Stupid Question RE: Odds

This is probably a stupid question, but wth.

Here is an example of what I have read in the forums:

"You're getting 2.8:1 odds to call opp's AI, and your hand is about 40% to win."

The part I don't get is how odds work together with a hands % to win in deciding to call. Is there a link that explains this relationship?

If the chance of you winning is greater than the % of money you're putting into the pot, then you're making a profit.

Suppose in some spot you have a 50% chance of winning. It's e $25 to call in a pot of $50. You'll be putting in 33% of the pot, which is less than the 50% of the time you believe you'll win, so you'll be +EV.

The basic application of this for beginners is learning pot odds, implied odds, and counting outs and translating that deciding if you should or shouldn't continue with draws.

Worth noting is that odds and %chance to win are different ways of expressing the same thing. You could reverse those types of notation and have it mean the same thing. 40% chance to win is the same as having 1.5 to 1 odds against you winning. 2.8 to 1 odds from the pot means you are break-even if you win 26.3% of the time.

The above is stated somewhat clumsily mainly because I am not comfortable with odds terminology. I know that you can lay odds, take odds, have odds for, odds against and being odds-on - and what it all means I only have a flimsy understanding of. I do begin to have something of a basic grasp of the odds mathematics.

Pot odds: The pot is $3 and you have to pay $1 to come along (and that ends all the action) - that means you get 3-1 odds from the pot. When converting from an odds notation to a % notation you have to make some adjustments to the numbers. It should be obvious from my example here that when you call $1 the pot grows to $4, and yet we always say that you risk $1 to win $3 - not $4. An odds notation has a number of useful properties that makes it immediately applicable. Having played with odds a bit I know intuitively from looking at this example that if I take this bet 4 times, win 1 and lose 3 I will be breakeven. That means if my chance to win is 1 in 4 or 25% I am breakeven. It means that if my odds of winning are 3-1 against - I win 1 in 4, giving me a 25% chance of winning and being breakeven on the bet. That +/-1 when converting to or from odds is crucial to get right.

Some people find it easier to convert the pot odds to a % to win necessary to be breakeven notation - others do it the other way around. In your example you can translate 40% chance to win as 1.5-1 odds against (win chance) | 100 / 40 = 2.5 | 2.5 -1 = 1.5 | and if they win more than $1.5 per $1 they put in (like $2.8 in your example) - it's a bet with positive expected value (+EV). In your example you can translate 2.8-1 into 26.3% | 2.8 + 1 = 3.8 | 1 / 3.8 = 0.263 = 26.3% | say it is the amount of the time you need to win for the bet of calling $1 to win $2.8 to be breakeven. And since you win 40% of the time, which is more than 26.3% of the time, it is a profitable bet for you to invest your money in.

These explanations were very helpful. Thanks!

If only there were a post about simple poker math people who play poker need to know..

Someone should get on that. Spoon?