Gambling / betting math(s) question

Sometimes it would be more advantageous to back a sports result than lay the opposite result.

In football/soccer for example, you have three possible outcomes. Here are some example odds:

2.4 (Home)
3.3 (Draw)
2.75 (Away)

Now, it’s easier enough to Lay, anyone of those, say Home

A stake of $100 will either return $124 (win) + $100 (stake), or not … and you lose the stake.

However, sometimes it’s a good option to do exactly the same thing but in reverse, in other words to back the other two results.

I just can’t work out the combination of back stakes on Draw and Away that roughly equals a Lay bet on Home - any ideas very gratefully received …

I have no idea what you mean by this. If you are trying to work out how much you could lay the home side for to risk $100 @ $2.40 the answer is $71.43.

If you were trying to win $71.43 backing both the draw and the away side you would have to bet $142.81.

There is no reason other than a fluke anomaly in the markets why it would be advantageous to back both other results rather than lay the first result.

There is for in play markets.

Why should that be? Other than the tiny variances between the laying and backing percentages on exchanges such as Betfair it doesn’t make any sense. Since any lay bet is just the opposite side of a win bet why would anyone take the lesser option?

Do you have a real example?

Okay. Sometimes, at SP, I want to Lay the home team but the lay odds are just a little too high.

Becasue no goal has been scored, the odds on the home team will eventually get longer - taking tem further from a price I want.

However, if no is scored both the draw and away odds tend to shorten (away for a while, the draw until a goal is scored), and I think I can get the original lay price I wanted by the back odds on the other two getting a little shorter in play.

This doesn’t seem correct. Are you sure the Home bet doesn’t return $140 + $100 stake; i.e. 2.4 -for- 1 ? (And are you reversing the normal meanings of back and lay?)

Assuming mine is the meaning of the odds, you can see if the implied percentages add to 1.

2.4 implies 1/2.4 = 41.7% chance
3.3 implies 1/3.3 = 30.3% chance
2.75 implies 1/2.75 = 36.4% chance
These sum to 108.4%; the extra 8.4% is bookie’s vigorish.
In other words, if he’s laying Draw and Away, it’s as though he’s backing Home for about 3-for-1.

In your example, where three bets are mutually exclusive and cover all cases, let p, q, r denote the quoted odds (p-for-1, etc.) By my reckoning you can construct a back of p by laying q and r as follows:
Lay q with a total risk of (r*q - r) / (r*q - r - q) Lay r with a total risk of (rq - q) / (rq - r - q)
When you lose you lose 1. When you win you win (r + q) / (r*q - r - q)

This outperforms the simple back when
(rq) / (rq - r - q) > p

… Maybe. :eek:

Well no you can’t get different odds from back vs lay. You are getting different odds because as the game goes on without a goal both teams drift in the win market and the draw firms. But backing any two is still the reverse of laying the other one. Although you are not outlaying extra to lay the home team you are outlaying extra to back the draw.

No that’s great. Thanks! It’s further than I got and I think it’s correct to look at percentages.

I have also looked at ‘true percentages’ and will work on all of it over the weekend. Will get back to you…