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When using implied probability with betting odds, I get a weird result, that I cant seem to understand.

I should say I am looking at betfair exchange, so the odds are not set by a bookmaker, but by other betters.

When I take the odds, and calculate the implied probabilities, I do not get a sum of 100, which I think is odd.

The example goes:

$1 / 2.68 \times 100=37.31$

$1 / 2.78 \times 100=35.97$

sum = 73.28

I know bookmakers take margin, so the sum usually is above 100 (like 105 for example), but I have never seen it below.

And even better (for me), with both odds > 2, I can bet both an get a sure profit (arbitrage). So I don't understand this..

Martin Sleziak
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  • Could you be more specific about the odds. (Perhaps even including a screenshot?) Since they are close to each other, maybe one of them is for backing and one of them for laying? In case it might be helpful, I'll mention that I wrote a bit about laying in my answer here: Mathematics of hedging bets. (As a side note, you have mentioned Betfair - it is probably worth mentioning that this is betting exchange, maybe explaining what that means or at least adding a link to Wikipedia.) – Martin Sleziak May 08 '21 at 08:21
  • Just to include one specific examples, if I take the odds from here, I have 5.8, 1.67 and 4.2 for backing and the sum 1/5.8+1.67+1/4.2 is close to one, as expected. (Slightly larger than $1$, so I cannot get an arbitrage.) Similarly, I will get a number close to one from the odds for laying. – Martin Sleziak May 08 '21 at 08:28

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