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Expected Value – Why You Should Care That I Care

So what is ‘Expected Value‘ and why should you care?

‘Expected Value’ is the likely outcome given the probability of something happening. Look at these common betting scenarios:

  • Flipping a coin

    50/50 chance – if you get even money (1/1) then in theory you could play for ever and statistically you are likely to break even

    Expected Value: Break Even

  • Backing a single number at European Roulette

    37 numbers but you only get paid at 35/1

    −1 × ​3637 + 35 × ​137 = −0.0270 (2.70% house edge) (See Wikipedia – House Edge)

    Expected Value: Lose 2.70% of your money EVERY SPIN

  • Backing or Laying every horse in the 2019 Prix de l’Arc de Triomphe

    We can see from the image below that the ‘Back’ book is currently 102% and the ‘Lay’ at 99.1% with ~5% of winnings to be deducted due to Betfair commission.

    Expected Value Back: Lose 2%
    Expected Value Lay: Lose 0.9%
Expected Value When Betting on Horse Racing
Betfair Expected Outcome – Prix de L’Arc de Triomphe (using Betfair Prices at 10am)

How Does ‘Expected Value’ affect betting?

If I offered you 6/5 about a coin flip and asked how many times you would like to play then your answer should be ‘infinite‘.

If you are getting 6/5 about something that is 50:50 (Even money) then statistically you are going to come out in profit.

If I offered you 5/6 and asked you the same question then you would decline the invitation – as statistically you are set to lose.

How to Apply ‘Expected Value’ to Horse Racing?

As previously mentioned in the ‘Marked Horse Racing Cards‘ post (please read before continuing if you haven’t already) I maintain my own database of horse racing information.

I apply this information to any given horse race and I use it to adjust the odds for each of the runners to what they potentially should be.

In many cases this may not highlight any betting opportunities and we leave the race alone, however in other cases it highlights horse racing bets with a significant positive ‘Expected Value’.

For example, let’s say we are getting 4/1 about a horse we have strong information for and our re-calculated odds estimate the horse should be 2/1.

We are going to win that bet 33% of the time and we are going to get paid out at 4/1.

Let’s see how that looks over 9 bets where we win 3 and lose 6:

Bet NoResultProfitBalance
1Win£400£400
2 Lose-£100£300
3 Lose-£100£200
4 Win£400£600
5 Lose-£100£500
6 Lose-£100£400
7 Win£400£800
8Lose-£100£700
9 Lose-£100£600

Based on those statistics and probable outcomes based on our revised book we are starting to make significant profits.

Back to the coin flip example – if we are getting 6/5 about an even money shot how often should we bet?

My Service is to find Positive ‘Expected Values’. The bigger the value the bigger the advised stake.

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