Odds Or Evens?

A couple of months ago, Argentina played Tunisia in the Confederations Cup. Argentina were quoted at 1.16 to win the match. So to make a value bet, I had to decide whether I thought Argentina were more or less likely to win than the 1.16 suggested by the Bookmakers.

"What else has a chance of happening 6 times out of 7? Not throwing a 7 on a 7-sided dice? Not being born on a Sunday? "

So 1.16? What didthat mean? Did I think they should be 1.18 perhaps? Hmmm, not an easy question. Perhaps it would be easier in fractional form. I changed the options on the website from decimal odds to fraction odds. The 1.16 was replaced by 1/6.

So, 1/6, or 6 to 1 on. Well that means 6 chances out of 7 for success. If the match was played 7 times, Argentina would be expected to win 6 times. That made more sense than 1.16, but I wanted to compare those odds with something similar.

What else has a chance of happening 6 times out of 7? Not throwing a 7 on a 7-sided dice? Not being born on a Sunday? I did not have a good feel for those situations. In fact, I could not think of a good way to mirror the 6 chances out of 7 situation. I wanted another way to think about those odds.

What about percentages? No option for that on the bookies website! But I have always favoured converting odds into percentages. 6 chances out of 7 is about 86%. I was getting a better feel for the odds now; 86% or 86 times out of a 100.

"All that was necessary was to re-frame the match situation into an evens, or fifty-fifty situation."

I was making progress. More or less than 1.16? More or less than 1/6? More or less than 6 chances in 7? More or less than 86 times out of 100?

Normally that would be it for me. Convert the odds into percentages, and assess the value from there. But on this occasion, I started questioning my methods.

Why was I comfortable with converting odds into percentages? Well, that seemed obvious enough. Instead of dealing with odds like ‘3 chances out of 4’, or ‘2 chances out of 5’, everything was now ‘chances out of 100’. There was the familiarity of dealing with ‘chances out of 100’ every time.

But my next question was far harder to answer. Did I really have more knowledge of situations that happened 86 times out of 100, rather than 6 times out of 7? Quite simply, the answer to that was, ‘No’. I did not really have anything to compare 1.16 to.

I did not place a bet on the game (Argentina won) but over the next few days I started thinking about the problem. 6 chances out of 7 really meant very little to me. It did not matter in what form the odds were re-written. I had no experience in dealing with situations that occur 6 times out of 7.

So what odds was I comfortable with? Well, that was easy. Anything quoted at evens. More or less chance than evens? Odds on or odds against? More than 50% or less than 50%. Yes, there was no doubt about that at all. Anything quoted at evens and I would be confident of deciding on one side of the bet or the other.

All that was necessary was to re-frame the match situation into an evens, or fifty-fifty situation.

Well, if I thought it was an equal chance that an event would happen, as opposed to an event not happening, then the odds would be evens, or fifty-fifty.

That is, looking at the match, if I had thought the chances were equal that Argentina would win the game, or not win the game, I would have been looking for odds of evens, or 50%, on Argentina.

"What if I imagined that Argentina were to play Tunisia in two consecutive matches?."

Taking this a step further. What if I imagined that Argentina were to play Tunisia in two consecutive matches?

And what if I had thought that in this case the chances were equal that Argentina would win two matches in a row, or not win two matches in a row. In this case I would have been looking for odds of 71% (square root of 50%) on Argentina. (That is, if Argentina’s odds for a single game were 71%, then their odds for winning two consecutive games would be 71% * 71% = 50%.)

Similarly, if there were three consecutive matches, and I had thought the chances were equal that Argentina would win three matches in a row, or not win three matches in a row, then I would be looking for odds of 79% (cube root of 50%) on Argentina.

This was a new way for me to look at the odds. If the Argentina – Tunisia match were played over and over again, with the same initial conditions, how many consecutive games would I expect Argentina to win? More especially, with odds of 1/6, how many consecutive games were the bookies expecting Argentina to win?

50% chance of this number of consecutive wins	Chance to win one match	Decimal odds to win one match
1	50%	2.00
2	71%	1.41
3	79%	1.26
4	84%	1.19
5	87%	1.15
6	89%	1.12
7	91%	1.10
8	92%	1.09
9	92.6%	1.08
10	93.3%	1.07

From the table, 6 chances out of 7, or nearly 86%, meant the bookies were expecting there to be a fifty-fifty chance for Argentina to win about 5 games in a row, as opposed to not winning 5 games in a row. (For the record, I don’t think Argentina should have been that short now!! I would have expected Tunisia to hold Argentina to a draw in at least one of those five hypothetical games…)

I have used this table a few times since then – and I have to say I have found it a whole new way to look at odds. It is especially suited to extreme odds situations, where one selection is heavily odds on.

I hope the table can add another dimension to your thoughts about odds.