How to estimate tournament expected value

Expected value is a probability-weighted average, not the amount one entry will return. A tournament can have positive estimated value for one player and negative value for another if skill affects results.

Start with the visible spread

For a contest with 10 paid entries at $1 and total listed cash prizes of $8:

gross paid entries = 10 × $1 = $10

visible spread = $10 - $8 = $2

prize return ratio = $8 ÷ $10 = 80%

The $2 spread is not automatically the operator’s net profit. Bonus entries, overlay, refunds, taxes, processing, and promotional funding can alter the economics.

Equal-chance baseline

If every entry had an equal chance and all $8 were cash prizes, the average prize per entry would be:

$8 ÷ 10 = $0.80

Against a $1 cash fee, baseline expected net value is negative $0.20. A player would need an advantage large enough to overcome that gap, after considering ties, fees, and uncertainty.

Prize-specific formula

For two prizes, $5 and $3:

EV = (P[first] × $5) + (P[second] × $3) - $1 entry fee

The probabilities must be mutually consistent and based on comparable contests. Do not set both from your best historical finish or assume a recent win rate will continue after matchmaking changes.

Break-even estimate

For a winner-take-all head-to-head with a $1 entry and $1.80 prize, ignoring ties and fees:

break-even win probability = $1 ÷ $1.80 = 55.56%

A measured rate above 55.56% can still be noise in a small sample. Opponent strength, rule changes, and selection of only favorable results can bias it.

Check how probability changes the result

In this original example, $1.80 is the total cash returned on a win, including any portion that represents the entry fee. No extra dollar is returned on top. A loss returns $0; there are no ties, refunds or additional fees.

Assumed win probability	Average prize	Net EV per entry
50%	$0.90	-$0.10
5/9, approximately 55.56%	$1.00	$0.00
60%	$1.08	+$0.08

A positive calculation under an assumption

Assume a true 60% win probability and the $1.80 total cash prize defined above.

EV = 0.60 × $1.80 + 0.40 × $0 - $1 = +$0.08

The mathematical average is eight cents per entry. One actual entry ends at +$0.80 or -$1.

If 60% is unsupported, so is the result. An extra $0.10 fee per entry would turn this example into -$0.02.

Do not count the same dollar twice if an interface separates “returned entry” from “winnings.” Keep losses and ties in a sample of games; a selected list of wins does not estimate the probability across all entries.

Cash and bonus accounting

Keep cash entry, bonus credit, cash prize, and restricted prize separate. A promotional entry with no cash cost can have a different personal EV, but its prize might carry withdrawal conditions. Do not value nonwithdrawable credits at one dollar each.

Data to record

• exact contest and rule version;
• cash fee and promotional fee;
• field size and prize allocation;
• opponent or rating band when shown;
• score breakdown and errors;
• ties, refunds, pending entries, and voids;
• cash eligible for withdrawal;
• payment and withdrawal fees.

What +EV does not mean

A positive estimate does not guarantee profit, make an entry affordable, or establish that the app is legally available. It can be wrong because probabilities are uncertain. Use a conservative range, then test whether the conclusion changes at the lower end.

Never chase a negative session because a spreadsheet says the long run should recover it. Check legal eligibility and set stop limits before estimating EV.

Source for bonus treatment

Skillz describes entries funded by cash and Bonus Cash, and how those portions return after a win. That is a rule of that platform, not a universal split. The probabilities and prizes on this page are original calculations, not estimates of a reader’s skill or an app’s return.