Situation I had the other day that left me wondering whether or not I made a mistake. Your typical staggered limit game. Multiway pot, I think I had 5 or 6 opponents in besides myself. I was holding pocket 5's. Flop misses me completely, someone bets behind me and I get a bunch of callers, with 2 players ahead of me that I was confident weren't going to raise. Pot was laying 18.25 to 1, a little shy of the 22.5 that I would need to justify a call purely on pot odds. I made the call because I figured with the amount of players I still had in the hand and all of them calling to the turn, the implied odds were good. The turn came and missed me again and I promptly folded. But my question would be, was the flop call a mistake or did I judge the situation correctly?

I'm not really sure, as I've just started to look into the math behind implied odds lately. Your question, though, was the first thing that I wondered about, when beginning to learn about it. Someone with a much better grasp of it will probably come along and give you a sure answer, 'cause I doubt that mine is even half-way correct yet.
I would guess that since the pot is laying 18.25:1 and you need 22.5:1 to justify a call, that the difference of those two ratios would be a starting point. So, 22.5 - 18.25 = 4.25. So, I think you'd need to be sure that if you hit on the next street, that you can get paid 4.25:1 more money than what is in the current pot.
The way I think of it and do the math for that is: okay, say the pot is $1,000. Well, we know that you need 22.5:1 to justify a call. The way I think of it is that the $1,000 pot is the whole pie (%100), and so is the 22:5 odds that you need. So, 1000 / 22.5 = 44.45. That $44.45 would be one unit of the whole pie and you need 4.25 of those units to bring your offer of 18.25:1 up to 22.5:1. So, 4.25 * $44.45 = $188.91. You'd absolutely need to get paid that $188.91 in addition to what's currently in the pot, if you hit your winning out on the next street. But, there are also alot of unknowable variables to account for, so I guess that maybe you'd want to expand that needed 4.25:1 portion of the pot and multiply it by something like 1.5 or 2, just to be sure that over time your wins make up for your losses and the times that you get pushed of the hand on later streets. Another main consideration, I think, when judging if you can get your Implied Odds or not is the other player types. Like, if your out comes on the board, will they be able to read the board enough to instantly fold if they suspect that you hit? Or, are they calling stations and will pretty much pay you off most times? Things like that...
That's about as much as I currently understand on the math behind Implied Odds and how much IO you'd need to justify that call. Just read this post for the thinking process behind the decision because it's not a very definitive answer, and someone else will likely respond with a good rule of thumb, like your question asked for. I believe I read a long time ago that it was 1.5 or 2 times the amount, but I can't be sure now.
I would have used percentages to make the example above more understandable, but the figures for the odds ratios (18.25 and 22.5) are ones that aren't in my memory, so I couldn't do the math in my head quickly like in-game.

Here's one way to start thinking about it:

The Mathenoobics of Poker - Implied Odds

but it's more an art than a science because while you can work out to the fourth decimal place how much you need to win after calling, your assessment of how likely that is depends on subjective stuff like how hidden your draw is, and most important of all, opponent tendencies.

Good Luck.

Yeah, definitely read DiamondDog's article on Implied Odds, in Mathenoobics. That whole series is good. There're some other ways to think of IO at http://forumserver.twoplustwo.com/32...stion-1343855/


EDIT -- There's a type error in my above post, on the 12th line down.
"and so is the 22:5 odds that you need." <-- That ratio should be "22.5:1" and not "22:5"

Here is how I see the math of OP’s question. OP did not explain how he got his 22.5 pot odds requirement, but let’s assume it’s valid. I will now use pot odds to mean (pot before your investment) / investment, which is the typical definition for a call decision.

We are deciding to call a bet on the flop. If the pot is 1000 before your investment and you are getting pot odds of 18.25 that means you have to invest 55 approximately. In order to have 22.5 implied pot odds for this 55 investment, the pot has to be 55*22.5 =1237. Therefore, to make this 55 investment have +EV, you need at least 1237-1000 = 237 in implied winnings if you hit a winning out on the turn .

@statmanhal

So, then a ballpark formula for your method would be:
$IO_NeededToCall = [((POT) / (PotOddsOffered_LeftSideOfRatio)) * (PotOddsRequired_LeftSideOfRatio)] - (POT)

... That is handy. So, let's say that the pot is $500. The pot odds being offered are 7:1 but Hero needs 9:1 to call. Would the amount of his implied winnings, if he hits a winning out on the next street, be about $143 ?


NOTE - I probably could've used less brackets in the above formula, but I was confused on the order of operations. I remembered PEMDAS, but then I also thought that it went, "both Division and Multiplication, from left to right".

@MidPair

Given Pot, Pot Odds (PO)and Required Pot Odds (RPO), what are the needed implied winnings (IW)?

(Pot + IW)/Bet = Pot/Bet+IW/Bet =RPO;

PO + IW/Bet = RPO

IW = (RPO-PO)*Bet

But, Bet = Pot/PO, so

IW = RPO*Pot/Po – Pot = 143,

which is what you got stated a little differently.

I’m a little embarrassed at this. I usually state the formula I use but many times posters in this forum thank me for the answer (assuming it’s right ) but claim that the math is beyond them at this point. So in this case I tried to explain it logically. I thank you for showing the formula.

I believe I'll eventually be able to add that to my in-game thought process for the applicable decisions. I'm plugging the formulas into a spreadsheet as I learn them, so that I can start to review my hand histories soon, and start posting the questionable ones. I think that I've learned more in the last month than I did in the previous ~6. Once a few EV calculations start to make sense, it gives poker a whole new meaning. Thanks for showing me that way to calculate 'needed implied winnings'. My wordier formula just makes it stick into my memory and, after I can recite it without having to look it up, I'll shorten it to your variable names.