# Beyond ranges

Before going beyond ranges, let me first give a quick review of what range theory is.

According to range theory, a player in a given position will have a given range. A range refers to the possible combinations of two hole cards they can have. A card combination is either in the range, i.e. consistent with past action, or it is not. When faced with a decision, some (or possibly none) of the combinations will fold, some will check/call some will bet/raise, and some will shove. All the combinations that bet/raise will do so with the exact same amount to obscure intentions.

This is the standard theory that almost all poker players follow.

However there has been no hard proof that this is the best way to play the game. In fact recent findings from AI research seems to indicate that it is not the best way to play.

What we can say in itâ€™s defense is that playing based on ranges is a really solid and strong way to play. And it has the advantage that it is easier to learn and reason about.

So if range theory is wrong, what is right? The correct way to play seems to be more deceptive in a way. Instead of always playing the same situation the same way, you should play it differently different times, so the theory goes. As an example a given hand preflop may bet for value most of the time, but then occasionally limp to sneak up on the unwary.

Further, because of the increased deception that comes from playing differently different times another possibility is enabled. Betting different amounts with different holdings. Betting big with big hands and small with small hands is normally a surefire way to tip the other players off to what you are up to. But if you bet big 60% of the time and small 40% of the time itâ€™s not as predictable anymore.

Another consequence of using some randomness in how you play is that a given play is not â€ścorrectâ€ť or â€śincorrectâ€ť by itself. Well it can be incorrect if itâ€™s really stupid. But more often a given play will rather be on the scale â€śdo this rarelyâ€ť vs â€śdo this a lotâ€ť. This is of course very dangerous for human psychology, as any play can be rationalized, and rationalization is a big bankroll killer.

@bluffmasta, your post doesnâ€™t refute â€śrange theoryâ€ť at all. More modern range theory incorporates playing employing a mixed strategy with certain hands in the range - generally when EV is close between two given actions. For example, in a certain spot with QhJh, if EV is +35 with a full-pot bet and +38 with a quarter-pot bet, with an EV of +8 on a check, a mixed strategy might employ betting full-pot 40% of the time and betting a quarter of the pot the remaining 60% of the time, utilizing a randomizer to select between the two. However, if the optimal range always bets full-pot with KhQh in that same spot, then on later streets KhQh will show up more often in the playerâ€™s range than QhJh.

We shouldnâ€™t disregard the value of ranges. Most actions with most holdings will still be incorrect. Understanding what hands could end up in a particular spot by studying the ranges that will take those lines is necessary for balance and gaining edges on competitors.

Well technically we should only randomize if the EV is exactly the same. It just turns out to be exactly the same a lot.

Range theory is just another tool,
it can be used and used against youâ€¦

In the end Poker comes doesnâ€™t come down
to any 1 thing. Math, theory, psychology, storytelling,
pressure, and Iâ€™m sure a few more things. Poker is
the symphony of all these things, along with being
very situational. In the wrong posistion, the same play
will be wrong alot of the time.

Sassy

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Wrong on a few fronts:

• The EV of two actions will rarely be exactly the same.

• Even if two actions with the same hand might have similar EV, that particular hand might be more valuable balancing out the full range for one action or the other, so a solver might lean in that direction a bit more heavily. Bluffing is a good example - taking a line that might be less EV-positive, or even EV-negative in isolation, for an individual holding may make the entire betting range more EV-positive by increasing the likelihood youâ€™ll get called with the value portion of your betting range.

As an aside, itâ€™s possible to randomize a decision between two actions with a ratio other than 50-50. Letâ€™s say I think I should call preflop in a certain spot 75% of the time, and 3-bet the other 25%. If I look at the second hand on my watch and itâ€™s reading more than 15 seconds into the minute, Iâ€™ll call; if itâ€™s less than 15 seconds into the minute, Iâ€™ll 3-bet. Boom, instant randomizer with a not-necessarily-equivalent distribution between two options.

In the end, poker comes down to math. Everything else is mere justification for not understanding the math.

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No â€“ it comes down to mathâ€¦ and lies.

A watch with a second hand? WTH year is this?

Way more common than one might think. Any time youâ€™re using a mixed strategy between two lines against an optimal player then the EV of those lines must by definition be the same - otherwise you would always take the higher EV line.

Then how do you explain bluffs? Why choose the weakest hands in your river range to bluff? Surely looking at those individual holdings the EV of that decision is negative, and a check would be better! However, because youâ€™ll also have extremely strong value hands in your betting range, you need to balance the range with those weak holdings. The higher EV of your value hands more than compensates for the loss of EV of your bluffs.

The mixed strategy comes into play when the holdings are marginal. In other words, including an individual holding in one range or another creates very little change in EV to either range/line. It wonâ€™t often be the case that the EV of that action, for that holding will be the same for both actions.

We bluff to get chips from folds (and the occasional lucky win). Not to make other holdings more profitable.

Well that is the game theoretical point of view anyway. In exploitative play, a sacrifice bluff can be correct.

EDIT: Yes we should be balanced, but not by doing suboptimal EV moves.

If betting your weakest hand is the most +EV action you can take with that particular hand because you can get folds, then it would be the most profitable line to take with all your holdings, because your other holdings would also get value when called. However, itâ€™s rare that youâ€™ll want to bet the river with your ENTIRE range. So why bet only with your weakest hands as bluffs, and your stronger hands for value? Why ever have a check/call range?

Thatâ€™s a pretty key edit. The point is to optimize EV of your entire range, even if it will result in a less-than-optimal EV for an individual holding within the range.

Thatâ€™s not what Iâ€™m saying at all. We should always go for optimal EV for any individual holding. It just so happens that doing that leads to balance.

In a river situation, letâ€™s assume that weâ€™re betting a polarized range where we have the nuts or nothing. If youâ€™re playing a balanced strategy and so is your opponent, then the EV of the bluff part of your range is going to be exactly 0. Against a balanced opponent they are calling just enough to stop our bluffs being profitable, but as a consequence they are also having to pay us off when we have a value hand.

0 is also the EV of checking back with a hand with no showdown value of course.

The reason we choose to bluff hands with no showdown value is because if we check back a hand with some showdown value we will win the pot some of the time - so the EV of checking back with a hand with some showdown value is greater than 0.

If this was to be true, then on coinflips, everytime you hit an even number youâ€™d also get a perfect distributionâ€¦ 1/2 , 2/4, 10/20, 100/200, ect ect ect. Since this never occurs, then â€śâ€śThe Mathâ€ťâ€ť is yet another guideline, not a factâ€¦ because the math or Odds are 50/50.

If on the other hand, you mean math as in odds, ev, ect ect ectâ€¦ bacisally all the math in everything that uses math, then since there is crossover here there kinda is only â€śmath in xxxxxxâ€ť and â€śmath in yyyyyâ€ť ect ect ect.

Since there is potential to learn something, please explain how you define â€śMathâ€ť WannabeCoder cause Iâ€™ve taken up thru Calculus, and have a solution to PvNP.
Sassy

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lmao

Check the year hand on the watch, it should tell you.

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It seems wrong that my bluffâ€™s EVs should be zero. If I bet the pot with a given bluff, my opponent will need to call with the same frequency he folds in order for me to have an EV of zero. However, heâ€™ll be paying the size of the original pot in order to potentially gain double that, so shouldnâ€™t he call twice as often as he folds?

Similar for a half-pot bet: for me to have an EV of zero, I need V to call twice as often as he folds, but heâ€™s getting 3:1 on a call, so Iâ€™d think he should call 3x as often as he folds here.

However, we make up for that slight negative EV with our bluffs by offsetting it with more-positive EV with our value hands. Overall, the EV of the betting range (probability of having a given holding times the EV of that holding, summed over all holdings in the range) should come to the size of the pot.

If thereâ€™s something about this Iâ€™m misunderstanding, Iâ€™m open to learning more! Can someone with a stronger grasp of the theory chime in?

Also, Iâ€™d think that sizing your bluff bets in order to balance your EV with an individual holding to net it to zero would create differences in bet sizing between different hands in your range, thus creating tells which can then be exploited. Right?

Edit: My math was not right here so retracting thisâ€¦

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