152→ Odds

1,000 parlays

Pick a parlay, how much goes on each one and how much money you start with. The calculator plays 1,000 in a row and shows where your money ends up.

Legs in each parlay

How many parlays in a row

Ends with more than it started2.4%Runs out of money on the way: 95.3%

Each parlay pays 6.86 and wins about once in 7.9. After 1,000 of them, the middle result is $514.

Average final money$3,036started with $50,000
Average per parlay-$136the margin: 13.6%
Bad luck (1 in 10)$78or less
Good luck (1 in 10)$924or more

All the possible endings (exact)

ran out of money 95.3%below the start 2.4%above the start 2.4%

The 4.7% that still have money

start$3,401$174,876+

12 runs drawn at random

$50,000

The lines are only examples. The percentages above are exact: they count every possible path.

Show the formula

Parlay odds D = d to the power of legs = 6.86; chance P = 12.59%

After t parlays with w wins: money = start + w × stake × D − t × stake

Each step: with chance P one more win, otherwise one more loss; when the money does not cover the stake, the run stops.

Average per parlay = stake × (P × D − 1) = -$136.16

Illustration: 1,000 parlays

The starting example

  1. The parlay3 legs at 1.90 each: odds of 6.86. It wins about once in 7.9.
  2. The moneyYou start with $50,000 and put $1,000 on each parlay, one after another.
  3. The priceEach parlay loses $136 on average: the bookmaker margin, 13.6%.
  4. The endingAfter 1,000, in 95.3% of cases the money has already run out. Half end with $514 or less.

The longer you play, the more the margin shows

Parlays in a rowEnds above the startRuns out of money
10027.4%7.8%
1,0002.4%95.3%
5,000< 0.1%> 99.9%

With the starting example. Exact: it counts every possible path, it is not a simulation.

A few against many

A few parlays

  • Luck rules
  • A couple of hits put you ahead
  • Results vary a lot from run to run

Many parlays

  • The average rules
  • The margin is charged on each one
  • Runs look more and more alike
ParlaysThe maths of a single parlay, leg by leg.Expected valueThe average of a bet and how far results stray from it.

Questions

Are the lines in the chart a prediction?

No. They are examples drawn at random so you can see what a run can look like. The percentages above are exact and count every path.

What does running out of money mean?

That what you have left does not cover the next parlay, so the run stops there.

What if I change the amount on each parlay?

With more money per parlay you go broke sooner. With less you last longer, but the margin is charged on every one all the same.