Bet Trader and Analytics

The Bet Trader and Analytics tool estimates expected profit for a sequence of exchange (or matched-book) trades with a constant average edge and constant stake. Three inputs: Trades (default 50), Avg Edge (default 2%), Stake per Trade (default $100). Expected Profit = trades × stake × (edge/100). On the defaults, 50 × 100 × 0.02 = $100.00. The second line echoes Trades = 50 so you can see the sample length next to the dollar mean.

That $100 is linearity of expectation again: fifty $100 shots at +2% EV. It is not a guarantee, not a Dutch-book lock, and not a market-making P&L after commission. Betfair-style exchanges charge ~2–5% on net winnings; 2% “edge” before 5% commission is not 2% after. Type the net edge you actually estimate. If your average edge is 0.5% on $100 × 50, expected profit is $25, not $100.

Stake / Trade is the typical matched amount, not the liability on a lay. A lay at 4.0 of $100 has £300 liability on a 3/1 shot; this form still treats $100 as the “stake” you typed. If you want liability-normalized EV, convert before you enter. Avg Edge is a percent of that stake. Market makers who quote both sides and earn a spread can think of edge as half-spread minus adverse selection; that reduction is on you.

Raise Trades to 500 at the same 2% and $100: expected profit $1,000. The mean scales; the standard deviation scales with √trades if trades are i.i.d., so the coefficient of variation falls. The tool does not print sd. It is a mean calculator for people who already believe they have a 2% edge, which is the hard part. A 2% edge on an exchange is a professional number; most recreational “edges” are CLV-negative.

Use it as a session plan: 50 trades, $100, 2% → $100 expected. Then compare to commission, to time, and to the Bankroll Safety units you actually have. Dutch-book language in the about section is the intellectual cousin — locking a sure profit across prices — not what this multiply implements.

Bet trading is betting’s market-making cousin: back and lay on an exchange, scalp a price move, or hold a green book. The Dutch book theorem (de Finetti, Ramsey, and the betting-interpretation of probability) says that if your prices violate the axioms, someone can trade against you and lock a sure gain. Exchange trading in the opposite direction — being the someone, or being a market maker who captures a spread — is how professionals extract a small edge many times. SorteCalc’s analytics page does not construct a Dutch book. It multiplies n × stake × edge, a first-moment plan for a trader who already estimates an average edge.

Why 2% and 50 trades? Because a classroom scalp might be a tick or two on a soccer match, 1–3% if you are sharp and the market is slow, and a busy afternoon might be dozens of fills, not thousands. High-frequency sports scalpers do more; recreational in-play traders do less. The $100 stake is a round unit, not a Kelly output. Pair with the Bet Size Optimizer if you want the stake to come from bankroll and odds.

Commission dominates this niche. A 2% gross edge with 5% commission on winnings can reverse the sign depending on win rate and whether you are backing or laying. Many traders quote edge after commission; do that here. Currency risk, void rules, and unmatched exposure are out of scope.

Limits: constant edge, constant stake, no inventory, no correlation across the 50 trades (a night on one match is one bet in disguise), no adverse selection (the act of being filled may mean you are on the wrong side — the “winner’s curse” of quoting). A true market-making model needs a fill model and a toxicity model. This is lite.

History: betting exchanges (Betfair 2000, later clones) made lay betting retail. The mathematics of making a book is older than that — 19th-century bookmakers balanced a book to a Dutch-ish overround. De Finetti’s coherence is the philosophical frame: prices should not be Dutch-bookable. This calculator assumes you are the one with a +2% mean, which already assumes coherence plus a bit. Educational: $100 expected is 50 × $2. Whether you get it is a random sum.

Expected profit for a sequence of constant-stake trades is linearity of expectation in one line. Multiply the number of trades by the stake per trade by the average edge as a fraction of that stake. The teaching defaults are fifty trades, a two percent average edge, and one hundred dollars per trade: 50 times 100 times 0.02 equals 100, reported as 100.00 dollars. That is fifty shots at a two-dollar mean. It is not a Dutch-book lock, not a path, and not a market-making result after commission.

Huygens stated that the value of several games is the sum of the values, with no need for independence. Variance does need a second-moment model: if the trades are uncorrelated with common variance, the variance of the sum scales with the count, so the standard deviation scales with the square root. Doubling the count doubles the mean and multiplies the standard deviation by the square root of two. Fifty trades at two percent remain a small sample for detecting a two percent mean against a typical binary-bet scatter of tens of percent of stake.

A Dutch book, in the sense of Ramsey and de Finetti, is a different construction. If prices on a partition sum to less than one, backing all of them with suitable stakes locks a sure gain; if they sum to more than one, laying them can lock a gain, commission aside. A two percent statistical edge is not that lock. Paths can still lose. Convert any exchange commission into a net edge before you multiply. Five percent of net winnings on a winning back changes the mean return; typing a gross two percent then printing 100.00 dollars is a category error.

Worked contrasts keep the arithmetic honest. Fifty trades, one percent, one hundred dollars yield 50.00 dollars. Fifty trades, two percent, two hundred dollars yield 200.00 dollars. Five hundred trades at the original two percent and one hundred dollars yield 1,000.00 dollars. The mean scales; the coefficient of variation falls only like one over the square root of the count if the trades are truly separate. A night of fifty fills on one match is often one bet in disguise.

Assumptions: the typed edge is the true mean return on the typed stake, the count is the number of such exposures, and the stake does not compound. Liability on a lay is not the same object as a back stake; convert before you enter if you need a liability-normalised mean. Adverse selection, unmatched leftovers, and voids are the usual ways 100.00 dollars fails to appear. The figure is exact arithmetic on the defaults, not a simulated path.