A Deeper Look at Implied Odds

So everyone knows what implied odds are. You have suited connectors and are drawing without outs but you know your opponent has a monster and that if you hit you'll more than make up for the loss in pot odds with bets on later streets. But I'm going to look a little deeper.

Here's a standard situation. Let's say 1/2 blinds with stacks of 400, no units, all that matters is the proportion. Anyways, a few limpers limp in preflop, button has AA, raises 6x (12) to isolate, gets one caller (pot size around 30 now). Flop comes out 259, 2 hearts. He raises to eliminate the draws, bets 3/4 to 1 times the pot size (say 25). Guy calls (pot size 80 now), Q of diamonds comes. Again a pot size bet (160). This time he re-raises (he makes it 250 from 80, new pot size = 410, 170 to call), instead of calling he pushes all-in, putting his opponent on something like AQh, thinking that with TPTK + nut flush draw he could possibly have the best hand, so AA pushes all-in (pot size is 580 after call, I haven't been calculating pot size, so let's say it's around 806, 400*2 + 3 limpers*2). He gets a call, caller flips over Q5o. So the AA curses at him, "how could you call with Q5o with a 6x PFR and then call an almost pot size bet with mid pair?

I'm sure you'd never do that, but let's look at the odds we are being offered on the flop bet. Preflop is tougher so we'll ignore that. So we're getting 55:25 = 2.2:1 on our money. But really if we hit trips or 2-pair we end up winning the entire stack. So that means we win 55+(400-12-25) = 418 and we only need to risk 25, so we're getting 418:25 = 16.72:1 odds!!! We only need to hit 5.64% of the time for this call to be profitable. We have 5 outs, which is 10.6% of the time, in fact, we average a 19.3 chip gain per hand ((418-9*25)/10). Remember this is at 1/2 so that means we average almost 10 times the big blind per hand (note that we rounded 10.6% down to 10%, so I'm rounding 19.3 up to 20, not exact, but close enough). Not a huge gain, but a profitable call. Yet how many people would call with Q5 to a flop like that, assuming you called with it preflop.

Now you probably notice, if the person with AA is able to lay them down and get a read that they are beat, this play is NOT +ev. This also raises the question, would AA be able to lay down to trips, seeing the pair on the board? Most of the time I'm guessing not but this significantly cuts into the profit (although eliminating 2 outs still leaves us 3 outs, and 3/47 = 6.38%, high enough to still be profitable). It's also possible that another heart could slow him down, but if we assume our pair is paired with the a heart on the board, and say our Q is of hearts, no calculations change (this also helps us without knowing the other hand, because if we hit the 2-pair or trips, opponent will not hit his flush if he has one).

So does this mean that people who call with hands like this are playing smart? Probably not. They probably aren't thinking this through, but I have a theory that a lot of people who chase way too much actually help themselves by giving themselves implied odds. Way too many people will bet big and assume that means they don't have a draw. If they'd quit making that assumption, chasing draws would not be profitable. But as long as people assume that a big bet being called means they aren't on a draw, calling this bet gives us implied odds.

I just have to laugh at people ridiculing the poor play of their opponents, when the mere fact that they called all the way through gave them the implied odds they needed. Sure there are a ton of suckouts where implied odds are not offered, but when the draw hits, it's easy to see if the other player was giving implied odds based on the action after the draw hits. Try a calculation next time you see someone call another person a donkey for chasing and hitting. Of course a lot of the times they are bad calls and even when they are good calls the person probably didn't actually think through implied odds, they just called because they had a chance to win. But if the stacks are deep (note that in this example both players had twice the max buy-in), you'd be surprised how many times the player complaining about the donkey at the table actually made the play by offering implied odds, paying him off the one time he did hit.

Which brings up another interesting question I've been pondering: how would poker be different if players were deep-stacked. What if the max buy-in were 1,000 big blinds? This kind of thing actually occasionally happens in a tournament, but usually multiple players aren't there. I'm talking a game where everyone has a ton of chips in front of them in comparison to the blinds. Simply raising AA 3-4x BB would no longer be profitable, unless you could make really good reads and fold it to a rag rainbow flop. Implied odds would then be everything and instead of bets being in comparison with the pot to take away pot odds, they'd be in comparison with stacks to eliminate implied odds. You may see things like AA raising 20x BB. Gut shot draws calling 3x pot bets... correctly. It's a very interesting topic to think about.

Big assumption there. I often fold overpairs (including AA) if I feel I'm beat. Somebody pushing all-in usually means exactly that.

Now, of course I know that most people will instacall with AA no matter what, but I still don't agree with your theory.

Looking at your example of a flop of 259 - what if the opponent has a pair of tens and a King comes on the turn? Or an Ace? What about a third heart? Will he really go broke with TT?
Or what if he simply c-bet a pair of sevens? Do you think he'll put his entire stack in the middle, or would he rather check-fold it down after you call on the flop?

There are a ton of situations where you won't be able to stack your opponent. In fact, I'd say that in most cases your opponent won't have a hand strong enough to go broke with. And even if he does, he might just have Aces Up or a bigger set...

well I meant in the case of AA, and I specifically included that condition because many people I've seen play like that. I've seen people bet hard with TT in that scenario, and keeps pushing because they're thinking "that donk couldn't have called with an over card". I'm talking about people who complain about poor play, and usually aren't that great themselves. The point is that playing badly, calling all the way, actually rewards the "bad" calls.

Chris has a point; it all depends on what kind of players are and whether or not they're likely to stack you with as little as an overpair.

To take it to the end of the spectrum, if you look at HSP they're often stacked with like 500k at 300/600 blinds. That's huge, but you don't often see stacks without some massive bluff or two monster hands (see set over quads ) because the players are so good that they'd rarely stack with an overpair without a very good read.

On the other hand, very bad players might stack with as little as TPxK if they're poor enough.

Yes, but how do you know that your opponent has an overpair? Since most players will c-bet almost all the time, you really have no idea about how far your opponent is willing to go with his hand.

Also, you shouldn't be in the pot with Q5o to begin with. Preflop, you're certainly not getting odds to call.

Right, I don't think you understand my point. The person playing Q5o is not a good player, but they unwittingly are making the correct play because of the poor play of the opponent. If you call your stack with AA, you are giving implied odds to any hand basically. That's all I'm trying to say, not that you should call with Q5o, but that if you have AA and you call all the way down, you shouldn't be surprised when you lose money overall to suckouts, because you are actually giving them correct implied odds, although the person with Q5o probably doesn't understand that. I don't know what kind of limits you play but I see that kind of thing happen all the time at 5/10c and 10/25c. If the players are good, you're right, but when you're playing with players who are not very good, but think they are, you run into a lot of people who make a poor play and then complain about the poor play of others, even though their own poor play made the other poor play a good play (if that makes any sense).

Zach, you almost make sense, but that 16:1 odds number seems fetched from thin air. Since we don't have a theoretics poker physics lab here with guys who this sort of thinking , this could be so far over my head, and then certainly over most folks heads as to need telescope. Please clarify where that number came from.

IF poker were all about the math, then computers would play it and in the end all the computers would net zip. Poker numbers are a fraction of the info one wants to make decisions.

I think somehow, this notion, the way you put it, along with my donk factor solution of 8% belong together.

It's also interesting to me personally that you picked Q5. For a long time in my early online playing, I ascribed all sorts of magic to Q5. I think what happened was that before I knew any better, I played Q5 every time and probably won 5 or 10 hands with it in a row. It is just a footnote now, but a significant one.

If your thought persists for another day or two, try clarifying it.

It obviously comes from the average temperature of the universe found by the Cosmic Microwave Background calculated at time of recombination. DUCY?

I think implied odds are very important, but people often try to justify horrible plays with weak hands through implied odds. Even most professional players don't use implied odds without marginally strong or drawing hands. You would really have to be playing an extremely deep stacked full-handed game and have a lot of information on your opponent to be calling based on implied odds with a pair of fives in that spot. Especially for the play to be profitable. You would have to put your opponent on a very small range of hands if not an exact hand.

Most importantly, and something practically no one does while computing implied odds, is you didn't factor into your calculations that the two pair could be counterfeited or an ace hits on the river which is a close percentage to the Q5 hitting its outs in the hand anyway. The AA would be roughly 18.18% to win the hand after the turn, which isn't too much worse then Q5's 22.12% on the flop, not to mention that the Q5 is only 12.12% preflop (which in my opinion is a very weak call). So, a lot of mistakes were made by the Q5.

Implied odds are important, but in the hand you explained for the play to be profitable, you would need an enormous bankroll to sustain hits and not drop down in levels. Which is definitely not possible if you play the hand like that and lose it 10x in a row, which is very probable since you are only winning it 12.12% of the time. Secondly, I don't suggest making marginally profitable plays like this in larger variance games like NLH, especially in a $1/2 game where people make so many mistakes. More ideal situations will arise than this in my opinion.

lol, I think the problem is everyone's just looking too far into it. Nothing in this thread can be applied to improve anyone's play unless of course you are accustomed to holding onto AA with deep stacks on a non-pair board regardless of action. Then you can learn why that play is a bad one.


the 16:1 number (16.72:1 in my post), comes from the fact that the pot bet is 25, and the effective pot (knowing that will call all the way if we hit. THIS is the point people seem to be misunderstanding. I'm not saying we know that, I'm saying that if AA does go all the way, they made it so the 25 chip call was correct in this particular hand) is 418. 418:1 = 16.72:1

Your point about math is a good one, but the point is that this math is dependent on AA calling off his entire stack unimproved. If this guy called his entire stack when the other guy 2-paired, we know this to be the case. Therefore, if this particular hand played out a million times, the player with Q5, despite having mid pair vs. an over pair would win money, assuming he folds unimproved on the turn. So for this particular hand, the AA vs. Q5 with the board as I said it, the call was +ev with Q5. This does not mean that you should call here with Q5, it does not mean you should call with Q5 even after seeing your opponent has AA, it means that you should call with Q5 if you are positive that first of all 2-pair will win the hand and second of all your opponent will call off his entire stack unimproved.

Read the post I just posted, that should clear up the second part of this. For the first part, all of poker is based on when the money goes in. Q5 called 25 chips with a 22.12% to win. We are assuming that AA will call off his entire stack (forget the exact amount but significantly more than 25) with 18.18% to win. Actually, I'll recalculate it including that.

With this call, he is 10.6% to hit the turn. If he wins the hand after hitting the turn, he wins 418 chips. If he loses after hitting the turn, he loses 418+25 = 443 chips. If he misses the turn he loses 25 chips.

So his expected gain? 0.894*-25 + 0.106*.1818*-443 + 0.106*8182*443 =
7.53 chip gain per hand. So although that's a far cry from my 19.3 estimate, assuming we win every time we hit, it's still a +ev play if we know the 2 hands and we know that they will call an all-in on the turn.

To re-iterate. If the approach of AA is to call all the way unimproved and the approach of the Q5 to fold the turn unimproved and push and end up getting all in on the turn if getting trips or 2-pair, and this particular hand was played out a million times, Q5 would emerge the winner. Doesn't make it a good play, but in this situation playing like that against an opponent like that is a winning play. And for AA to ridicule a call like that, when it's AA's own fault for giving the other player implied odds, putting all his money in after Q5 hits, is just plain silly.

Implied odds are important, but in the hand you explained for the play to be profitable, you would need an enormous bankroll to sustain hits and not drop down in levels. Which is definitely not possible if you play the hand like that and lose it 10x in a row, which is very probable since you are only winning it 12.12% of the time. Secondly, I don't suggest making marginally profitable plays like this in larger variance games like NLH, especially in a $1/2 game where people make so many mistakes. More ideal situations will arise than this in my opinion.[/quote]

A little quick math using your facts.

Over 30 such hands you'll bet 6 units 30 times pre-flop. Lets assume 1 of 3 you will hit something. So, 10 times you will call 25 on flop. 1 of 10 times you will improve.

(30x6)+(10x25)=430 invested.
Where are these implied odds you speak of

Please come to my table.

goldog

Did you read either of my posts at all? Just so you know my VP$IP with Q5o is 6.04 with a PFR% of 3.36%. Although I do lose overall with the hand, my net without the blinds is positive (meaning if I just folded every blind and hand I got Q5o I'd have less than now). This is over 149 times of having Q5o. I don't play that way, don't endorse playing that way, and if you believe I do you obviously didn't read what I wrote.

[x] A+ use of smileys

Zach, I'm not accusing you of anything. I see where you say you don't play this way, I'm just using your numbers to show how it simply won't work out +EV, implied odds or not. You can still play at my table but I won't expect to see Q5o

Just curious, if you don't play this way and you don't want to discuss real numbers, what is your point?

Not to yell at the donkfish? I'll yell at whoever the hell I want to.
And I don't even need to be right. In fact I'd rather be wrong!

Well, not really, NH sir.


goldog