Balancing Flop Caps

[PokrLikeItsProse]

[ QUOTE ]
thanks for the feedback eric.

also, thanks for correcting some points that i left unclear or stated in error. my plan for this post was to come up with a range from a game theory POV. after that i wanted to come up with adjustments to the range based on certain player tendencies(in other words how to exploit certain mistakes made by opponents and how to adjust our range in relation to this).


[/ QUOTE ]

I think we would go about this by determining our raising range and dividing that into hands we would raise with and fold to a three-bet, raise with and call a three-bet, or raise with and cap vs a three-bet. (More cases with a five bet cap.)

To do this, I think we would start by determining the game theoretical strategy for our opponent to three bet. This can be complicated because you must consider the competing strategies of capping and putting your opponent into check-call mode where you may check behind on the turn vs just calling and planning on raising on the turn where your opponent may not bet the turn or bet-fold. In fact, an answer to the questions in the original post is incomplete unless you take into account your tentative plans on future streets. If you cap with a flush draw, are you checking behind if you miss on the turn and are you checking behind with any other hands as well?

One could think of adjusting optimal strategies to player tendencies, but it may just be easier to solve for specific profiles. We could imagine an opponent who a) will only three-bet the flop with a made hand that is two pair or better or b) likes to jam draws on the flop regardless of his opponent's raising range c) plays top pair hands aggressively on the flop regardless of kicker, but may like to slowplay sets. In all of these, we would be defining out opponent's three-betting range, but it's more like solving for different strategies rather than figuring out adjustments. It amounts to the same thing, but viewing the problem thusly might make things easier to understand.

My guess is that the game theoretical capping range is going to be close to capping with all strong draws plus enough made hands to make it difficult for our opponent to bluff you on later streets. I don't think the range is going to be containing hands like AKo or 77.

[elindauer]

[ QUOTE ]
To do this, I think we would start by determining the game theoretical strategy for our opponent to three bet.

[/ QUOTE ]

You're on the right track. To figure out what our opponent 3-bets, we need to know our raising range, from which we need to know opponent's betting range...

The tricky part is that we can't know opponent's betting range until we see the EV from the counter-strategies it produces! So to really know the answer, you have to solve the entire system mathematically, all at once.

This is really hard, but fortunately you can make some arguments about what it's likely to look like. I agree with your general premise that it should contain lots of good draws, and won't contain 77 / AKo.

You can also help find these optimal strategies by noting the definition... an optimal strategy can't be exploited. It has the right mix of bluffs / value bets no matter what cards hit. etc. Any strategy that is exploitable is wrong, so you adjust it to elliminate that and you are moving toward the optimal strategy.

One of these days I'm going to have to put together a tool for calculating the true optimal strategy...

-Eric

[James.]

Here's my range in regards to a situation when the action primarily involves a raise pf. Also, assume we have position. I'll discuss my adjustments for the other factors later(being OOP, an unraised pot, etc.)

BB bets, I raise, SB folds and BB 3bets. Here’s my range in that situation(on this board):

33(2)
99(2)
TT(2)
9T(9)
AA(3 combos b/c1/2 the time I wait for the turn)
KK(3 combos b/c 1/2 the time I wait for the turn)
QQ(1 combo b/c 2/3 the time I wait for the turn)
JJ(1 combo b/c 2/3 the time I wait for the turn)
QsJs, QhJh(2)
KsQs, KhQh(2)
AhKh(1)
AhQh(1)
Asxs(10)
7s8s(1)
7h8h(1)
KsJs(1)

Made Hands
23
Drawing Hands
19

Notice how close the drawing hands are to the made hands(combo wise). For balance and deception purposes I tend to try to keep this number sort of close.

You might notice that I’m not capping some 78 and QJ hands. It’s because I wait for the turn to semibluff these 4 combinations.

I’m going off on a tangent here, but let me explain why I don’t cap the flop with these hands and why I wait for the turn with some other pair hands(noted above). First, notice I’ve done some combination discounting because there are a certain % of one pair hands I wait for the turn to raise. It’s a semi-common strategy I employ and I have a couple reasons for doing this.

Most commonly, it’s on very drawy boards(particularly in HU pots). I don’t do it solely in an effort to gain value, as usually the best way to build a pot is jam the flop(although charging the draws an extra sb certainly plays a bit of a factor).

I wait more often with some hands whose equity might change the when the turn comes good or bad(referring to primarily QQ and JJ in this instance). This is particularly the case when a draw or weakish top pair hand is a very significant portion of my opponent’s range. There is a reason for this and I’ll get back to it in a minute. Of course, if I only waited with fairly vulnerable hands it would be easy to counter strategically so I mix in AA and KK as well(to account for these I’ve taken the simplistic approach and discounted according to the frequency: wait for the turn with AA ½ the time so (.5*6combos)). The primary reason, however, for waiting for the turn is to increase the effectiveness/balance of my turn semibluff raises. If I only waited for the turn with made hands, this could be easily countered(exploited) by simply bet/folding the made hands that don’t fair well against my range of made holdings.

So there’s 16 combinations of made hands I raise on the turn, and to balance this I semibluff raise the turn a portion of the time. I often use the average pot size as the primary function in determining what combinations of drawing hands I will wait and raise on the turn(feel free to jump in if you don’t think this is correct). According to my OP there should be about 6sb in the pot on the flop. After 3 bets go in two ways on the flop that makes it 6bb+1bb(villain’s turn lead) for a total of 7bb in the pot. When I raise it makes the pot 9bb and it indicates to my opponent that he will need to put in 2 more bb to call me down. This gives him effectively 4.5-1. My goal is to semibluff about once in 5 times so he’s just short of the price he would need on a calldown. So this means about 20% of the range of hands I might wait for the turn will be semibluffs. This is effectively 4 combos added to the 16 combos of made hands raising the turn. This is where those omitted combinations(7d8d, 7c8c, QcJc, QdJd) come in to play. It’s 4 combos that should be about right for the range as I’ve tried to show above.

I apologize it’s taken me so long to respond to this post. I also apologize my response was so longwinded. I wanted to get as much conversation going as possible prior to giving my range. Now maybe elindauer can come in and blow it up showing me where I’m completely wrong. [img]/images/graemlins/tongue.gif[/img]

[elindauer]

Good stuff James.

[ QUOTE ]
Now maybe elindauer can come in and blow it up showing me where I’m completely wrong.

[/ QUOTE ]

I think your range is a significant improvement on my initial attempt. The biggest thing you are doing is to consider how your capping range effects your calling range. My first shot left the calling range far too weak. That's a HUGE improvement. I think your handling of overpairs is great. Saving some draws / made hands for turn raises / semibluffs is very strong. I really like your logic for choosing which hands go in which range... you mix concepts like waiting with cards whose value changes a lot on the turn with game theory concepts like avoiding being exploited very nicely. This is exactly the kind of thinking that leads players from good to great, I think.


You are making a few small mistakes though. Here are the ones I notice.

[ QUOTE ]
QQ(1 combo b/c 2/3 the time I wait for the turn)

[/ QUOTE ]

QQ has 6 combinations. 1/3 of 6 = 2.

[ QUOTE ]
I often use the average pot size as the primary function in determining what combinations of drawing hands I will wait and raise on the turn(feel free to jump in if you don’t think this is correct).

[/ QUOTE ]

This is totally correct. Pot size is critical in determining how you play your range.

[ QUOTE ]
When I raise it makes the pot 9bb and it indicates to my opponent that he will need to put in 2 more bb to call me down. This gives him effectively 4.5-1.

[/ QUOTE ]

This isn't quite right. As stated in other posts, your turn raise doesn't obligate you to bet the river. In fact, if you know he's thinking about calling the turn only if he can call the river, you'd be a fool to follow through with a river bet with your entire range. You'd have to bet less. But then his turn calling range would be wrong. But then you'd bluff more. Back and forth.

The right answer is, I think, to think of each street a bit more in isolation. So focus on him getting 9:1 to call the turn, and semi-bluff accordingly. Note though that your bluffing hands have excellent equity, and take that into account. For example, if your bluffing range has 20% equity, then:

made + .2*draw : .8*draw should offer him 9:1 (where made = # of made combos you raise, and draw = # of draw combos you semibluff raise).

Rearranging...

draw = made / 7

in a pot this size. So your raising range actually encourages him to call a bit more than the optimal strategy would suggest, not a bit less (I think).

[ QUOTE ]
I apologize it’s taken me so long to respond to this post. I also apologize my response was so longwinded.

[/ QUOTE ]

There's no other way it could be. We're in the very early stages of understanding this logic, so we have to discuss both the process and the results at the same time. It'll get faster with practice.

good luck.
Eric

[One Outer]

I keep thinking if I read this enough times I'll understand it. I'm silly.

[James.]

[ QUOTE ]
You are making a few small mistakes though. Here are the ones I notice.

[ QUOTE ]
QQ(1 combo b/c 2/3 the time I wait for the turn)

[/ QUOTE ]

QQ has 6 combinations. 1/3 of 6 = 2.

[/ QUOTE ]

doh. sorry. i'm at work and get distracted multiple times in making a post that long. i apologize for the oversight.

[ QUOTE ]
[ QUOTE ]
When I raise it makes the pot 9bb and it indicates to my opponent that he will need to put in 2 more bb to call me down. This gives him effectively 4.5-1.

[/ QUOTE ]

This isn't quite right. As stated in other posts, your turn raise doesn't obligate you to bet the river.

[/ QUOTE ]

thanks again, eric. i don't know if this matters, but when i'm giving these odds what i'm saying is that(when put to the decision on the turn) my opponent must infer that he will be forced to call a bet on the river; not that i actually will(or intend to) bet the river.

sort of like in NL, when you make a big pot sized or 2/3 pot sized bet on the flop or turn you are in effect telling your opponent, "get ready to stack off" if he calls your intitial bet.

[One Outer]

[ QUOTE ]
thanks again, eric. i don't know if this matters, but when i'm giving these odds what i'm saying is that(when put to the decision on the turn) my opponent must infer that he will be forced to call a bet on the river; not that i actually will(or intend to) bet the river.

sort of like in NL, when you make a big pot sized or 2/3 pot sized bet on the flop or turn you are in effect telling your opponent, "get ready to stack off" if he calls your intitial bet.

[/ QUOTE ]

I agree with this. If aren't we exploiting our opponents by taking the free showdown sometimes?

[elindauer]

[ QUOTE ]
thanks again, eric. i don't know if this matters, but when i'm giving these odds what i'm saying is that(when put to the decision on the turn) my opponent must infer that he will be forced to call a bet on the river; not that i actually will(or intend to) bet the river.

sort of like in NL, when you make a big pot sized or 2/3 pot sized bet on the flop or turn you are in effect telling your opponent, "get ready to stack off" if he calls your intitial bet.

[/ QUOTE ]

Totally understand this, and it's a very important concept for play in practice. You're opponent may very well think like this.

However, when considering what the game theory perfect play of your range is, you begin with the assumption that your oppnonent knows what you are doing and will play his hand perfectly against you. In this context, it's incorrect to say that the calldown ratio is important. So I'm trying to show what odds you really should be using to mix in bluffs, and that is, I think, the true odds your opponent is receiving immediately.

It might seem like hair-splitting, but I don't think so. It's a common flaw in limit holdem players to make calldown-all-the-way-or-not decisions, which can be exploited by bluffing early and giving up later in the hand. I think this is a hole that prevents lots of TAGs from moving up. So elliminating this hole in our understanding of game theory and seeing the effect it has on the default range can be important in helping us understand how we should deal with tough players in spots like these.

-eric

[elindauer]

[ QUOTE ]
I agree with this. If aren't we exploiting our opponents by taking the free showdown sometimes?

[/ QUOTE ]

I don't understand your question. Rephrase?

I think the answer though, is that if your opponent only calls with made hands that can stand to call the river also, then he is folding too much. You exploit this mistake by bluffing more on the turn and then giving up if called. He counters that by calling more and bluffing the river. You counter by giving up less. Back and forth. This back and forth is the defition of an imperfect solution.

-eric

[elindauer]

[ QUOTE ]
I keep thinking if I read this enough times I'll understand it. I'm silly.

[/ QUOTE ]

I'm sorry I'm not a good enough teacher to make it clear. I'll keep trying. Stick with it.

-eric