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Jacks for Three Bets Jacks for Three Bets

06-08-2016 , 09:11 PM
Quote:
Originally Posted by OnTheRail15
You are the first person I've ever heard (who has played w Mason) describe him as anything but a massive nit. That is why he is certainly incorrect when he says that no one views him that way.
I'll probably regret this, but I'll go the other way. I kind of like dinesh's snug as the vibe he's giving off. I also think that MM plays a few hands in some spots that you'd be surprised that he had, but I'm not sure if those were adjustments or mixing up game things or just being looser than I thought overall. We only played a couple hours, so I don't really trust my reads that much.

FTR, I think you're the single most intimidating LHE player I've ever played with, and that includes tpirahna. Thus, you can adjust any credibility based on that. We sat together for a couple hours, and you could tell me my hand on every hand. Never played with anyone who hand read as well as you do.

On a more serious note, I wonder about range construction where your UTG open is so strong that a person could correctly snap fold AQo. How do you have any post flop balance for your EP hands when the only hands with a J or below are AJs and like 18-24 combos of PP? It just seems like you've already made a mistake if people are correctly folding AQo to your open or JJ to a reasonable 3 bet -- you've already played your hand face-up.
Jacks for Three Bets Quote
06-08-2016 , 09:15 PM
If you're ever cold in the Bellagio, MM could make you a sweater before the dealer change
Jacks for Three Bets Quote
06-08-2016 , 09:36 PM
Quote:
Originally Posted by Mason Malmuth
Hi Bob:
What up?
Quote:
With this opening range you're playing 8.45 percent of the hands which in my opinion is somewhat tight for the players that I play against where I assume 10 to 12 percent UTG.
Do you think that's a good default frequency? I think it's a bit loose without reads.
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AQo is 46.52 percent which in my mind puts it slightly under the borderline but if you choose to play it, it won't matter.
I think it does matter because if it's unprofitable, then I'm losing money. If it is profitable and I fold, then I'm again losing money.
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AJs is 42.16 percent which I would now not play.
Fair enough. Have you looked at likely scenarios where either a blind calls, and or a player in position calls? Seems to me that we're either getting heads up with dead money or we're going to see a multiway pot, both of which I think are profitable for AJs.
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So against this opening range I would recommend 3-betting with 99+, AKo, AQs+, but if you used 99+, AQo+, AQs+ it shouldn't make any difference, and since there are only four combinations of AJs adding them in won't matter much either unless someone wakes up with JJ.
Sorry, couldn't help it.
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There also should be a qualifier here. Because there is additional blind money, it's clear that you should 3-bet with hands which are a little under 50 percent but exactly where that cut-off should be is debatable, and many factors should come into play. So someone else may feel that going to lower percentages on your 3-betting hands is fine, and there is really no way to dispute that.
Fair. However, I think that we could agree that going lower than 40% would be unprofitable unless the opponent makes many frequent mistakes of postflop overaggression.
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Best wishes,
Mason
Thanks you too.
Jacks for Three Bets Quote
06-08-2016 , 09:51 PM
Quote:
Originally Posted by Verona
This assumes all hands show down, correct?
Hi Verona:

Yes. This assumes that all hands go to the river and then are turned up. It also means that you need to think about how difficult you think a hand is to play. So in this example of jacks in a three way pot, if you think the jacks are difficult to play you would want better than 33 percent. If you think they're easy to play, you could make due with less than 33 percent.

Best wishes,
Mason
Jacks for Three Bets Quote
06-08-2016 , 11:07 PM
Quote:
Originally Posted by Jon_locke
my UTG range depends on a lot of factors, how many drinks have I had, do I find the BB annoying and it humors me to open UTG more, how bored am I at the table and other standard factors.
So what's your point? Does this mean you're such a great player that you can play however you feel like at the moment? I doubt it.

And to give you a specific answer, and this doesn't matter what your position is, my job against a preflop raiser is to decide what his range is at that moment and then come up with an appropriate 3-bet range. So if I think you're in one of your good humor modes I should 3-bet with a wider range than if I think you're in one of your tight modes. If I'm not sure, then I'll try to error on the conservative side.

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If I found myself in a very tough game I would likely open AJo+, 88+, KQs+.
While it may surprise you when I played online FR, I played extremely tight in EP and basically played the above range (still got snap 3 bet by A-10+ daily)....
Why would I be surprised. I'm sure you want to win and also sure you'll play the way in which you think you'll win the most. That's what most everyone does and why would you be any different?

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But in a live game where I have 6 people ready to snap cold call J-10+ its gonna be very hard to convince me to fold ATo and KQo
Let's talk about this in some detail. I agree that in a game where lots of people are ready to snap call with JT+ hands like ATo and KQo will do better than folding (which has an expectation of zero) when these bad players hold a hand like you describe.

But on the other hand, when one of these players actually holds a good hand like a big pair or AK, now you'll be playing with a negative expectation instead of the zero expectation that you would get for folding. So does this balance out?

I come from a statistical background, and I often look at these situations differently from the way most poker players look at them. One thing I know, and which we have added to a couple of our books, is that when you look at statistical distributions, minimums and maximums tend to be broad. This means that you can expect approximately the same results whether you are right on the optimal number or a little bit off.

Now let's go back to the game you're describing. If you think it's correct to play ATo and KQo UTG and these are your minimal hands, your range is right where a typical player is in the games I play which is about 10 percent. Now if you choose to play a few more hands than this or a few less, it should have virtually no impact on your overall expectation. But your standard deviation should go up which may explain why your standard deviation (if I remember correctly) is so much higher than mine.

The only exception to this is if you're playing (for some reason) a very tight range. Now a small change in the number of hands played can make a difference.

The following is a short excerpt from Winning in Tough Poker Games by Grudzien and Herzog. It's not exactly the same thing as we're addressing here, but I think it's related enough that it has value:

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Opening the Pot for a Raise


Texas hold ’em is a game of balance. Often times, the correct strategy requires balancing two opposing considerations. For example, if you seem to be getting good enough odds to draw when you have flopped bottom pair, you are usually in a multi-way pot — thus increasing the probabilities that you are already up against a big hand (like top two-pair or a set), or that your hand will be vulnerable to redraws (to hands like straights and flushes). As another example, if you flop top pair in a 3-handed pot, you may want to raise to force out one player, but that same raise may let a third player three-bet. Being able to decide which option carries the best ratio of risk to reward is what makes a successful poker player.

There is also balance in pre-flop strategy. Small suited connectors — hands like: 54s, 65s, 76s, 87s — increase in value in loose games because the pot is more likely to be multi-way. However, tighter games where your opponents are more thinking and observant, tend to be played at the higher limits. Therefore, the small suited connectors have value, even if heads-up post-flop, because by playing them, you make it more difficult for your opponents to read your hand.

Because of this balance inherent in hold ’em, we recommend that when you are deciding whether to open the pot for a raise, you should follow a rote strategy based almost exclusively on your two hole cards and your position. We are basically saying that the many other factors that would change your starting hand requirements offset, simply getting you back to where you started. The largest argument against following a pre-programmed strategy is that your hand range is too well defined. This may be somewhat true for your play in the first few positions at a 10-handed table, but aside from that, your range will be wide enough and contain enough different types of hands. In other words, the hand values in a vacuum are more important, on average, than any deception value you may create. There may still be specific cases where deception is warranted, but our opinion is that players tend to overuse this as an excuse to do something they feel like doing, rather than having the discipline to stay the course and be consistent.
and

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Many would argue that you should always consider more factors, such as, how the table has been playing and your opponents’ post-flop play. However, the mood of the table is far less important in high-stakes online games where most of your opponents are playing four or more tables at one time. Also, how your opponents play post-flop is generally balanced by the looseness of the game.

For example, it may seem unnatural to open the pot for a raise with a pair of sevens if you are 5 off-the-button in a very loose game. However, in very loose games your opponents tend to play worse post-flop, so the decreased likelihood of stealing the blinds is balanced by a gain in post-flop expectation.

In other words, if you get many callers behind you, you will be in a multi-way pot with many poor players and a hand that has good implied odds. Moreover, the pot will be large. Thus, your poor playing opponents will be tied to the pot, allowing you to collect a lot of bets when you flop a big hand. This same reasoning holds for opening with a hand like queen-jack suited if you are 5 off-the-button.
By the way, for everyone else reading this thread, I strongly recommend that you get this book and start studying, the same goes for The Intelligent Poker Player by Philip Newall.

Mason
Jacks for Three Bets Quote
06-08-2016 , 11:15 PM
Quote:
Originally Posted by DougL
I'll probably regret this, but I'll go the other way. I kind of like dinesh's snug as the vibe he's giving off. I also think that MM plays a few hands in some spots that you'd be surprised that he had, but I'm not sure if those were adjustments or mixing up game things or just being looser than I thought overall. We only played a couple hours, so I don't really trust my reads that much.
Hi Doug:

As one example. In blind versus blind, I play about 90 percent of my hands when the small blind raises (and I'm in the big blind).

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FTR, I think you're the single most intimidating LHE player I've ever played with, and that includes tpirahna. Thus, you can adjust any credibility based on that. We sat together for a couple hours, and you could tell me my hand on every hand. Never played with anyone who hand read as well as you do.
Now this is just speculation on my part, but the looser you play the better you need to be at reading hands. That's how an expert can turn a normally negative expectation hand into a slightly positive one.

Also, this idea is easy to see. Suppose the only hand you played was aces. While this would not be a very good strategy, reading hands would have virtually no value.

Quote:
On a more serious note, I wonder about range construction where your UTG open is so strong that a person could correctly snap fold AQo. How do you have any post flop balance for your EP hands when the only hands with a J or below are AJs and like 18-24 combos of PP? It just seems like you've already made a mistake if people are correctly folding AQo to your open or JJ to a reasonable 3 bet -- you've already played your hand face-up.
I can say with confidence that in the games I play in this virtually never happens. But in HPFAP we do recommend to occasionally play a hand like 76s up front to guard against this.

Best wishes,
Mason
Jacks for Three Bets Quote
06-08-2016 , 11:23 PM
Quote:
Originally Posted by Bob148
What up?

Do you think that's a good default frequency? I think it's a bit loose without reads.
An 8.45 percent range UTG in a full ring game is better than what most of my opponents play, but I do play tighter in this spot.

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I think it does matter because if it's unprofitable, then I'm losing money. If it is profitable and I fold, then I'm again losing money.
This is a mistake that many non-statistician type players make. Whether the hand is profitable or not, it's going to be close to zero expectation, and folding hands with close to zero expectation will have very little impact on your long term results.

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Fair enough. Have you looked at likely scenarios where either a blind calls, and or a player in position calls? Seems to me that we're either getting heads up with dead money or we're going to see a multiway pot, both of which I think are profitable for AJs.
I've looked at lots of scenarios and it's well worth doing.

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Fair. However, I think that we could agree that going lower than 40% would be unprofitable unless the opponent makes many frequent mistakes of postflop overaggression.
I agree.

Best wishes,
Mason
Jacks for Three Bets Quote
06-08-2016 , 11:28 PM
Except that being willing to take neutral ev makes it so people wont even consider folding JJ preflop
Jacks for Three Bets Quote
06-08-2016 , 11:34 PM
Quote:
Originally Posted by ZOMG_RIGGED!
In order to take advantage of a nit perception, you have to be aware that you're perceived as a nit
Not really. You still get to take advantage of it in some ways without realizing it if you are otherwise playing well, but it would lead you to some universal conclusions about poker that are not true.
Jacks for Three Bets Quote
06-08-2016 , 11:35 PM
Quote:
Originally Posted by ZOMG_RIGGED!
Except that being willing to take neutral ev makes it so people wont even consider folding JJ preflop
Hi Zomg:

I'm just talking hypothetically here since people folding jacks preflop almost never happens. But if an opponent always plays a certain way and sometimes it's wrong to play that way, then why would you want to make sure that they always play correctly. Isn't that what you're doing?

MM
Jacks for Three Bets Quote
06-08-2016 , 11:39 PM
Quote:
Originally Posted by Mason Malmuth
But on the other hand, when one of these players actually holds a good hand like a big pair or AK, now you'll be playing with a negative expectation instead of the zero expectation that you would get for folding. So does this balance out?
wouldn't the best way to answer this just be to play a few million hands and see what happens, then extrapolate the data to softer live games.
Jacks for Three Bets Quote
06-08-2016 , 11:45 PM
Quote:
Originally Posted by Mason Malmuth

Now let's go back to the game you're describing. If you think it's correct to play ATo and KQo UTG and these are your minimal hands, your range is right where a typical player is in the games I play which is about 10 percent. Now if you choose to play a few more hands than this or a few less, it should have virtually no impact on your overall expectation. But your standard deviation should go up which may explain why your standard deviation (if I remember correctly) is so much higher than mine.
I guess this is where we disagree, as I think in lots of games AJo/ KQo can be a decent winner and I have no interest in sacrificing my $/hour to reduce my standard deviation (although to be honest I prob would if I was playing bigger). But in games I play everyday I basically just try and make the most profitable decision possible at the time and eat the swings

Last edited by Jon_locke; 06-08-2016 at 11:52 PM.
Jacks for Three Bets Quote
06-08-2016 , 11:46 PM
Quote:
Originally Posted by Mason Malmuth
But if an opponent always plays a certain way and sometimes it's wrong to play that way, then why would you want to make sure that they always play correctly. Isn't that what you're doing?

MM
Why do you take it for granted that the times its "wrong" automatically out weigh the times its "right?"
Jacks for Three Bets Quote
06-08-2016 , 11:48 PM
Quote:
Originally Posted by Jon_locke
wouldn't the best way to answer this just be to play a few million hands and see what happens, then extrapolate the data to softer live games.
Perhaps. But by the time you finish your few million hands the games can change. Second, if you think you need a few million hands to see this clearly then you're conceding that the decision is close, so why bother.

And third, relationships between hands in hold 'em are not always linear. This means that extrapolating the data to softer live action games may not be as valuable as you think (even though in this third case I don't believe this idea is very strong in this situation).

Just to see this third case, in a heads up pot I would prefer ATo over A9s. But in a large multiway pot the A9s is clearly better. If the relationship was linear the ATo would still be the better hand.

Best wishes,
Mason
Jacks for Three Bets Quote
06-08-2016 , 11:49 PM
Quote:
Originally Posted by ZOMG_RIGGED!
Why do you take it for granted that the times its "wrong" automatically out weigh the times its "right?"
I never said this.

By the way, assuming your posts are legitimate and are not designed just to troll, and you really have these questions, I strongly recommend that you read and study The Intelligent Poker Player by Philip Newall. It should change how you perceive many of these issues and my guess is that it could improve your results by a lot.

MM
Jacks for Three Bets Quote
06-08-2016 , 11:56 PM
Quote:
Originally Posted by ZOMG_RIGGED!
Why do you take it for granted that the times its "wrong" automatically out weigh the times its "right?"
He didn't say that. He said that them doing something that is wrong some of the time is better for you than if what they do is right all of the time.
Jacks for Three Bets Quote
06-08-2016 , 11:57 PM
Quote:
Originally Posted by Jon_locke
I guess this is where we disagree, as I think in lots of games AJo/ KQo can be a decent winner and I have no interest in sacrificing my $/hour to reduce my standard deviation (although to be honest I prob would if I was playing bigger). But in games I play everyday I basically just try and make the most profitable decision possible at the time and eat the swings
Assuming you're adequately bank rolled that's what you're supposed to do. I also agree that in the games you describe, playing these hands won't hurt your long term expectation. So assuming I'm right and you don't object to the swings, playing them won't hurt you. But on the chance you may be correct (instead of me) and they'll raise your long term expectation up some amount, again there is certainly nothing wrong in playing them.

Best wishes,
Mason
Jacks for Three Bets Quote
06-09-2016 , 12:00 AM
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Originally Posted by chillrob
He didn't say that. He said that them doing something that is wrong some of the time is better for you than if what they do is right all of the time.
I realize that, but this limit. You can't always force people to mistakes in multiway pots. I worded my other post poorly, but who cares if their play is "right" or "wrong" as long as my play makes me more money?
Jacks for Three Bets Quote
06-09-2016 , 12:07 AM
Quote:
Originally Posted by Mason Malmuth
Perhaps. But by the time you finish your few million hands the games can change. Second, if you think you need a few million hands to see this clearly then you're conceding that the decision is close, so why bother.

And third, relationships between hands in hold 'em are not always linear. This means that extrapolating the data to softer live action games may not be as valuable as you think (even though in this third case I don't believe this idea is very strong in this situation).

Just to see this third case, in a heads up pot I would prefer ATo over A9s. But in a large multiway pot the A9s is clearly better. If the relationship was linear the ATo would still be the better hand.

Best wishes,
Mason
I realize this, but if we were to take a given hand and then add a stupulation that people now need to cold call with hands that are dominated by our hand that they previously folded then certainly that hand will win more.

The fact that A9s is worth more than ATo is irrelevant. All that matters is Ato is worth xx bb/hand. Now when 2 players in the game cold call JTo+ its going to be worth xx bb/hand + something more.

We don't get to pick if we are dealt A9s or Ato, we only get to pick if Ato is profitable to play...then if A9s is profitable to play
Jacks for Three Bets Quote
06-09-2016 , 12:36 AM
Quote:
Originally Posted by Jon_locke
I realize this, but if we were to take a given hand and then add a stupulation that people now need to cold call with hands that are dominated by our hand that they previously folded then certainly that hand will win more.

The fact that A9s is worth more than ATo is irrelevant. All that matters is Ato is worth xx bb/hand. Now when 2 players in the game cold call JTo+ its going to be worth xx bb/hand + something more.

We don't get to pick if we are dealt A9s or Ato, we only get to pick if Ato is profitable to play...then if A9s is profitable to play
The A9s/ATo example was just to demonstrate that linearity between hold 'em hands doesn't always hold well, and thus extrapolating from a large data base from tight tough games may not be that meaningful in loose soft games. It had nothing to do with what you're talking about.

And in your example, I think you're getting hung up in how you're handling mathematical expectation. Yes you're correct that when players call your ATo with hands like JT or KQo that increases your expectation. But you also need to consider that when you play ATo and run into a big pair or an AK/AQ type hand it hurts your expectation, and you don't seem to want to consider this. And to know whether it's better to play the ATo in a game where people will call with these weaker hands you must also consider the consequences when they hold a stronger hand versus the alternative of not playing the hand at all which produces an expectation of zero.

In my opinion, as in the material I quoted from Winning in Tough Hold 'em Games, the effect should be to roughly cancel out. And if you want to take it one step further, when the opponent calls with the weak hand, the big blind is now getting terrific odds to also play and even though as the initial raiser you'll have the initiative, the call of the big blind given you're holding a hand like ATo may also reduce your expectation in many spots.

Now this doesn't necessarily mean you're wrong. But it does say to me that you can't conclude that you're right and not playing these hands in the type of game that you describe is leaving money on the table.

Mason
Jacks for Three Bets Quote
06-09-2016 , 12:47 AM
Quote:
Originally Posted by Mason Malmuth
But you also need to consider that when you play ATo and run into a big pair or an AK/AQ type hand it hurts your expectation, and you don't seem to want to consider this.
ummm, I did consider it. The other 8 players at the table will get dealt hands that dominate AJ at the same frequency regardless of how well they play. And if they are the best player in the world or the worst player they are going to play these hands versus us at the same exact rate. Example, we open AJ UTG in a tough 9 handed 200-400 game, we get run into AA just as often as we do in a incredibly soft 9 handed 20-40 game.

This is taken into account by our winrate over our last million hands. It is impossible to run into AA more often over our next million hands so we dont need to consider what better hands do to our winrate because thats the very factor the created pur winrate.

..... But when we only add in hands that we dominate, we can't help but increase our winrate......

If our winrate is already positive in games where people consistently fold hands that we dominate then our winrate can only increase when they now play the exact same range of hands that dominate us but now play hands that we dominate as well.

So for example (making these #s up) if you were to play 100k hands of 30-60 FR online and win $12 a hand with AJo, you can basically be certain that AJo will win > $12 a hand in a live 30-60 game (would actually be $15 hour if a time game)
Jacks for Three Bets Quote
06-09-2016 , 01:25 AM
Quote:
Originally Posted by Jon_locke
ummm, I did consider it. The other 8 players at the table will get dealt hands that dominate AJ at the same frequency regardless of how well they play. And if they are the best player in the world or the worst player they are going to play these hands versus us at the same exact rate. Example, we open AJ UTG in a tough 9 handed 200-400 game, we get run into AA just as often as we do in a incredibly soft 9 handed 20-40 game.

This is taken into account by our winrate over our last million hands. It is impossible to run into AA more often over our next million hands so we dont need to consider what better hands do to our winrate because thats the very factor the created pur winrate.

..... But when we only add in hands that we dominate, we can't help but increase our winrate......

If our winrate is already positive in games where people consistently fold hands that we dominate then our winrate can only increase when they now play the exact same range of hands that dominate us but now play hands that we dominate as well.

So for example (making these #s up) if you were to play 100k hands of 30-60 FR online and win $12 a hand with AJo, you can basically be certain that AJo will win > $12 a hand in a live 30-60 game (would actually be $15 hour if a time game)
I'm sorry, but the logic here is way off. And don't take this as an insult, but perhaps you should consider a basic statistics course since statistical thinking can at times be counter intuitive to many people (as we'll see below).

Let's assume with a hand like AJo you don't play it UTG in a tough game. This means in those spots where you don't play it your expectation is zero.

But now you sit in an easy game. What will your expectation be if you choose to play it UTG?

Well, keeping things simple, there are two reasons why you don't play it in a tough game. First is that your opponents won't play bad hands against you and second is that with lots of players still to act, the probability of running into a strong hand is at a maximum.

Now let's say you're in the same game but several people have passed and you have the AJo. First, since your opponents know your opening range is now wider they'll play more hands against you and this should include some hands which your AJo does well against. Second, with less players still to act, the probability of running into a strong hand has gone down. And neglecting lots of other factors, this combination should produce a positive expectation.

Now suppose you're in an easy game. Here we'll assume that some of your opponents will play weaker hands against you just as they would in the tough game where you open the pot after a number of people have passed. This is to your advantage.

But the probability of a strong hand being out against you is now at a maximum sine you're UTG and no one has yet passed. So this is to your disadvantage just as it is in the tough game when you're UTG.

Now when you look at this, clearly being UTG in the soft game with AJo is better than being UTG in a tough game. We know, and you'll agree that in the tough game your expectation is negative. But can you conclude that it's positive in the soft game?

I will certainly agree that your expectation in the soft game is higher than it is in the tough game. But you need other data to be able to conclude that it's positive in the soft game.

Now what exactly is other data? It can be detailed results from a massive data base or it can be just the experience of playing that an expert player may have. So if you want to argue that AJo in the soft game is profitable to play then this is how you do it. Not by what you have above.

There's another way to look at this. In a tough game, and let's use your $30-$60 game as an example, I think you agree that you should not play AJo UTG. That means your win rate in this spot is negative (if you choose to play it). Now it might be that your win rate in this game when dealt AJo averages $12 per hand, but it can certainly be negative in some spots and much more than $12 per hand in other places. But if you also agree that in this game it should not be played UTG, then you're saying that your UTG win rate with AJo is negative and not $12 per hand.

Now let's assume you move to an easy $30-$60 game. Should you now play the AJo UTG? Well we know that in the tough game you didn't play it in that spot because the expectation was negative, and we now know that in the easy game the expectation should be higher than before. But without other specific information, just because we know the win rate is now higher, it doesn't mean that it's positive.

Also, one slight correction. You wrote:

Quote:
Example, we open AJ UTG in a tough 9 handed 200-400 game, we get run into AA just as often as we do in a incredibly soft 9 handed 20-40 game.
You don't know this. What you do know is that you expect to run into AA just as often. This is why small sample sizes can sometimes be very misleading.

MM
Jacks for Three Bets Quote
06-09-2016 , 01:34 AM
Quote:
Originally Posted by Mason Malmuth
You don't know this. What you do know is that you expect to run into AA just as often. This is why small sample sizes can sometimes be very misleading.
I don't understand how what you are saying here is different from what JL said.
Jacks for Three Bets Quote
06-09-2016 , 01:47 AM
Quote:
Originally Posted by chillrob
I don't understand how what you are saying here is different from what JL said.
Hi chillrob:

This is a typical error that a non-statistician makes. He's saying that we'll be dealt the same number of aces for every million hands that we play. In reality, the numbers can be quite different. All we can say is that we expect to be dealt the same number of aces for each million hands that we play.

Now for purposes of the argument being made by JL this error didn't matter because I knew what he meant. But in other places it can lead to misunderstandings.

And to give a more relevant example, poker players often talk in terms of win rates, but due to something called the standard deviation, your win rate based on your results can vary a lot. For example, suppose your true win rate for some form of poker is $40 an hour. It would not be surprising, even if you play a fair number of hours, to have a win rate of $30 an hour one year and $50 an hour the next year even though your expectation was to win at $40 an hour each year.

This is also the reason why it's so difficult to come to the correct conclusion in the issue being addressed. Depending on whether you've been running good or bad, your judgement can be affected. This is another reason why a good statistician will error on the conservative side.

Best wishes,
Mason
Jacks for Three Bets Quote
06-09-2016 , 02:11 AM
let me try it this way before I take a stats course. If you play 2 million hands online, open AJo UTG for 2 million hands and win .2bb/ hand with it (made up number) you can be certain that if you open it in a softer game that you will win > .2BB/hand with it
Jacks for Three Bets Quote

      
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