Long time poker player, but still have a pretty basic question:

If I have an A5 and the flop comes 25Q, I think it’s not looking good for me with middle pair and 4 other players in the pot unless an A comes or another 5, and if an A or a 5 comes out, my 2 pair will win the pot many of the times.

Preliminary Question: if I’m thinking I have 5 outs (2 fives and 3 aces), the chances of one of those coming on the turn is about 10% (5*2), and then same for the river - is that right?

Main question: If the above premise is right, regardless of what’s in the pot right now (for the most part), and someone bets $10 after the flop, is it right to account for implied odds by thinking that if I think I will ultimately win $110 from the pot (not including money that I will put in on the turn and the river, but including money that I have already put in), then calling a $10 bet is EV positive (because it’s greater than $100)?

Then of course I have to deal with the pre-river bet, but that can be part 2. Just trying to figure out the basic math behind implied odds.

implied odds isn't a math thing to calculate so to speak, it's a concept to roughly gauge whether you can make what's an immediately bad call with the idea that you will get paid off on a future street if you hit. so it's really just weighing up general factors:

- will villain become a nit if you start betting out at him and folding? if he is going to fold the instant someone wakes up, then you're not getting paid.
- will villain continue to bet? if he's going to keep firing regardless, our situation looks better
- how many outs do we have?
- is our hand going to stand up if we hit? in your example, it's all well and good saying an ace is an out, but if villain has AQ (or, for that matter, 43) then it isn't
- how much money does villain have back? we have no implied odds if villain's flop bet is all in

Sixfour makes some good points summarizing the implied odds issue but I disagree with the statement that it can’t be modeled. I developed a very complete implied odds model and programmed it in Excel: Here is a brief summary of it

“This program determines the size of a future bet you must make to assure +EV. It assumes an implied odds situation where hero hits his outs with Pr(Hit) and wins with Pr(Win|Hit). If Pr(Win|Hit) is less than 100%, then reverse implied odds are in play. If hero doesn't hit, he folds and loses the current street call amount. Three EVs are calculated; immediate, which is negative, one where villain may not call and one where villain always calls. A goal seek option is available for determining the future bet to be made when villain calls with a probability that depends on the user input of villain's calling probability.”

See the following blog for model details.

https://holdemmathology.tumblr.com/p...s-model-part-1

The basic math of Implied Odds is 'calculating' how many more chips you 'must' win (or more) in order to make up for a -EV call.

it's most commonly used for set mining where you typically need a minimum of 8 to 1 on your chips just to break even. This typically makes (pure) set mining when HU a not-so-profitable venture. If you see Flops 3-4 ways you are technically halfway there .. and then you need to get the rest on Turn and River.

Your example is complicated since you may improve with an Ace but still lose to AQ or an unlikely (but possible) 34.

Typically when considering an Implied Odds call you want potential 'well' beyond the break even point since you are betting a longer shot and also need to make up for the times you improve but yet lose anyway .. four-flush, better holding, counterfeit, et. Most Players look for at least 10 to 1, if not 18-20 to 1 in set mining spots depending on the size of the pair.

As stated above, sometimes the largest factor in Implied Odds is actually getting paid. But there's always two sides to look at. If you have an opponent who wont pay off, then you open the door up to more bluffing opportunities where you can steal chips with lesser holdings. GL

You think you have five outs which give you implied odds - but what do you consider is the guy betting with on such a board with 4 players in the hand? At the very least a queen.

Three of your outs are aces. Do you really think that player will put a lot (or any) money in the pot when an ace comes on turn or river and you start betting big? No.
So you need to consider that you have very little implied odds with 3 of your outs (the aces)...unless someone else is also holding an ace and does not have 2-pair and will stay in the hand against the bet. But in that event you don't have 3 ace-outs but only 2.

You have implied odds if the 5 hits. But even in that case it's unlikely someone will put their entire stack in with just one pair. Given the flop a 2-pair is unlikely (this would need someone to be in the hand with Q2, Q5 or 52...all of which hands most people fold preflop...even worse: Q5 and 52 have you beat in that case with full houses and Q2 has just been counterfitted (so the former will take your stack and the latter will fold)...of course somone could be holding a pocket pair but even they would not put a lot in the pot unless it's specifically KK).