Worked Examples

These examples walk through the full per-cohort and per-Power-Slot accounting for a 100-ticket game under two different fee configurations. The pool math, claimability rules, and notation are defined in the Specification.

Example A — No deposit fee

Config: e = 0.01 ETH, B_g = 7, B_v = 3, p_g = 7000, p_v = 3000, f_bps = 0, N = 100.

Fund split

v = 0.01 * 3000 / 10000 = 0.003 ETH/ticket
g = 0.01 - 0.003        = 0.007 ETH/ticket
G = 100 * 0.007         = 0.7 ETH
V = 100 * 0.003         = 0.3 ETH

Grand prize

W = floor(log_7(100)) + 1 = 2 + 1 = 3 Power Slots
P = floor(0.7 / 3) = 0.2333... ETH per Power Slot

Power Slot IDs:
  j=0: position 1   → ID 100
  j=1: position 7   → ID 94
  j=2: position 49  → ID 52

Dust = 0.7 - 3 * 0.2333... ≈ 0.0001 ETH

Virality cohorts

C = floor(log_3(100)) + 1 = 4 + 1 = 5 cohorts

Cohort 1: IDs 1–2     (2 members)
Cohort 2: IDs 3–8     (6 members)
Cohort 3: IDs 9–26    (18 members)
Cohort 4: IDs 27–80   (54 members)
Cohort 5: IDs 81–100  (20 members, partial — max is 162)

Pool balances

Pool[2] = 8  * 0.003 = 0.024 ETH   (IDs 1–8: cohort 1→2 redirect + cohort 2)
Pool[3] = 18 * 0.003 = 0.054 ETH   (IDs 9–26: cohort 3)
Pool[4] = 54 * 0.003 = 0.162 ETH   (IDs 27–80: cohort 4)
Pool[5] = 20 * 0.003 = 0.060 ETH   (IDs 81–100: cohort 5, partial)
                Total = 0.300 ETH ✓

Team prizes

Pool[2] / 1 team  = 0.024 ETH → cohort 1                CLAIMABLE (5 > 2)
Pool[3] / 2 teams = 0.027 ETH → cohorts 1, 2            CLAIMABLE (5 > 3)
Pool[4] / 3 teams = 0.054 ETH → cohorts 1, 2, 3         CLAIMABLE (5 > 4)
Pool[5] / 4 teams = 0.015 ETH → cohorts 1, 2, 3, 4      NOT CLAIMABLE (last cohort)

Per-member payouts (claimable pools only)

Leftover (host revenue)

Pool[5] = 0.060 ETH → host claims after game ends

Full accounting

Grand prizes paid:        3 × 0.2333 = 0.6999 ETH
Virality paid (cohort 1): 2 × 0.0525 = 0.105 ETH
Virality paid (cohort 2): 6 × 0.0135 = 0.081 ETH
Virality paid (cohort 3): 18 × 0.003 = 0.054 ETH
Host leftover:                         0.060 ETH
Grand prize dust:                     ≈0.0001 ETH
Virality rounding dust:               ≈small
                               Total ≈ 1.000 ETH ✓

Example B — Same game, 1% deposit fee

Config: e = 0.01 ETH, B_g = 7, B_v = 3, p_g = 7000, p_v = 3000, f_bps = 100 (1%), N = 100.

Each player still sends exactly e = 0.01 ETH per entry — the fee does not change the price an entry costs. Aggregated over N = 100 tickets:

Total msg.value    = 100 * 0.01 = 1.000 ETH       ← same as the 0% fee example
effectiveValue     = 1.000 ETH                    ← no dust refunded
feeAmount          = 1.000 * 100 / 10000 = 0.010 ETH  ← skimmed from entry revenue
poolContribution   = 1.000 - 0.010 = 0.990 ETH    ← what reaches the pools

Pool splits (reduced by fee)

v = 0.990 * 3000 / 10000 = 0.297 ETH   ← virality pool total (was 0.300 at f=0)
g = 0.990 - 0.297         = 0.693 ETH   ← grand prize pool total (was 0.700 at f=0)
G = 0.693 ETH
V = 0.297 ETH
W = 3 Power Slots (unchanged — fee does not change the slot count)
P = floor(0.693 / 3) ≈ 0.231 ETH per Power Slot (was ≈0.2333 at f=0)
C = 5 cohorts (unchanged)

Host revenue

Fee revenue (claimable any time):     F = 0.010 ETH
Last-cohort leftover (post-game end):  Pool[5] ≈ 0.0594 ETH (was 0.060 at f=0)
Total host take:                      ≈ 0.0694 ETH

Sanity check

Total ETH into contract   = 1.000 ETH
  Grand prizes paid        ≈ 0.693 ETH   (3 × 0.231)
  Virality paid to cohorts ≈ 0.238 ETH   (cohorts 1–3 from claimable pools 2–4)
  Host leftover (Pool[5])  ≈ 0.0594 ETH
  Host fee revenue         = 0.010 ETH
  Rounding dust            ≈ small
                     Total ≈ 1.000 ETH ✓

Comparison

The fee shifts 1% of the gross entry revenue (0.010 ETH) from the payout pools to accruedDepositFees. Players pay the same 0.01 ETH per entry in both cases; only where that ETH ends up changes.