
250 WATT = 250,000,000 micro-WATT
24,783,194 micro-WATT = 24.783194 WATT

Reward Distribution

Accumulator Formula

The smart contract uses an accumulator pattern:

ACC_SCALE = 1,000,000,000,000 (1e12 for precision)

// Global accumulator update
slots_elapsed = current_slot - last_reward_slot
total_reward = slots_elapsed × current_emission_rate
acc_increase = (total_reward × ACC_SCALE) / total_network_hashpower

new_acc = old_acc + acc_increase

// Player pending rewards
acc_diff = global_acc - player_last_acc
pending = (player_hashpower × acc_diff) / ACC_SCALE

Simplified Player Rewards

Player Rewards Per Slot:
reward_per_slot = (player_hashpower / total_network_hashpower) × emission_rate

Player Rewards Per Day:
reward_per_day = reward_per_slot × 216,000

Example Calculation

Given:

  • Player hashpower: 1,000

  • Total network hashpower: 100,000

  • Current emission rate: 24,783,194 micro-WATT/slot (Stage 1)

Calculation:

Player share = 1,000 / 100,000 = 0.01 = 1%

Reward per slot = 0.01 × 24,783,194 = 247,831.94 micro-WATT/slot

Reward per day = 247,831.94 × 216,000 = 53,531,699,040 micro-WATT/day
= 53,531.699 WATT/day
≈ 53.5K WATT/day

Reward per week = 53,531.699 × 7 = 374,721.89 WATT/week
≈ 374.7K WATT/week

Network Share Dynamics

Share Calculation

Player Network Share (%) = (Player Hashpower / Total Network Hashpower) × 100

// Example:
Player: 500 hashpower
Network: 50,000 hashpower
Share: (500 / 50,000) × 100 = 1%

Share Change Over Time

Day 1:
- Your hashpower: 100
- Network hashpower: 1,000
- Your share: 10%

Day 30:
- Your hashpower: 500 (you 5x)
- Network hashpower: 50,000 (network 50x)
- Your share: 1%

Result: You grew 5x but network grew 50x, so your share decreased 10x → 1%

Farm Economics

Farm Configurations

Level
Card Slots
Energy Capacity
Cost (WATT)

0

0

0

N/A

1

2

6

FREE

2

4

12

1,000

3

7

20

2,000

4

10

40

4,000

5

13

70

8,000

6

16

110

16,000

7

19

230

32,000

8

22

420

64,000

9

24

800

128,000

10

25

2,000

256,000

Card Statistics

Card Data

Rarity
Hashpower
Energy
Efficiency
Drop Rate

Common

4

2

2.00

50%

Uncommon

12

4

3.00

25%

Rare

36

8

4.50

15%

Double Rare

108

16

6.75

6%

Very Rare

324

32

10.13

3%

Super Rare

972

64

15.19

0.9%

Mega Rare

2,916

128

22.78

0.1%

Efficiency Calculation

Efficiency = Hashpower / Energy Consumption

Examples:
Common: 4 / 2 = 2.00
Uncommon: 12 / 4 = 3.00
Mega Rare: 2,916 / 128 = 22.78

Expected Value Per Pack

Expected hashpower per pack:
= (0.50 × 4) + (0.25 × 12) + (0.15 × 36) + (0.06 × 108) + (0.03 × 324) + (0.009 × 972) + (0.001 × 2,916)
= 2 + 3 + 5.4 + 6.48 + 9.72 + 8.748 + 2.916
= 38.264 hashpower per pack (on average)

Expected energy per pack:
= (0.50 × 2) + (0.25 × 4) + (0.15 × 8) + (0.06 × 16) + (0.03 × 32) + (0.009 × 64) + (0.001 × 128)
= 1 + 1 + 1.2 + 0.96 + 0.96 + 0.576 + 0.128
= 5.824 energy per pack (on average)

Expected efficiency: 38.264 / 5.824 = 6.57

Staking Pool Math

Share Calculation

Your Staking Share (%) = (Your Staked WATT / Total Staked WATT) × 100

Reward Distribution

// SOL Rewards
Your SOL Rewards = Total SOL Deposited × Your Share

Example:
- You stake: 50,000 WATT
- Total staked: 5,000,000 WATT
- Your share: 1%
- This week's SOL deposits: 100 SOL
- Your SOL rewards: 100 × 0.01 = 1 SOL

// WATT Rewards
Your WATT Rewards Per Slot = Token Reward Rate Per Slot × Your Share

Example:
- Token reward rate: 100,000 micro-WATT/slot
- Your share: 1%
- Your reward per slot: 100,000 × 0.01 = 1,000 micro-WATT
- Your reward per day: 1,000 × 216,000 = 216,000,000 micro-WATT = 216 WATT/day

ROI Calculations

Farm Upgrade ROI

ROI Time (days) = Upgrade Cost / Additional Daily Earnings

Example:
- Current earnings: 5,000 WATT/day
- Upgrade costs: 16,000 WATT
- New capacity allows +3 cards
- +3 cards = +36 hashpower (uncommons)
- Assuming network share stays constant, +36 hashpower = +360 WATT/day
- ROI Time: 16,000 / 360 = 44.4 days

If you earn back the cost in < 30 days → GOOD ROI
If > 60 days → BAD ROI (emissions might end!)

Booster Pack ROI

ROI Time = (Pack Cost × N) / (Additional Daily Earnings from N packs)

Example:
- Buy 10 packs: 2,500 WATT
- Expected: 383 hashpower
- Assuming you can stake all of them and network share 1%
- Additional earnings: 383 hashpower = ~3,830 WATT/day (Stage 1)
- ROI Time: 2,500 / 3,830 = 0.65 days

Verdict: Packs have MUCH better ROI in early game!

Burn Projections

Network-Wide Burn Formula

Total Burned = Σ(All Player Spending) × 0.8

As player activity increases, burns increase exponentially!

Break-Even Analysis

Mining vs. Buying

Question: Is it better to mine or buy WATT?

Mining income (with starter cards, Stage 1):
- Hashpower: 12
- Network share: 0.001% (assuming 1.2M total hashpower)
- Daily earnings: ~60 WATT

Time to earn 10,000 WATT: 10,000 / 60 = 167 days

vs. Buy 10,000 WATT from DEX:
- Cost: 10,000 × $0.001 = $10 (assuming WATT @ $0.001)
- Instant

Conclusion: If you value your time, buying is better. If you want to play free-to-earn, mining works!

Summary Formulas

Key Formulas Reference (expand)
// Time
days_to_slots(d) = d × 216,000
slots_to_days(s) = s / 216,000

// Tokens
watt_to_micro(t) = t × 1,000,000
micro_to_watt(m) = m / 1,000,000

// Rewards
player_reward_per_slot = (player_hashpower / total_network_hashpower) × emission_rate
player_reward_per_day = player_reward_per_slot × 216,000

// Network Share
player_share = (player_hashpower / total_network_hashpower) × 100

// Efficiency
card_efficiency = hashpower / energy_consumption

// Burns
total_burned = total_spent × 0.75

// ROI
roi_time = cost / additional_daily_earnings

// Staking
staking_share = (your_staked / total_staked) × 100
your_rewards = total_rewards × staking_share

Use these formulas to optimize your strategy and dominate the network! 🧮⚡

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