How To Calculate The Odds Of Entering A Competition

[DanDaFootyMan]

Basically if I enter a competition that pays £100 to first place and costs £5 to enter, I want to know how I calculate when the odds are in my favour. In the other words if only two people enter then the odds are in my favour, if 1000 people enter then they are not. How do I calculate the point where it changes from being in my favour to not being in my favour?

[Cloverjo]

If more than 20 people enter, the odds are not in your favour. Seems logical, but I'm ready to be corrected by Buenchico or jim360.

[Prudie]

I looked at it like cloverjo at first but actually odds being in your favour is a totally subjective phrase. If only 2 people enter you have a 50% chance of winning (assuming this is just a raffle and quality of entry is irrelevant). If 10 people enter you have a 10% chance of winning - it's your opinion when that becomes a risk not worth taking. The only times the odds are really in your favour is if you are the only entrant.

[Prudie]

The 20 people comes from 20 x £5 = prize money. That has nothing to do with being the point at which the odds become out of your favour.

[jim360]

How does the game work? It depends on how the odds depend on the number of entrants or not.

[Zacs-Master]

Don't the odds go, simply, like this:
Only you. Guaranteed win
2 people entering 2-1
3 people entering 3-1
4 people entering 4-1
Etc, etc, etc.....

[THECORBYLOON]

ZACS, you need to reduce the first figure by one so that if two folk enter, the odds are even, three folk are 2-1 and so on.

[THECORBYLOON]

The odds are in the OP's favour if he has more chance of winning than losing and (if allowed to enter more than once) he ends up in profit. If he enters fewer than twenty times and wins, he'll be in profit, if his entries are more than the others combined, then the odds are in his favour.

That means the most entries he can have is nineteen and the others is eighteen or thirty-seven in total, if there are any more than thirty-seven entries in total, the odds are no longer in the OP's favour.

[factor-fiction]

Assuming all entries have an equal chance of being selected then divide the prize money by the entry cost (in your case £100 divided by 5 = 20) and the resultant figure tells you the point up to which the game is cost neutral to the organiser. In your case if 20 people enter then the competition is fair. If more than 20 enter the organiser makes a profit; if fewer than 20 enter then the organisers make a loss and it's a game worth playing for participants.

If you know the number of participants you could calculate the expected return by dividing the prize money by the number of participants. If the expected return is greater then the entry fee then it's worth having a punt (assuming you can afford to lose). if the expected return is less than the entry fee then the competition is stacked in favour of the organiser.

I'm sure most competitions are stacked in the organiser's favour

[Prudie]

I'd like Dan to come back and qualify as several answers relate to different scenarios. I've understood it that irrelevant of entries the prize money remains at £100 or does it vary depending on number of entrants.I also understood it to be a one off rather than a repeated competition - when it becomes along similar lines as red/black bets in roulette.

[New Judge]

This is all very well, but there is one vital piece of information missing which has been requested by jim but not supplied. That is, how does the competition work?

Is there guaranteed to be a winner (i.e. is it a "raffle" style affair when one of the entries is "drawn from the hat"). All of the answers so far seem to make this assumption.

Or is it a competition where one of the entrants has to succeed in accomplishing something? An example of this is matching three balls in the National Lottery. This pays a fixed prize of £25 (for a £2 stake) regardless of the number of entries but, importantly, it is theoretically possible for nobody to win (i.e. nobody matches three numbers). If it is a competition of this type the number of entries is irrelevant and the odds against winning remain the same for each £2 staked. (In the Lottery the odds against matching three numbers are 56-1). If your competition is of this type you need to establish the odds against you (or anybody else) winning and the number of entrants is immaterial.

[aelmpvw]

the odds aren't in your favour if only two enter :-)

[DanDaFootyMan]

Wasn't sure if this was the right way to respond. It is fixed prize paid out regardless of the number of entrants, and to give more detail there may be 20 different competitions with differing prize money, entrance fee and number of entries so I was trying to work out a formulae to see which is more in my favour. I think I basically calculate the prize money divided by number of entrants and if it is more than the fee to play then the odds are favourable

[Prudie]

"It is fixed prize paid out regardless of the number of entrants" then sorry you're wrong. if there were 20 entrants, entry was £5 and the prize was £100,000 you have exactly the same odds of winning as if there were 20 entrants, entry was £5 and the prize is £100.

[DanDaFootyMan]

I guess it's not just about the odds, it's the value of the odds as well. I need a calculation to show me which is the best game to enter and also when an individual game is not in my favour so the £5 entry £100 prize with 30 entrants isn't good value. If these are the games which is the best value

£1 entry 100 entrants £150 prize
£5 entry 75 entrants £500 prize
£10 entry 120 entrants £1000

[New Judge]

You seem to be confusing "odds" with "value".

In the examples you quote:

Example 1 you have 1 chance in 100 of winning at odds of 149-1.

Example 2 you have one chance in 75 of winning at odds of 495-5 (99-1)

Example 3 you have one chance in 120 of winning at 990-10 (99-1)

The odds against you winning the prize depends on the number of tickets sold. The value of the prize determines the odds you will be paid out at if you win.

Example 1 looks to be good value. You win 149 times your stake. However, the odds against you winning this prize are longer than in Example 2 where you only win 99 times your stake.

To even this out a bit, imagine you spend £10 on each of the examples:

Example 1 you would have 10 chances in 100 (1 in 10) of winning at (effective) odds of 140-10 (14-1).

Example 2 you would have 2 chances in 75 (1 in 37.5) of winning at odds of 490-10 (49-1)

Example 3 you have one chance in 120 of winning at 990-10 (99-1) - i.e. unchanged.

This clearly indicates that you have by far the best chance of winning in (1) but your payout is considerably less. Conversely you have the least chance of winning in (3) but the potential reward is greater.

The number of participants (or tickets sold) clearly effects your chances of winning but it has no bearing on the potential gain you may make should you win. You pays your money and takes your choice.

[THECORBYLOON]

NJ, I know that we speak about "odds" in a betting context but I think you are confusing it with the return on the money staked. If the probability of an event is 0.01, the betting odds which determine the return may be anything under the sun but the TRUE odds are 99 to 1.

[New Judge]

Yes quite so, Corby. In my post above you can substitue "probability" for "odds" (making the appropriate conversion). In this case, the probability and odds match, however.