The formula
For each selection with decimal odds d_i, compute
its share of the bankroll as
f_i = (1 / d_i) / S, where
S = sum of (1 / d_j) across all selections. Multiply
f_i by the total stake T to get the
dollar stake on selection i. The return on any
winning selection is T / S, the same number for
every row.
If S is less than 1, that return is greater than
the total stake and the bet locks in a profit no matter what
happens. This is an arbitrage (or "arb"). If S is
greater than 1, which is the normal case at a single
sportsbook because of the vig, you are guaranteed to lose the
amount T * (1 - 1/S) regardless of outcome.
When Dutching makes sense
Three common uses. First, when you think the favorite will not
win but you do not know which of several underdogs will,
Dutching the contenders covers the field at a controlled cost.
Second, when shopping odds across multiple sportsbooks, you can
sometimes find prices that sum below 100% across books, which
is a true arbitrage. Third, in races with a dominant
pari-mutuel pool, Dutching can convert your race opinion into a
cleaner risk profile than a single win bet.
What the combined book percentage tells you
The combined book is S * 100. At a single
sportsbook on a two-way market, a typical -110/-110 line gives
a combined book of 104.76%, so you lose 4.76% by Dutching both
sides at the same book. A combined book below 100% across
books or across a multi-way market is the arbitrage signal:
back every side in the right proportion and the return is
fixed.
Inputs accepted
Each odds field accepts American (+150,
-200), decimal (2.50,
1.50) or fractional (3/2) odds. The
calculator detects the format from the value you type. Leave a
row empty to ignore it.
Dutching Calculator FAQ
What is Dutching?
Dutching is staking proportionally across multiple selections
so the total return is identical no matter which one wins. The
stake per selection is inversely proportional to its decimal
odds, then normalized to the total bankroll.
How do I Dutch three horses in a race?
Enter the decimal odds of each horse, set your total stake,
and the calculator returns the dollar stake to place on each.
The return on any winning horse is the same. If the combined
book is above 100%, you lock in a guaranteed loss equal to
stake * (1 - 1 / combined book); if it is below
100%, you lock in a guaranteed profit.
What is the difference between Dutching and arbitrage?
Dutching is the staking method. Arbitrage is the outcome.
When the combined book on the selections you are Dutching is
below 100% (which usually requires combining prices from
multiple sportsbooks), the Dutched bet is also a true
arbitrage. When the combined book is above 100%, Dutching
still works as a way to spread risk, but the expected outcome
is a small loss.
Why is my combined book above 100%?
Because a single sportsbook prices both sides with a vig
baked in. To find a true arb, you usually need to take the
best available price on each selection from different books,
or use a prediction market where the spread is tighter.
Can I Dutch more than three selections?
Yes. This calculator supports up to six. The math works
identically for any number of selections; just add the
additional rows and the totals update automatically.
What happens if one of my Dutched selections ties or pushes?
A push refunds the stake on that selection only. The return on
a winning selection still pays out at the calculated amount,
but you do not collect from the tied row. Most sportsbooks
follow this rule; check the house rules for the specific
market.