LP pool

Wagering infrastructure · LP pool

The Chain
LP Pool

One pool backs every bet that operators run on chain.wtf. LPs earn a share of each bet's edge and carry the swings of wins and losses. A fixed formula sets that share and every max bet.

Pick a market How it works

The LP share, on every bet

LP share = clamp( 15 × risk ÷ edge × T × (1 + H) × D ÷ (2 × pool), 0.1%, 35% )

risk: What recent bets put on the pool: each bet's stake² × its game's variance, summed over the last 7 days (or the last day, if that is higher).
edge: What the same bets earn on average: stake × the game's edge after the provider's cut.
pool: The pool's current value: LP capital plus everything it has earned.
T: Growth trend, 1 to 1.5. Rises when this week's risk per day runs above the 30-day average.
H: Limit pressure, 0 to 1. The share of risk from bets placed at 95% or more of their max bet.
D: Drawdown brake, 1 and up. Rises while the LP share price is below its high.

Risk price λ 15 LP share 0.1–35% of edge Biggest single win 16.25% of pool Drawdown brake 10% scale Open bets covered 99.99%

Pick a market

You set the market: how much is bet, by whom, and how much LP capital starts in the pool. The formula and its parameters are the same in every market.

Wager at launch

Wager in month 24

Bettors

Typical High rollers Whales

LP capital at launch

Type any amount, e.g. 600000, 750k or 2.5m. LPs then add capital while the pool's yield beats 13.5% a year and withdraw below it, up to 20% in and 10% out a week.

Stress events Whale wave and volume jump in month 10

For three weeks the biggest bettors play three times as often, and from month 10 on volume doubles at once.

ready

What LPs get

200 simulated 24-month markets. A 12-month return is the change in the LP share price over any 12 months, after all fees, weighted by how much LP money was in the pool.

LP share price

typical run90% of runs insidestart = 1.00

Every LP holds shares of the pool. The price moves with LP income and with the pool's wins and losses; deposits and withdrawals happen at the current price and never move it.

Spread of 12-month returns

gainloss

How far the share price sits below its high

typical runworst 5% of runs

The drawdown brake starts to bite here: from 10% below the high it raises the LP share and cuts max bets hard.

LPs' share of each bet's edge

typical run90% of runs inside35% ceiling

High when the pool carries a lot of risk for its size; lower as the pool grows. The operator always keeps at least 65%.

Pool size

typical run90% of runs inside

LP capital plus everything the pool has earned. Grows with deposits when yield is high.

Max bet per game

Max bets follow the pool: a bigger pool takes bigger bets, and they fall fast when the pool is below its high. Example game mix; log scale.

How the formula works

Every bet runs through the same six steps on-chain, in this order. Nothing in them is discretionary: the parameters are fixed and the code is below.

A bet comes in and its edge is split

A game's edge is what it keeps on average: 1 − RTP. The pool takes the stake and pays the win, so it is the only party whose result depends on the outcome. The fees are paid on the expected edge the moment the bet is placed, win or lose.

edge = stake × (1 − RTP) provider fee = edge × provider cut to the game's provider LP income = (edge − provider fee) × LP share LP investor income, added to the pool operator fee = (edge − provider fee) × (1 − LP share) to the operator

Risk and edge are measured

Each bet adds its edge and its risk to running totals over the last day, the last 7 days and the last 30 days. Risk grows with the square of the stake: one $1,000 bet carries as much risk as a million $1 bets but only the edge of a thousand. That is why big bets on high-multiplier games cost LPs the most.

risk = stake² × σ² + 15 ÷ (3 × pool) × stake³ × κ₃ σ² = the game's variance per $1, κ₃ = its tail edge = stake × net edge net edge = edge after the provider's cut

The LP share is priced from that risk

The pool charges for the risk it carries. The charge is set so that LPs are paid in proportion to the risk per dollar of edge, scaled to the size of the pool, and kept between 0.1% and 35% of the net edge.

LP share = clamp( λ × ratio × T × (1 + H) × D ÷ (2 × P), 0.1%, 35% )

λ = 15price of risk

The price of risk. Risk ÷ 2P is what a pool of size P gives up by carrying it (the Kelly rate); the pool charges 15 times that, a cautious setting.

ratiorisk ÷ edge

Risk the pool carried per dollar of edge it earned, over 7 days, or over the last day if that is higher, so a sudden whale night is priced the same day.

Ppool size

A bigger pool spreads the same risk thinner, so the share falls as the pool grows.

T1 to 1.5

Growth trend: risk per day this week against the last 30 days. Pays LPs more while bigger bets arrive. Off for the first 14 days.

H0 to 1

Limit pressure: the share of risk from bets placed at 95% or more of their max. Pays LPs more when bettors push the limits.

D1 and up

The drawdown brake (step 4). Raises the share while the pool is below its high.

T and H only change what LPs are paid. They never cut max bets, so a busy day can't shut games down.

The drawdown brake

When the LP share price is below its high, D rises: gently in shallow dips, steeply in deep ones. It raises the LP share and shrinks the biggest single win and every risk budget by the same factor, so max bets fall about as fast as D rises.

D = e^( (min(depth, 20%) ÷ 10%)² ) depth = how far the share price is below its high

Max bets against depth below the high

D stops growing at 20% depth, so games stay open. Beyond 15% the brake's own high moves down 2 points a day, so after a large hit the pool can earn its way back instead of freezing; LP drawdowns are still measured against the true high. Bugs and exploits are not the brake's job: a per-game pause and a drain monitor handle those.

Max bet: the smallest of four limits

Every game gets its own max bet, recomputed on every bet. It is the smallest of the four limits below; under $0.01 the game pauses until the pool recovers.

Biggest single win

stake ≤ 16.25% × P ÷ D ÷ (M − 1)

No single bet can win more than 16.25% of the pool (less while the brake is on). M is the game's top multiplier.

Usually sets the limit on slots and other high-multiplier games.

Risk budget

λ·D·x²·σ² ÷ 2P ≤ 35%·x·ne + spare

A bet's risk charge must be covered by the most LPs could take from it (35% of its edge) plus the spare room under the ceiling.

Sets the limit when the LP share is near its ceiling.

Break-even rule

stake ≤ 4 × P × ne ÷ (λ × D × σ²)

No bet's risk charge may be more than twice its own edge. Bets beyond this cost more in LP share than they bring in.

Usually sets the limit on low-multiplier games like coinflips.

Reserve fit

reserve(open bets + this one) ≤ P

After taking this bet, the pool's statistical reserve for all open bets (step 6) must still fit inside it. Otherwise the stake is cut to fit.

Rarely binds; it matters when many big bets are open at once.

Open bets are covered at 99.99%

A bet stays open until its random draw settles, usually in less than a second. The pool does not set aside every possible payout of every open bet; that would freeze most of its capital for wins that almost never land together. It holds a statistical reserve instead: rare top wins are counted with their exact Poisson odds, everything else with a risk-of-ruin bound, so that all open bets together are covered with 99.99% certainty. LPs can't withdraw into that reserve.

reserve = max( Tier 1 + Tier 2 + shared-draw groups, largest single open max payout ) Tier 1 rare top wins on jackpot-style games: as many as can hit at once with 99.99% certainty (Poisson) Tier 2 every other outcome: expected result + 3.72 standard deviations (a 0.01% chance of needing more) groups bets settled by one shared draw, at their full combined max payout LP withdrawals ≤ pool − reserve

The parameters

Parameter	Value	What it does
Risk price λ	15	How much LPs are paid per unit of risk.
LP share floor and ceiling	0.1% · 35%	Bounds of the one LP share every bet pays. The operator keeps the rest.
Biggest single win	16.25% of pool	Caps what one bet can win.
Drawdown brake	10% scale · stops at 20% · fades beyond 15% by 2 pts a day	Raises the LP share and cuts max bets while the pool is below its high.
Break-even multiple	2	A bet's risk charge may be at most twice its own edge.
Windows	1 · 7 · 30 days	Fast and main risk-to-edge windows, long window for the trend.
Trend cap	1.5 · off for 14 days	Most the growth trend can raise the LP share.
At the max	95%	A bet at 95% of its max or more counts toward limit pressure.
Minimum bet	$0.01	A game pauses when its max bet falls below this.
Reserve	99.99% (z 3.72)	Statistical cover for open bets; LP withdrawals stop at pool − reserve.

The formula as code

The reference implementation of the formula, with a 10-day example you can run.

chain_lp_formula.py · LP share, max bets and reserve on every bet
README.txt · how to run it

Read chain_lp_formula.py here