I've noticed a few threads on Straddling (especially in the LLSNL forums). A lot of the advice and debate is ancedotal or based on experience however, there wasn't a lot in the way of solid Math or Theory.

I wanted to change all that with a thread that put some solid math and theory behind straddling. I encourage all you theorists and math gods to add your own scenarios and calculations to the thread.

Here is the scenario/question that was brought up in LLSNL.

---There was a player who would straddle every hand and then squeeze. Is straddling, what are the conditions in which this strategy is profitable?

Here was the scenario I programmed to start tackling this question. As the thread progresses I will incorporate more complicated models.

MODEL A):

Hero will straddle and then squeeze in an attempt to just fold everyone out and take down the pot. The table will only call with a certain predefined range.

To simplify the math, we will assume that Hero loses 100% of the time if he is called and that villains will fold 100% of the time unless they have a hand that corresponds to our predefined range.

Here are the variables I intend to model

A) # of limpers
B) Size of Hero's Squeeze (his raise)
C) limp/raise calling range of Villains


Again, if you have a scenario you'd like to model or have done some math on this feel free to throw it in this thread. Also, any theory, debate, etc on the subject is likewise encourage but the focus of this thread is to quantify our arguments as much as possible.

Model A)

For this first run, I am assuming that the table is very weak tight but limp passive. I'm assuming that the table will limp with a fairly wide range however will ONLY call Hero's squeeze if they have a top ten hand. AJs, AQ, AK, JJ-AA, KQs.

Hero will start off squeezing fairly light and then progressively increase his squeeze amount. This is where some subjectivity comes in if you were to apply the results here. You would have to figure out the threshold where the table would call a raise in relation to the size of the pot. For example, if there's a straddle (2bb) and 5 players limp, pot is 12bb and Hero 3bets to 6bb, is the table really going to fold getting 4.2:1 on their money?

IN the model, each line represents a different squeeze amount. Hero starts squeezing at 8bb, then 14bb, etc. and each squeeze is run through the computer model to generate the graph. Each trail was run 5,000 times. Y-axis is in big blinds, X-axis is # of trials/hands. Positive slope is good and +EV, Negative slope is bad and -EV

In the model, each villain has a 4% chance of being dealt a top ten hand (Odds of being dealt a hand found at http://www.rivered.co.uk/poker_percentages.html ).

VARIABLES
Villains limp/3bet calling range: Top Ten hands: AJs, AQ, AK, JJ-AA, KQs.
Hero Squeeze: 8bb - 32bb
Limpers: 4 - 6

Model B)

In this model I widen the 3bet calling ranges of all the villains to: AJ-AK, KQ, TT-AA. Adding TT, AJo, KQo makes a pretty profound difference. Of course, the 100% win/lose assumptions are still in effect, even though this is a simplification, the data and trends should be representative enough to determine whether the resultant play is +EV, 0EV, or -EV

VARIABLES
Villains limp/3bet calling range: Top 7% of hands: AJ-AK, KQ, TT-AA
Hero Squeeze: 8bb - 32bb
Limpers: 4 - 6







RESULTS/CONCLUSIONS

Initial results are that straddling UTG and then stealing with a squeeze is profitable at extremely weak tight nitty tables where villains need to have a top ten hand to call your 3-bet. However, if villains are willing to just widen their calling range to include AJo, TT, and KQo it quickly becomes unprofitable.

Next models will be a little more involved to include more accurate use of equity (getting away from the 100% simplifications) and including some more preflop and postflop conditions. I will also have to set some better initial conditions like stack sizes

I fall into the catagory of expericne and opinion, and don't have the math & theory aspect of straddling....so I'll be watching this thread hoping to learn something new.

One consequence you should run into is where villains call with entire range, your bet size does not matter for your model and you run break even. Multiple streets out of position against multiple opponents may make this harder down the line as you develop your model. In that case, assuming villains call with their entire range on the flop, you should start to dip into -EV by betting less assuming villains only call when hitting a piece of the flop. If villains continue to call everything and not bet or raise on every street, then the seemingly ideal strategy would be limp-check-check-shove value hands. Will be interesting to see what you come up with.

At a 1/2 game, you can probably exploit most opponents by raising more with your value hands when you squeeze and raising less with your weaker hands. At least in your model, this will lead to better results.

UTG straddle = big blind. So if it works in the straddle than it should work in the big blind. Why not just make a thread about big blinds? If you start habitually squeezing from the big blind people will start playing all their pre flop raising hands as limp raises treating your squeeze play as a super big blind. Not saying there is not the occasional game where it might be +EV the first time you do it, but after you have done it two or three times in a row even the dumbest players are likely to adjust somehow. It only takes one or two players with half a clue for your maths to fall down.

What I find much more interesting is button straddles which have a much better chance of being +EV every time.

Good:
You double the game size when you have the best position.
You double the game size when you are the best player in the game. (Assume true for everyone reading this thread?)
The higher game level might put some players off their game.
You gain two positions pre flop. Which could be big if the blinds are particularly aggressive.
In passive games it is fairly close to neutral EV to limp with any two on the button.
People are likely to think you are looser than you actually are.

Bad:
You force yourself to at least call with any hand some of which are likely -EV.
If someone raises you are likely to just loose your straddle.
The amount of dead money form the small and big blind is half what it would normally be.
People are likely to think you are as loose as you actually are.

Need to put some numbers on the above and get a clear picture of when button straddling is good.

Unfortunately, most places don't allow a button straddle

At least the places I play at don't allow button straddles. Anyways, one math problem at a time

Okay boys and girls, I've updated my models making them a little more complicated and truer to life and am incorporating Hero's equity vs Villain's equity if called

Hero will straddle UTG and then when the action gets back to him, Hero will shove with ATC. For the purposes of the model, Hero is considered short stacked so we don't get into your awesome post flop skills and plays which would be impossible to model.

For this round of modeling Villains will call if and only if they have AT-AK, KQ, TT-AA and they will fold all other hands. Each villain has a "chance" of being dealt the above hand so hero will face anywhere from 0 to 6 villains per squeeze at a 9 handed table.

The model steps through various squeeze amounts. Obviously, villains aren't likely to fold for 10bb if there are 6 villains limping, however, the math doesn't change as far as profitability is concerned. However, what you can do is use your "intuition" to pick the bet sizing that you would squeeze based on the situation and then match that up to the model and see where it falls EV wise.

All bets are made in terms of big blinds. I used Poker Stove to determine Hero equity in the event of 1-6 callers. As this thread progresses I will "widen" the calling ranges of Villains and show the results









CONCLUSIONS:
If we are at a weak-tight table in which villains will only call our shoves with AT-AK, KQ, TT-AA, and we are short stacked, its profitable to shove fairly wide if we can isolate a lot of dead money. So we need 4, 5, and 6 limpers for routine squeezes to be profitable. The more limpers the better obviously. Similarly, we want to squeeze the "least" amount possible that will generate fold equity. We don't want to squeeze 50bb in situations in which 25bb would generate the same FE.

For the next rounds of modeling I'll tighten up Hero's range as well as widening our Villains ranges.

EDIT: doesn't "only" apply if we are short stacked, i'm just unable to model post flop play. So if you are 100bb you can still use these results as a baseline and structure to work around and then just incorporate your post flop game...

One reason to straddle is table image, when people see you do it your image will be less serious. People will now be willing to play more pots with you. You can straddle for 4bbs then you are not risking much. It's +EV for me I think because sometimes I get an image of a rock if I'm too card dead.

One fear many players have when trying to steal/squeeze is getting called by "wild" players who will "call with anything".

So, I decided to create a model to see how this plays out and I was surprised!!!

Here is the situation.

HERO
Hero has tightened up his range and instead of squeezing with ATC, he is now squeezing with 66-AA, and Broadway cards JT-AK (range is 16.6%)

VILLAINS
-SIX Villains are strict ABC players who will only call a squeeze with TT-AA, AT-AK (range is 7%)
-TWO Villains are super gambooolers who love the thrill of big pots and will call a squeeze with 54s+, 64s+, 98o+, Ax, Kxs, 22+ (range is 40%)

MODEL ASSUMPTIONS (same as post #8):
Hero will squeeze and if called, equity applies. The model will step through a series of bets, for the purpose of modeling, each bet/squeeze can be considered an all-in. Unfortunately, modeling postflop play would be near impossible so the equity is a straight evaluation preflop. Despite this limitation, the model should be fairly accurate in terms of determining +EV trends. Lastly, in terms of squeezing, you can use your intuition to match what you would "squeeze" in a certain situation and then match that up to the model...

Lastly, a "straddle" is when the UTG player (Hero) bets 2bb in the dark and gets last action. So 5 limpers means pot is 12bb by the time it gets back to Hero and Hero squeezes...

Below are the models based on the above assumptions









CONCLUSIONS:
In a word, WOW!!! When I first saw the results I almost didn't believe it and I completely tore my model apart and put it back together and empirically stepped through the simulations but they held up. But then once I really stepped back and thought about it, it makes sense. If we are shoving with a semi-decent range and we got two gambooolers willing to get it in with a much wider range, then we should be ahead. Similarly, when we are up against "solid" ABC players who are only calling a squeeze with AT-AK, TT+ this means that they end up folding 80% of the time. Thus, Majority of the time we are either stealing the limps or being heads up against players whose ranges we crush.

Interesting but IRL the fact is straddling UTG in anything that is not a fishy game, is going to be -EV and if is done will be fore meta mostly...

Contrary to what OP says the button straddle is becoming more widespread in casinos around the world and is obviously a much more interesting proposition to study in this thread, and i think a mathematical study of it could very interesting and a potentially important edge.

I appreciate the comments but I want this thread to be more than just opinion. Is there any way to put some math/theory behind this statement?

The math for this theoritical exercise APPLIES to any straddled pot from any position. I'm merely just stating that in this case Hero is the straddler.

If Hero is on the BTN and UTG straddled and there are 4 limpers prior to action getting to Hero, then the 4 limper models would apply to Hero at the time he makes his decision...

In essence, at this point, this thread is really about Squeezing moreso than about "straddling". Its just that the "squeezing" aspect is fairly easy to model.

I would always straddle if everyone agreed to also straddle. Huge edge cuz most players never raise the option. Also, if you balance your squeeze range, it should be prof regardless of number of limpers. Just adjust to their ranges and be sure they are not privy to yours.

Again, I appreciate your opinions, but can you provide any math or theory or deductions for why the above would translate into profit???

DGI, not sure what you are actually trying to show here.

This is not really showing anything about the profitability of straddling or not, only some maths about the profitability or otherwise of plays when it is limped to you in the straddle, which as others have pointed out should be the same from the big blind.

Even given the scenario is so unrealistic as to be fairly useless IMO (I know this is poker theory so I have no problem with that, just wondering if you believe the results to have any practical use.) there seems to be one huge flaw in your process. You never mention a limping range. If it is 100% then I don't see why you need a simulation to tell you that if people are limping super wide and calling raises super tight it will be profitable to raise ATC. If they are not limping 100% then that will affect their calling frequency. Obv if somebody calling a raise with 3% of total hands but only limps with 4% he's calling 75% of the time.

I admit that so far, this model is really about "squeezing" moreso than Straddling, but this aspect is the first step.

Second, I disagree with it being useless. Whenever I'm playing, Someone ALWAYS straddles and the MOST COMMON situation that occurs is that someone straddles and the entire table limps.

So, in my mind this seemed the first step in modeling "Straddles". Since I ROUTINELY squeeze straddled pots with a pretty wide range and find my squeezing to be profitable, I also had an interest in modeling the squeeze aspect of straddles first.

I guess the question I have for you is simple?

How often do you squeeze straddled pots?

The reason imo that "straddled" pots are different is because villains are likely to INCREASE their limp range because straddled pots illicit more action and fun. Fish love straddled pots and they all want to limp and get a piece of it. Thus, this situation is DIFFERENT than the normal pots.

So basically, I think this is far from useless.

Similarly, if something I said above is wrong, I'm all ears.

So you are giving the limpers 100% range?

I appreciate the need to simplify problems but in this case I find the over simplification so great that the model can't tell you anything that logic wouldn't.

IE wide limping ranges and tight calling ranges make stealing profitable.

Sorry if that sounds over critical, that's not my intention. I realize you are trying to take this further and that you need to "walk before you run" so to speak. I was just surprised by your surprise at the results.

For me it's enough to know that straddle is not profitable.
Every decent poker player loses money only in BB and SB. Adding UTG as another losing spot is a very bad idea.
Regarding the math... just multiply ~2 times the loses from BB .

Yes and no.

Of course it would be profitable, but what my models do is they identify the exact conditions from where it goes from profitable to unprofitable and that is something deductive logic cannot do.

Similarly, if you aren't surprised by my latest round of results then I don't know what to say, you are a genius. Those results say that if you are at a table with TWO wild players that the EV in squeezing 10bb is the same as squeezing 50bb. To me, at least, that is pretty surprising looking at those curves overlap like they did to the point of being almost identical.

Did you look at the last batch of results, I noticed you quoted one of my earlier models. Similarly, I intend to play around with Hero's ranges and table conditions. And again, yes, I have an intuitive feel for whether something is profitable or not. However, that intuitive feel can't tell me HOW profitable or what conditions result in the MOST profit.

So basically, I'm trying to quantify all those things that intuitive logic would deduce. And i'm sure before this is over I will uncover some more suprises.

No, its not so simple. UTG straddle cuts all effective stacks involved by half. So if the table is 100bb, if you straddle, you cut eff stacks to 50bb. Similarly, players are more likely to widen their limping range with a straddle than a normal pot. Then factor in that there are a certain breed of players that love squeezing straddles (I haven't modeled this yet but plan to) and then adjusting to squeezes in a straddled pot or anticipating a squeeze and limping with strong hands...

Basically, if you regard straddles as "nothing special" then you are wrong. THey alter the table dynamics and cut effective stacks in half.

Any bet lowers effective stacks, that doesn't make random blind bets profitable. The only way straddling can be profitable is if a) it's constantly profitably for you to squeeze ATC from the BB b) people respond to straddles in weird, inconsistent ways.

What are the limping ranges?

RIght now, the limping ranges are irrelevant, so you can think of them as 100%.

The reason they are irrelevant is because the limp range has no correlation with the squeeze calling range. If there was a correlation between a limp range and a squeeze calling range, then the limp range would matter.

Another reason is that when you model something you have to isolate a variable, something has to be the "independant variable".

In future models, I can give limpers a range and then give them a squeeze calling range but in those models I would then have to "fix" the bet sizing for the model to be at all meaningful.

But so far, I'm fine fixing/isolating the number of limpers and then altering all the other "stuff" to see how everything impacts everything else.

Let me reverse your question.

Why would the limp range matter for the purposes of modeling the impact of squeezes???

Well, after the end of this thread, hopefully there will be more math to support or refute your assumptions one way or the other.

Similarly, I'd also hope to gain some new insights into the various situations straddled pots present (i.e. like squeezes) and then incorporate those learnings into my game.

I'm not trying to say Straddling is +EV, I'm just trying to model all the dynamics that take place in Straddled pots and identify the various +EV and -EV lines and their potential consequences/opportunities

Of course the limp range matters. You are calculating fold equity based on how often the limpers call. This is one of the reasons it is so unrealistic.

If villain is calling a "squeeze" with TT+ AQ+ (or whatever assumption you make) then your fold equity is a direct result of his limping range.

If he only limps 88+ AJ+ then you have virtually 0 FE. This is one of the reasons your results seem to indicate you can raise so profitably when in real life this is never the case.