Simulation Results
These are full games simulated across a range of configurations, so you can see how the Power Slots, cohorts, and both prize pools behave as a game grows. Every number here is computed by the same on-chain rules a live game uses.
Power Slot math (10,001-entry simulations)
Checked across log bases 2, 3, 5, 7, 10. For each base, the expected Power
Slot count floor(log_base(N)) + 1 matches the actual count, and the precise
winning entrant IDs are shown.
Base 2 — 14 Power Slots
Entry #10001 (1 = 2^0)
Entry #10000 (2 = 2^1)
Entry #9998 (4 = 2^2)
Entry #9994 (8 = 2^3)
Entry #9986 (16 = 2^4)
Entry #9970 (32 = 2^5)
Entry #9938 (64 = 2^6)
Entry #9874 (128 = 2^7)
Entry #9746 (256 = 2^8)
Entry #9490 (512 = 2^9)
Entry #8978 (1024 = 2^10)
Entry #7954 (2048 = 2^11)
Entry #5906 (4096 = 2^12)
Entry #1810 (8192 = 2^13)
Base 3 — 9 Power Slots
#10001 (3^0), #9999 (3^1), #9993 (3^2), #9975 (3^3), #9921 (3^4),
#9759 (3^5), #9273 (3^6), #7815 (3^7), #3441 (3^8)
Base 5 — 6 Power Slots
#10001, #9997, #9977, #9877, #9377, #6877
Base 7 — 5 Power Slots
#10001, #9995, #9953, #9659, #7601
Base 10 — 5 Power Slots
#10001, #9992, #9902, #9002, #2
Cohort-assignment math
For each virality base, the simulation builds the cohort table and verifies that sample entrant IDs land in the correct cohort.
Virality base 2
| Cohort | Range | Size |
|---|---|---|
| 1 | 1 | 1 |
| 2 | 2-3 | 2 |
| 3 | 4-7 | 4 |
| 4 | 8-15 | 8 |
| 5 | 16-31 | 16 |
| 6 | 32-63 | 32 |
Virality base 3
| Cohort | Range | Size |
|---|---|---|
| 1 | 1-2 | 2 |
| 2 | 3-8 | 6 |
| 3 | 9-26 | 18 |
| 4 | 27-80 | 54 |
| 5 | 81-242 | 162 |
| 6 | 243-728 | 486 |
Virality base 5
| Cohort | Range | Size |
|---|---|---|
| 1 | 1-4 | 4 |
| 2 | 5-24 | 20 |
| 3 | 25-124 | 100 |
| 4 | 125-624 | 500 |
| 5 | 625-3124 | 2500 |
| 6 | 3125-15624 | 12500 |
Virality base 10
| Cohort | Range | Size |
|---|---|---|
| 1 | 1-9 | 9 |
| 2 | 10-99 | 90 |
| 3 | 100-999 | 900 |
| 4 | 1000-9999 | 9000 |
| 5 | 10000-99999 | 90000 |
Configuration comparison (Power Slot counts)
| Grand Base | 100 entries | 1,000 entries | 10,000 entries |
|---|---|---|---|
| 2 | 7 | 10 | 14 |
| 3 | 5 | 7 | 9 |
| 5 | 3 | 5 | 6 |
| 7 | 3 | 4 | 5 |
| 10 | 3 | 4 | 5 |
Prize per Power Slot — assuming 70% grand-prize pool
| Grand Base | 100 entries | 1,000 entries | 10,000 entries |
|---|---|---|---|
| 2 | 10 | 70 | 500 |
| 3 | 14 | 100 | 777 |
| 5 | 23 | 140 | 1166 |
| 7 | 23 | 175 | 1400 |
| 10 | 23 | 175 | 1400 |
(Units: ETH per Power Slot.)
Reading the table
| Base | Personality |
|---|---|
| 2 | Maximum Power Slots, smallest individual prizes — best for wide distribution |
| 3 | Good balance between Power Slots and prize size |
| 5 | Moderate Power Slots, moderate prizes |
| 7 | Default — fewer Power Slots, larger prizes |
| 10 | Minimum Power Slots, maximum individual prizes — V1-style |
Prize distribution (1000-entry game, base 7, 70/30 split, 1 ETH entry)
| Quantity | Expected | Actual |
|---|---|---|
| Grand Prize Pool | 700 ETH | 700 ETH |
| Number of Power Slots | 4 | 4 |
| Prize per Power Slot | 175 ETH | 175 ETH |
| Current cohort | 7 | 7 |
Adoption-bonus pools at game end:
| Cohort | Pool |
|---|---|
| 2 | 2 ETH |
| 3 | 5 ETH |
| 4 | 16 ETH |
| 5 | 48 ETH |
| 6 | 145 ETH |
| 7 (last) | 81 ETH (host leftover) |
Deposit-fee math
Two test runs, identical except for depositFeeBps:
| Run | depositFeeBps |
msg.value per deposit |
Grand prize pool | accruedDepositFees |
|---|---|---|---|---|
| 1 (control) | 0 | 1 ETH | 70 ETH | 0 |
| 2 | 100 (1%) | 1 ETH | 69.3 ETH | 1 ETH |
After Run 2, host calls withdrawDepositFees():
Host balance delta: 1 ETH ✓
Edge cases
- Single-entry game: the lone entrant correctly lands the only Power Slot.
- Boundary tests (base 7): 7 entries → 2 Power Slots at positions 1 and 7; 49 entries → 3 Power Slots at positions 1, 43, and 49.
- isPower verification:
isPower(7, n)returns true forn ∈ {1, 7, 49, 343, …}and false otherwise — fuzz-tested.
Claim functionality (100-entry game)
| Total entries | 100 |
| Power Slots | 3 |
Grand-prize claims:
Entry #52 claimed 23 ETH
Entry #94 claimed 23 ETH
Entry #100 claimed 23 ETH
Adoption-bonus claim:
Entry #1 claimed 1 ETH from cohort 2
(Using a 1-ETH entry amount, dust visible in the lower-precision output.)
Full-game lifecycle (round-1 simulation, base 7 grand / base 3 virality)
A 12,346-entry simulation. Per-cohort milestones:
| Event | Cohort | Pool contribution | Per-team claim |
|---|---|---|---|
| Entry #2 finishes cohort 1 | 1 | — | — |
| Entry #8 finishes cohort 2 | 2 | — | — |
| Entry #9 starts cohort 3 | — | Pool[2] unlocked | Cohort 1: 240,000 |
| Entry #26 finishes cohort 3 | 3 | — | — |
| Entry #27 starts cohort 4 | — | Pool[3] unlocked | Cohorts 1, 2: 270,000 each |
| Entry #80 finishes cohort 4 | 4 | — | — |
| Entry #81 starts cohort 5 | — | Pool[4] unlocked | Cohorts 1, 2, 3: 540,000 each |
| Entry #242 finishes cohort 5 | 5 | — | — |
| Entry #243 starts cohort 6 | — | Pool[5] unlocked | 1,215,000 each (1-4) |
| Entry #728 finishes cohort 6 | 6 | — | — |
| Entry #729 starts cohort 7 | — | Pool[6] unlocked | 2,916,000 each (1-5) |
| Entry #2186 finishes cohort 7 | 7 | — | — |
| Entry #2187 starts cohort 8 | — | Pool[7] unlocked | 7,290,000 each (1-6) |
| Entry #6560 finishes cohort 8 | 8 | — | — |
| Entry #6561 starts cohort 9 | — | Pool[8] unlocked | 18,745,714 each (1-7) |
Final Grand Prize Power Slots (5 slots under base 7, 12,346 entries):
Entry #9946, #12004, #12298, #12340, #12346
(Units in this section: PLS, since the simulation uses PulseChain denominations to keep large numbers readable.)
Interactive visualizer
The prize-math visualizer and live simulator are built into the dapp at
/prize-math and /prize-math/simulate, so you can explore any configuration
interactively before you play.