Tournament Betting Facts

Which Is Better – Betting The Tournament Winner Market or . . . Betting Round By Round?

I am often asked the question of whether it would be more financially beneficial to back a player/team every match in a round as opposed to backing the player simply straight in the tournament winner markets.

The argument is often made that a punter would in fact make more by simply having an all-up wager on the one player for the same stake as you would back the player in the tournament markets.

Now this question becomes a little more involved when factoring the bookmakers margin in the equation. After all surely paying the margin four times as opposed to once would negate the chance of making more with an all-up bet or would it? Bookmakers will generally set their tournament markets at a much higher percentage then what they would the head-to-head type markets.

Let look at a typical example that is available on SportsTAB with a little more emphasis on the bookies margin. The bookies margin is the amount in which the bookmaker would expect to make on any match. It is his return on investment, so to speak.

Below we are going to analyse a make-believe knockout style tournament between 16 players, and hence four matches will win the tournament. Now SportsTAB will generally price their bookies margin at 130% for tournaments of this sort (for example currently the AFL premiership market is set at this amount, whilst their individual home and away matches throughout the year are set at around 108%.)

Considering that the tournament is between 16 players, and let’s assume every player has the same chance of winning. Therefore the odds should really be $16.00, but because of the 130% margin the odds are set to $12.31. As .

Odds for each match are set to $1.852 as .

So let assume that we have $100 to spend and we are going to bet on a team of which we believe has a 60% chance to win each match.

So we have a 0.60 x 1.852 -1 = 11.1% overlay on each game.

Chances of winning is 0.6⁴ = 0.1296 [i] .

Hence our expected profit for betting on the tournament is

When betting on each game, we bet $100 on first game and wins so we have a kit of 100 + 100 0.852 = $185.20

We bet again and it wins we have a kit of 185.20 + 185.20 0.852 = $342.99

We bet again and it wins we have a kit of 342.99 + 342.99 0.852 = $635.21

We bet one more time and it wins, we have a kit of 635.21 + 63521 0.852 = $1176.41

Hence we made a profit of $1076.41

Considering that the probabilities of winning the tournament are the same as previously mentioned, and betting on the tournament we made a profit of 100 11.31 = $1131, this means in this instance it was better to bet on the tournament despite the large bookies margin, as the return was greater if they were to win, with the same risk of $100.

So in this instance, when is it equal to bet on either one.

Lets say here that x = the expected profit that you would get when betting on the tournament when they win, and y is the expected profit that you would get for each individual match for a $1 bet. So in the above example the expected profit for the tournament would be equal to (12.31 – 1) = 11.31 = x, and likewise the expected profit for each match would be (1-1.852) = 0.852 = y.

So therefore with our $1 bank (as opposed to $100 above for simplicity reasons), we would expect that betting on each individual match would be equal to betting on the tournament if the profits were to be equal.

So naturally the profits for betting on the tournament is simply x for any $1 bet, but lets workout the profits when betting on each individual game.

In the first game, should the team win, we have placed $1 on them, and hence would gain $y in profit. So in the above example, we would have gained $y = $0.852 and would now have a bank of 1+ y or in the previous example 1 + 0.852 = $1.852.

Now in the second match, we bet all of our 1 + y again, and it wins again, and we make a profit of , and this means that our bank is now the original plus the profit we had just made, so our bank is: .

Now this is where it might get complicated for some. On the third match, we are now betting the bank that we have as mentioned above, and if that team wins, the profit we make is what we bet multiplied by y.

Hence after the third bet, our profit should be our previous bank, plus the profit that we make from the success:

And for the final bet, we bet the above bank once again for a profit of y, and hence our final bank balance is:

Looks complex, but the above formula can be simplied down to this formula:

Note that the above equation is our bank account at the end, hence it includes our $1 that we originally bet with. This means that the profit that we made is just the above formula minus 1, in other words

Now as we mentioned once again, should betting on the tournament be just as profitable as betting on each individual match, we would expect the above equation (profit for betting on matches) to be equal to x (profit for betting on the tournament).

Hence,

So for example, given that you would win at odds of $1.852 for each match (y = 0.852) the correct amount you should win is therefore

Hence the odds to be fair for betting on the tournament as well as the match should be equal to $11.76.

If all teams had odds of $11.76 then this would mean a bookies margin of

This means that a bookies margin of 136% on the winner of a tournament with 16 players all at the same price, is equal to betting on each match with a bookies margin of 108%. This also backs up that the odds for the original example.

By simply putting other values into the equation we can have a look at different bookies margins for tournaments and see what they should be for the matches to be equal in betting.

The graph above shows the relationship between Odds for the Match and Outright odds for the tournament. The line in the middle shows when betting on each event is equivalent. So for example, should the odds for the match be equal to $1.80, then you would be better off betting at the price of $12.00 instead of the match. Likewise betting on a match at odds of $1.90 would be better than betting on them in a tournament at odds of $11.00.

Naturally this will change given the amount of matches that it takes for teams to win the tournament. In the above example we had four wins, however there maybe some tournaments where only three wins or five wins is required.

Below is given the comparisons of bookies margins for odds that are equal for Match Betting and Tournament betting. This shows that the longer the tournament (ie the more matches one has to win), then the higher the bookies margin will be to win the tournament. A larger bookies margin however doesn’t mean that you are less likely to win of course, but this is a direct comparison of the two betting options.

It is interesting in that most people stray away from betting on tournaments because the bookies margin is that much higher, when in reality betting on a match that has a margin of 108% is equivalent to betting on the tournament with a margin of 160% when there are 6 matches in the knockout scenario, and betting on the tournament with a margin of approximately 117% when there are only two matches.