Exploiting your opponents errors.

I decided to write this because I was reading something from Harrington which was based on the old idea of Sklansky bucks and it really made sense to me.
Harrington said that when two skilled players play, neither really does anything particularly special. Its not that the winner does something that the other is not capable of, but rather that the loser makes more errors than the winner.
It may seem obvious, but its meaning is slightly subtler. The winner doesn’t really make that many great decisions, rather the loser makes more bad decisions.
So that got me thinking.. where in my game can I force my opponent to make errors?

I thought about a simple drawing scenario and the results were surprising.
The simple modle is that I raise in middle position with AhJc , the button calls, the blinds fold.
I know the button plays a lot of drawing hands, he likes to play flushes and would usually have rereised with hands like AA- JJ

The flop comes Jd 6d 3c

I figure that my TPTK is good and that he will usually fold to a c-bet, if he does not then he is most likely on a flush draw.

So how do I proceed?

We all know that charging draws is a good idea… so I charge the draw.. but how much?

Well some people say ½ pot so lets charge him 1/2pot.

Preflop I raise 3BB, he calls, the blinds fold. So the pot is 7.5 BB
A half pot raise from me is 4BB giving him an 11.5 : 4 decision (about 2.9 : 1) he needs pot odds of 4:1 to call (actually 4.22 : 1) so he has made a mistake.. I am happy he is a donkey etc etc.
But how big is his mistake?
Well to justify calling 4BB, the pot needed to be about 16 BB ( this would give him his 4 : 1 odds needed )
The pot was 11.5BB and he needed 16BB to justify the call so his mistake was 4.5BB (16 – 11.5).
So calling is a mistake, it has a negative equity but its not that big of a mistake, its 4.5BB
If he folds then his EV is -3BB (the amount he has put in the pot so far)
So whilst his mistake of calling is bigger than that of folding, in real terms its not that much of a mistake. His net error is only 1.5BB more than the cost of folding


The Turn comes 2h and so I decide to charge him another ½ pot. The pot is now 15.5BB as he called preflop.

Now I bet 8BB. He is faced with a 23.5 : 8 call (2.9 : 1).

He would need a pot of 32BB to justify a call of 8BB so his error is 8.5BB (32 – 23.5). When we compare this figure to his investment in the pot so far, which is 7BB, we see that his error is again only 1.5BB.
Folding is the better option, but in reality its only marginally better than calling.

So lets go back to the flop and try a 2/3 pot bet.. lets see how much of an error that causes.

Preflop, the pot is 7.5BB and so now ill bet 6BB (2BB more than previously)
Now he is offered a 13.5 : 6 call (2.25 :1)
To call call a bet of 6BB he would need a pot of 24 to give him 4 : 1 odds. Here his mistake is 10.5. He has already invested 3BB so his net error becomes 7.5BB.
So when we bet ½ pot we paid 4bb and got a net error of 1.5BB, when we bet 2/3 pot we paid 6BB and caused a net error of 7.5BB…. that’s a lot more bang for your buck.

Lets now bet ¾ pot on the turn

Now the pot is 19.5BB (he calls 6BB for the pot of 13.5BB)
We bet 2/3 pot .. say 15BB. He is offered a 34.5 : 15 call (2.3: 1)
He needed a 60BB pot to give him his required 4 : 1 odds so his mistake is 25 .5BB!!! (60 – 34.5). He has put 9BB in the pot so his net error is 16.5BB.

So ½ pot ½ pot caused a net total error of 3BB and cost us 12BB
The ¾ pot ¾ pot caused a total net error of 24 BB and cost us 21BB

Is there a better way?

What about we bet only ½ pot and the ¾ pot on the turn?

Well from before, the half pot flop bet 4BB and causes him to make a 1.5BB net error, but it also swells the pot a little so now our ¾ pot bet will be bigger that a ¾ pot bet made on the flop.

Now on the turn the pot is 15.5BB.
He faces a ¾ pot bet of 12BB giving him a 27.5:12 call.
He needs a pot of 48 BB to justify his call so his error is 20.5BB!!! His investment in the pot so far has been 7BB, so his net error here is 13.5BB!!
His total net error is 15BB and we have spent 16BB inducing it.

Now this might seem like we get less of an error out of him than when we bet ¾ pot ¾ pot and that is true, but we have actually beaten him in a subtler way.

¾ pot ¾ pot builds a total pot on the river of 49.5 BB

½ pot ¾ pot builds a pot of 39.5 BB.

By betting a smaller amount on the flop, we aren’t really charging him much for his draw, but at the same time we are setting up a turn bet which will charge him heavily plus we are reducing the size of the total pot. Our hand is small, its TPTK.. but if he makes his, its a flush.
Not only do we charge him on the turn for his draw, but we also ensure that we don’t build a pot big enough to justify playing his hand in the first place (in essence we kick him in the nuts!!)
In fact we can take the idea a bit further.. we can actually offer him good odds on the flop, say betting 1/3 pot. (2.5BB) he gets his correct 4:1 odds so makes no mistake by calling.. but errors made on the flop are relatively small to those made on the turn. So we set him up for a big error on the turn and build a pot of 30.5BB by the river.. that’s a nice sized pot for our hand but a nasty one for his.. even if he wins, its not much to win with a flush.

So by betting 1/3 pot on the flop, we make a small error.. but in return we get to cheaply force our opponent to make a bigger error on the turn and build a pot that he wont be happy with.

Now remember back to the start of my ramblings.. the loser is the opponent who makes more errors. By adopting this kind of thinking and questioning not only what and why we do things, but also how big of an impact does it have on our opponent, we can think about coming up with better strategies to force bigger errors from our opponents.

Nice post Stu and clearly explained.

Note that before the river though he's not making as big a mistake as you think. Say he calls with the flush draw then turn goes ch/ch and he bets half pot on river with 3 diamonds on board. You really folding?

Also I don't really understand what you mean by pot big enough for the hand. If we can force him to make as big an error as we can on the flop and then a still bigger error on the turn, why not do that? If we are reasonably sure we are ahead and he is drawing it doesn't matter what a good sized pot for a typical flush or a typical TPTK hand is. Hell if he'll call with a flush draw top pair is a great hand to get all-in with.

edit: also you talk of the "cost" of inducing a mistake. Remember that his mistake includes the fact that he sometimes wins our money (the reason he needs odds), thus there is no cost associated with us inducing the mistake, unless I'm misreading or misunderstanding what you're talking about.

Yes.

Oh btw OP--

does this apply to chess too?

Well our hand is TPTK.. what if he picks up 2 pair along the way, what if we get it wrong and he is playing a set? This time he isnt drawing, but keeping the pot down prevents us routinely paying off sets whilst charging draws. I think by building a large pot with a TPTK type hand we enhance our own errors (when we make them... and we will)

Obviously betting 3/4 pot 3/4 pot causes him to make the biggest mistake.. but the trade off he gets is that when he does win, its a pot worthy of playing a flush. In effect he plays badly but gets a correct payoff. what im advocating is that by keeping the payoff small we cause him to make an error.. the error being playing us in pots which we dont build big enough to justify playing flushes against us.

Many of the times he calls with SC in position he will not hit the flop, so when he does hit a flop, by keeping the pot size down we dont give him the payoff needed to justify playing the cards in the first place.


What I got from the whole 'people loose because of the errors they make' is that we tend to view winning in a results orientated way.. we see charging draws as the entire goal. By looking at it in a different way we see that his mistakes are bigger on later streets so by allowing him to make a smaller error on the flop.. or even to make the correct decision on the flop, allows us to force him to make a bigger error on the turn whilst not over-inflating the pot.

Chess.. football.. pretty much anything where the opponents are of equal ability

Correct me if I am wrong but I took your post to be not only about inducing mistakes in your opponent but also reducing your own. By betting the manner you suggest 1/2 then 3/4 rather than the more aggressive 3/4 3/4 with a TPTK you are trying to not only extract as much value as you can, you opponents mistake, but also limit your loss when you are wrong or he makes his hand which is just as important.

Obviously the better you are or the better your read is the more aggressively you can play the hand with greater confidence of being correct.

as usual I could be completely wrong too

Yes.. this is exactly what I was trying to get at. The traditional bet bet (extract maximum value) stratagy is setting us up for a bigger error when we are wrong.

By sacrificing some of that equity we force our opponent into a situation where he is always making more errors that we do.

By giving him an easier time on the flop (an error made by us) we are able to punish him on the turn at less cost to ourselves. We also avoid tougher decisions on the river etc etc.

Great article Stu, looks like a lot of time and thought went into this. I love what you have to say here, I've recently been playing around with this type of betting a bit more.

In past if I put my opp on a draw on the flop I haven't been betting 3/4 or whole pot as much, they seem to pot commit themselves this way. I've started betting about 1/2 the pot, if they don't hit on the turn then I'm betting 3/4 - whole pot to take away odds.

If they do hit turn then I haven't invested so much that I can't get away from the hand.

Obviously the factors vary and hands do but hopefully my meaning is understood.

Sorry but our goal should be to maximize our opponents' mistakes. I think you're getting too much into the pot size for each hand. Sure it's a good starting guideline, but I think people in general are thinking too much about that and misapplying the logic. The reason we want to build different-sized pots with different hands is simply what the opponent is likely to have and likely to pay us off with. Most opponents don't stack with 2nd pair, so trying to get all our chips in with top pair no kicker is usually a losing play. This is why in general we want to bet bigger on drawy boards. There is a lot more that calls us so let him make the bigger mistake.

But the biggest logical error I think you are making is discussing what we lose when he hits. Sure what we lose when we're wrong is totally relevant to the discussion, but think for a minute what you are doing when you calculate odds. You are calculating how much he will win when he hits and lose when he misses. Then you're counting what it costs us when he hits again? The size of the pot compared to our absolute hand strength is irrelevant. We want to think about the pot size according to relative hand strength. So it is not a "mistake" when we build a big pot with TPTK and are beating our opponent's range. Sure once in a while we're wrong, but if he calls with worse enough without odds, that's how we profit. We don't profit when we build a perfectly-sized pot with TPTK or cause him to build what we arbitrarily decide is too small a pot for a flush. It simply doesn't work like that, we need to think about comparative strength. Also note though that on such a drawy board that he is likely to raise sets, therefore we can get a lot more value out of our TPTK because when he calls he almost always has worse or a draw. So as long as we don't give him odds (including implied, we can't say we've denied him good odds then pay him off when he hits) we want to induce the largest mistake period. You said it yourself in the OP, our money comes from opponent mistakes. Our money doesn't come from building perfectly-sized pots with different hands. So if we can induce a bigger mistake, not doing it is simply burning money. It's that simple.

My thoughts are above fwiw.

I should add that I am trying to put words in Stu's mouth, this is just what I took away from the post, right or wrong as I might be.

No you seem to be thinking about it in the same way that I was.

I can see why Zach advocates bet bet bet.. the equity error that our opponent makes is larger when we are correct. But we increase our own errors the times that we are wrong (and no poker player is ever 100% right).

If we are correct often then bet bet bet will cause him to make larger errors more quickly so our payoff is bigger. But at the same time, if our opponent is making these errors far more often than we are, then is there really a need to risk more chips on a single hand in order to exploit him? Surely if we can put him in a situation where just about every choice he makes is wrong, and we can do that often, then we reduce our own variance by sacrificing some equity.

As a side note, by betting big on each round, we do give him at least one correct and easy choice.. that being to fold!!!

Part of what I was trying to do was to put some figure on our chips to the size of his error. What this showed was that the only bet that was really causing him to make a large error was the 3/4 pot bet. The half pot bet gave him incorrect odds, but didnt induce much of an error. The error is also bigger on later streets as the pot is bigger, so by sacrificing a smaller error on the flop, we induced a larger error on the turn at a lower cost (chips) to ourselves. I supose you could say that it reduces varience!

This.

Are we assuming that he is only on a flushdraw here? If so we want to charge him as much as he will call. I will gladly stack A high here if I knew he is on a flush draw, the strength of the hand doesnt matter at all. Like zach said, its a good guideline but it is not being applied correctly. The whole TPTK in general not being good to stack is because it doesnt play well on most boards against good opponants to raises and reraises. You are below the range(especially the players harrington is talking about) of the nits who are playing. It does not mean you should bet less so you lose less when they hit. What happens when the flush fills it goes ch/ch then they bet on river they have KJ? Im assuming you are folding or you are not taking everything into account.

This just isnt the point I'm trying to make. If you have read it fully and take away that point, then I am sorry.. I have just written the post really badly.

See this is the thing. In the long run variance evens out. So I'd rather take the higher equity higher variance route every single time.

Well obviously if we think he'll fold to a 3/4 pot bet or w/e we shouldn't make it. We want to bet as big as we think he'll call. If he'll call a pot bet we can make that. If we think he'll fold to a pot bet only 3/4 pot or w/e we think he'll call.

Right, it decreases variance, but that's what poker's about. We could just not play poker at all and have 0 variance, but then we would have no equity. Poker's about pushing edges and taking the variance along the way. Sure there are some spots where you may want to sacrifice your tiny edge for a huge variance play, especially when taking shots, but in general we should be maximizing our equity and ignoring the variance.

I can certainly see what you are saying.

Going a bit off topic.

How do we factor in the variance of our read being completely wrong?

Say we have TPTK, the board is a flush draw board so we start charging that. At the same time we are paying into a set.

Usually variance is meant when a miracle card comes, but I suppose it can also be used when our read is off (assuming that our read is good to begin with).

So how would that be factored into the decision?

Infact, should it be factored into the decision?

if you bet 1/3 of the pot it's still a mistake for a flush draw to call. the draw is getting 4 to 1 odds and needs 4.2 to 1 odds. as i understand sklanky its known as a battle of mistakes. it's not always who makes more mistakes but how big the mistakes are can factor into it. the key to it all is to make there mistakes more costly to them. if betting 1/3 the flop on a drawing board will get them to call a bigger turn bet do it. but IMO this is wrong. as they may call the flop bet for a little mistake but fold to the turn bet as the odds are no where close to good. this big turn bet helps them to play there hand correctly and not to make a mistake. i would think betting 1/2 to 2/3 the pot on the turn would still induce them to make a mistake. and as another poster points out you got to shut down if the flush happens to come out.

Well we want to use his range, and since we're never 100% sure he has a flush draw we need to consider part of his range flush draws, part of it better than us, part of it worse than us. So yes it should be factored in.

Sorry to get into this late but I believe there is a crital error In the orginal post. please correct me if I am totally wrong. The caluation take into consideration the amount if funds in the pot. I believe this is wrong. How much does this change your error numbers?

Yes it does.

At any point the -EV of folding is the money put into the pot. There are some situations where both calling and folding are -EV plays but calling is yields a smaller -EV than folding.

If you were given two choices.. one had a LR EV of - 50 and the other - 25. Both are loosing plays but one looses less money that the other and therefore is the better choice.

The reason I compared the error to the money in the pot was to show that although calling a half pot raise was an error, it was only fractionally worse than the EV of folding. When the raise became 3/4 pot the error of calling was significantly bigger than the cost of folding.

Calling in either case is a greater error than folding, yet with 1/2 pot raises the error is very small (in the region of 1.5BB.. which is less than a standard preflop raise.)

So in this case it isnt wrong to look at the money already put in the pot, I needed something to actually compare ther error of calling with

Thanks for the response. I understand why you did the comparison the way you did. It took me several lawn mowings of thought to find that i agree with you and your methodology. Buy yourself a beer . thanks.

Um... Folding is always zero EV. Each decision you start over. You might lose money on a hand but when you are deciding what to do on a flop or whenever if you fold the EV is obviously zero. Its more of an actual value of zero, but its what we compare any EV to.

No it isn't. Folding has an - EV its just usually significantly worse than calling

Everything I have read leads me to believe that you shouldn't look at the money already invested -- it's not yours any more -- it's gone. Each decision is separate after that point. The new situation would have never come up without the original investment.

Most of the time I would agree with this. But I think that its explained this way to prevent people from calling simply because they have already invested money. So most of the time its correct to ignore the money already in the pot.

However an ev of 0 is a break even play. It simply means that the outcome will neither cost nor make any money.

So if every fold has an EV of 0, then folding the absolute nuts should be seen as a break even play.

No, folding is zero EV. If you fold you dont make or lose money. If you have the nuts and fold its zero EV. Its a terrible play since if you bet or call you have a positive EV but that doesnt make it negative.

Well I decided to do a bit of research on the topic and so typed "EV of Folding" into google.

The First hit was a CC post from a year ago!!!

Calculating the EV of folding & questions about Calling on Draws

It does seem that myself and C9 have gone through a very similar thought process at some point in time!

Part of your argument here is based on your assumption that your opponent needs 4:1 odds to call. This is incorrect. You are assuming he has two diamonds, and let's say you are right. Which two diamonds is he playing? Either high ones or connected ones, I would think. If you put these cards into PokerStove, you find that you might actually be an underdog at this point (if he holds KdQd, you are an underdog -- two overcards could beat you in addition to the flush.) About the best you could hope for is for him to have Ad low-d, which you would have dominated with your J should an ace appear on the board. Even something like 8d7d is only a 1.5:1 underdog. Therefore, you are the one making a mistake in most scenarios. Why not check now and see what comes on the turn? Then you can make a better decision at that point.

I also don't think you can say your opponent has made a mistake if he calls your pre-flop raise and then decides to give up on the hand. He has no way of knowing what will come on the flop. It is not -EV for him to fold a past decision -- only current and some future (implied odd) decisions are relevant. You could just as easily make a bad call pre-flop and a good one post-flop as the other way around.

P.S. What are you going to do if he puts you all-in with a re-raise after your flop bet?

TBH that makes no difference on a logical level. I made the assumption to simplify the numbers. If you need to be sure of this then just go back and change all of the raises such that the pot odds given are 4.22:1, Then use drawing odds of 4.22:1 .. the net error will be a little different but not so much that the asumption changes what is being shown.

I did acknowledge this in the first line.

Its just an example. It doesn't really matter so long as you stick to a convention.. rather than use drawing odds of 4.22:1 requiring me to adjust the pot odds to 4.22:1 I used some approximations on the odds required to draw (4:1) but as I was consistent throughout with this it all evens out in the end.

There are also further aproximations used on the pot sizes.. thats partly why I didnt express the final answer in terms of a ratio.. there are far too many aproximations to be 100% precise, however the mistake made by the opponent in calling the 3/4 pot raise is significantly bigger than the 1/2 pot raise. Had the valuse been similar then there would have been a need to go back and use exact numbers, but as the difference was clearly noticable ther is no real need.

I don't mean that 4:1 isn't 4.22:1. I mean the odds to call are way better than that, mostly better than 2:1, and in some cases you are the underdog, so it doesn't matter how much you bet -- your opponent can never make a mistake by calling (if he knew you had TPTK). (Remember the Fundamental Theorem of Poker that you quoted recently.)

Im not sure what you mean. The odds are about 2:1 if you can get all in or if you can guarantee that the turn will be checked, otherwise its 4:1 on each street.

Is that what you are saying?

Edit: do you mean when he has more outs say when he has a flush draw but also holds a pair. I would have thought that in that case even though he has outs to two pair, I also havethe same number of outs to two pair so they cancel out

Actualy I do see what you are saying now. I put a scenario into pokestove and im a 2:1 favourite. Why am I only 2:1? I have a board where he he holds no pair and no 1 card draw!

Well, yes, I am assuming that there are two cards to come after the flop. Isn't that the way to calculate odds? PokerStove does it this way. When I put in the AhJc and say 8d7d with a Jd6d3c board, it gives the equities as 60% for you and 40% for your opponent. That's 1.5:1, right? Now if a diamond doesn't fall on the turn, we reevaluate and the 4:1 is more correct. If I enter the same info except use KdQd for the opponent's hand, he is actually a favorite, so it would be a mistake for him to fold no matter what at this point. Maybe next street he could make a correct fold, but you'd have to bet a lot to ruin his odds. He's still only a 2:1 dog with one card to come.