What does “slim odds”mean?

Question

The definition of slim odds by Webster 1913 Dictionary is :

low odds; poor chances; as, there are slim odds he will win any medal. - W. Irving.

The above definition is similar to that of slim chance:

a small possibility There's still a slim chance that we can win. (Merriam-Webster)

We know what low and high odds refer to:

Low odd means something is likely, and "high odds" means something is unlikely, but many people get the two confused.

Now, if odds refers to a ratio as suggested by ODO:

The ratio between the amounts staked by the parties to a bet, based on the expected probability either way.

High odds would be something like 42-to-1, that is one chance out of 42 that something may happen, while low odds would be something like 2-to-1 that is 1 chance out of 2 that something may happen.

Given all that, my question is about the above definition of “slim odds” as low odds. If low odds refer to something that is likely the above definition appears to be wrong, especially because they later add “poor chances”. In other words, it appears that “odds” is used as a synonym of “chances.” But that would add even more confusion to the usage of low vs high odds.

Questions:

1) Is “odds” in the “slim odds” definition used as a synonym of chance? If so, is that a correct usage?

2) What does “slim odds” really mean in the end?

Answer 1

Odds are a numerical expression, usually expressed as a pair of numbers, used in both gambling and statistics. In statistics, the odds for or odds of some event reflect the likelihood that the event will take place, while odds against reflect the likelihood that it will not. In gambling, the odds are the ratio of payoff to stake, and do not necessarily reflect exactly the probabilities. Odds are expressed in several ways (see below), and sometimes the term is used incorrectly to mean simply the probability of an event. Conventionally, gambling odds are expressed in the form "X to Y", where X and Y are numbers, and it is implied that the odds are odds against the event on which the gambler is considering wagering. In both gambling and statistics, the 'odds' are a numerical expression of the likelihood of some possible event. - Wikipedia

The definition you link to regarding low and high odds looks like it relates to betting odds. These are said to be expressed conventionally as odds against something.

In conversational usage (outside the technical terminology used in betting), however, odds are normally taken to be odds for or odds of unless the context clearly indicates that they are odds against.

You ask:

1) Is “odds” in the “slim odds” definition used as a synonym of chance? If so, is that a correct usage?

2) What does “slim odds” really mean in the end?

The synonymous phrase "poor chances" strongly constrains "low odds" to be the common (non-technical) usage of odds for or odds of. So "low odds" would mean that the event of interest is less likely to happen than not. This is consistent with the rest of the definition you've quoted regarding "slim odds".