Red Zone strategy discussion

If you aren't familiar with the M system from Dan Harrington, it's a number that tells you how many more rounds you can survive if you never play a hand, so it basically tells you just how much pressure you are under to make a move before you get blinded out. You take your total stack and divide it by the total starting pot to get your M. Once it is below 5 you are considered to be in the red zone. In my opinion knowing how to play correctly in the red zone is the most important tournament skill to have, because even if you are shortstacked its still very possisible to come back and get deep into a tournament. Here are a few questions what do you guys think is the correct answer?

How much do your hand requirments change when you drop from an M of 5 to an M of about 4? How much do your hand requirments change when you drop from an M of 4 to 3 (an M below 3 means almost any hand is good enough to push all in, even a king rag or a queen rag is usually good enough)? How about if the remaining players are huge stacks or very small stacks, they are less likely to fold when you make your move, so how do you hand requirments change?

do you have any specific Red mzone strategy hands to let us give our answer?
Here would be my general answer that doesnt answer your questions specifically:
My move depends on anybody coming in the pot (whether it be limping or raising) before me, or if im UTG is it more likely for me to pick up a better hand in the BB?

IT depends on stack sizes, your read on the table (for example dont push when there is a calling station is in the blinds unless you have a strong hand against the calling station's range.

It is read dependent and opponent stack size dependent

any specific hands would be much easier

Seem to remember this being discussed not very long ago - essentially, I don't think my hand requirements change at all from M=5 to M=2. You're talking about adjusting your range of calling hands over the space of... what, 20 hands maximum?

It might take a lot more than hands than that to get cards you're happy with in a situation you're happy with. So I don't see the point of saying "I'll shove K-x with an M of 5, but as soon as that sucker gets down to 4 I'm shoving Q-x down to J-7 as well"

I agree it doesn't matter what your exact M may be. Shoving or folding with a low M to me is about position (how many are left to act behind me) and the stack sizes of those left to act. I'll push with 8 5 os if it's folded to me in the SB and I can hurt the BB's stack if he calls.

It mostly depends on if you are first to act or not. This is one thing Harrington stresses in low M situations. Position is also important here as in any other situation. On the button with all folds to you is pretty much a shove with any 2 cards. If your UTG you still need a decent hand to push with although decent is lowered a bit. It's also important to know the stack sizes of the other players. Of instance if you are in middle position and the BB had a huge or very short stack you can almost be assured of a call so you need to factor that in when deciding what to play. Preferably you want to attack the medium stacks if possible.

So in order to answer the question you need a lot more information on position, stack sizes, action of other players so far, type of players yet to act, before you even begin to discuss your cards.

Another very important thing to remember is to shove even with bad cards before your M gets so low that you can't hurt anyones stacks. What good does it do to sit through the Blinds waiting for a decent shoving hand if you M drops to an insignificant amount. I would rather shove with M 4-5 with 10,9s than AK with an M of 2 because even if you double up your are still in the Red and not a threat without shoving again. Shoving earlier can buy you more time and more respect than waiting for a good hand with an insignifanct M.

I believe that there are two stack points which give you an advantage. One, the obvious, HUGE stack.

The other is the smallness of your stack. Any duckets they have above your stack amount mean nothing to you. As a matter of fact, the bigger the better. This makes is more likely that they will call your all in and play beyond you to another player.

I play a pretty good short stack, mainly because a $20.00 max buy in at a table where there are plenty of 40, 50 and 60+ stacks on the board means that you have to play short stacked every day till you hit. You learn to wait.

I just sit and fold. I do try to see every flop which isn't contested beyond the big blind amount. That's maybe two or three a round. Other than that, I wait, read, pick my nose, fart, wait, wait and wait some more.

-

Here is a thread you might find interesting.

Wow, that's very suprising that you guys have the same hand requirments with an M of 5 as you do with an M of 3. When I play, and my M is over 10, I really don't even think about M that much. I mean, if your M is 18 you can survive 162 more hands at a nine handed game before you're blinded out. With an M of 21, you can survive 189 more hands, not that big of a difference at all. But when my M drops below 10, I begin to calculate my exact M during every single hand, especially in the red zone with an M below 5.

With an M of exactly 5, you can survive 45 more hands. With an M of 3, you can survive 27 more hands. That's a huge difference! You can survive almost twice as many hands with an M of 5.

I often see players shoving all in with hands as weak as 10 8 or Jack 7 when it's folded to them and they have an M of 5 but is that really the right play? When they do steal the blinds there stack would go from 5000 to 6000, but when they get called they are an underdog to lose their entire stack. The risk/reward doesn't seem worth it to me, do you guys feel the same when your M is 5? I won't start pushing with any two cards until my M is 3 or lower. Now the risk/reward seems much more worth it to me. If your M is 3 and you push and take the pot uncontested, your stack goes from 3000 to 4000, which is a huge gain much bigger than the gain from 5000 to 6000. And I know there are other factors such as position, size of the remaining stacks, but your hand matters a lot also, since there's a decent chance that you will have to showdown your hand.

Also here's another question to think about. How small does your M have to be before it's correct for the big blind to call your all in with any two cards, assuming he knows that you don't have a big pair like AA KK QQ or JJ since it's so unlikely given your desperate situation.

Bentheman87 said:

Also here's another question to think about. How small does your M have to be before it's correct for the big blind to call your all in with any two cards, assuming he knows that you don't have a big pair like AA KK QQ or JJ since it's so unlikely given your desperate situation.

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The answer depends

1. What point of the tournament is it? Is it worth more to eleminate you the short stack or to get the extra chips?

2. How big of stack does the BB have? Obviously the bigger the stack the easier the call.

What I mean is how small your M has to be before it's mathematically correct to call your all in even with 7 2 offsuit. So just ignore his stack size and the point of the tournament. Say he somehow knows you have King 4 offsuit and he has a 8 5 offsuit. How small does your M have to be before its correct for him to call given his pot odds?

If you are in the red zone, and UTG, don't even look at your cards, just shove. You are the BB next hand at which time you have even less fold equity than you do if UTG, and that is already almost none. The only sane reason to go passively into the night would be bubble play.

Everyone at the table will see whats going on, they will know you are shoving with air most likely, and it is best opportunity you will have to suck out and more than double up . UTG you will at least create a tiny shred of doubt in their minds that you may actually have a hand.

If you wait till you are the BB, you will find someone raising before you have any chance to put any doubt in their minds. All other options available in the red zone are slightly less useless than the UTG shove. IMO.

Truly your best option is to catch lightning in a bottle, or somehow create the illusion you have done that. Low M situations pretty much nullify the illusion aspect of that equation.

And for what its worth, I would prefer J8 suited over A-little for the move...:icon_sant

Bentheman87 said:

What I mean is how small your M has to be before it's mathematically correct to call your all in even with 7 2 offsuit. So just ignore his stack size and the point of the tournament. Say he somehow knows you have King 4 offsuit and he has a 8 5 offsuit. How small does your M have to be before its correct for him to call given his pot odds?

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Well the K8o is only a 6.7% favorite pre flop to the 86o. The K8 is a 53.4% favorite to win to the 85o of 46.7%. The numbers never fail surprise me. I don't know if you have read Harrington on Hold 'em he does a very good job of explaining small M play, with statistical analysis. Bottom line though is that by the time one reaches the red zone the cards are much less important than timing the shoves. Not that getting great cards to shove isn't a great thing.

Steveg1976 said:

Well the K8o is only a 6.7% favorite pre flop to the 86o. The K8 is a 53.4% favorite to win to the 85o of 46.7%. The numbers never fail surprise me. I don't know if you have read Harrington on Hold 'em he does a very good job of explaining small M play, with statistical analysis. Bottom line though is that by the time one reaches the red zone the cards are much less important than timing the shoves. Not that getting great cards to shove isn't a great thing.

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No wonder these numbers surprise you, as they are totally wrong. K8o dominates both 86o and 85o, being about 70% in both cases to win.

aliengenius said:

No wonder these numbers surprise you, as they are totally wrong. K8o dominates both 86o and 85o, being about 70% in both cases to win.

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Too funny, I will see where I went wrong.

Darn Odds Calculator

aliengenius said:

No wonder these numbers surprise you, as they are totally wrong. K8o dominates both 86o and 85o, being about 70% in both cases to win.

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You are absolutely correct and I apologize for my incorrect post. I will be double checking everything from here on out, and leaving the math to AG and Cheetah for a while.

Steveg1976 said:

Too funny, I will see where I went wrong.

Darn Odds Calculator

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Here is a good one. Also, free software that a lot of people use here.

aliengenius said:

Here is a good one. Also, free software that a lot of people use here.

Click to expand...

thanks, I am work but will playing around with it tonight.


(I apoligize this thread got hijacked)

Bentheman87 said:

Also here's another question to think about. How small does your M have to be before it's correct for the big blind to call your all in with any two cards, assuming he knows that you don't have a big pair like AA KK QQ or JJ since it's so unlikely given your desperate situation.

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The chance to get a big pair dosn't depend on how desperate you are. So they should be included as well. So I think you are asking: When should the big blind call if they know you are pushing with any 2 cards?

If we ignore the fact that the big blind is already posted, then the pot odds would be 1:1 regardless of the size of the small stack. In that case, a big-stacked big blind can call whenever the equity in the pot is greater than 50%. The following hands satisfy this condition(the numbers are for the lowest hand in the group):

• T8+: 50.375%
• J7+: 50.343%
• Q5+: 50.782%
• K2+: 51.184%
• A2+: 55.541%

Of course these numbers change a little for suited vs unsuited, but the effect is only 1-2% in either direction.

For smaller stack sizes of the small blind, the pot odds deviate quite a bit when we take into account the posted big blind. For example, if the small blind has 3BB after posting the SB, then the pot odds for the big blind are:

pot odds = amount to win/amount to call = (1BB + 0.5BB + 3BB)/2.5BB = 1.8

As can be seen, this is significantly bigger than 1 if we ignored the posted big blind. Pot odds of 1.8 correspond to the following required pot equity:

Required pot equity = 100%/(1+pot_odds) = 100%/(1+1.8) = 35.714%

The above equity is satisfied by the following hands:

• 43+: 36.020%
• 53+: 37.122%
• 63+: 36.942%
• 73+: 37.461%
• 83+: 38.331%
• 92+: 39.927%

We can see that there is a dramatic change between calling profitably a small stack and a big stack just because of the posted big blind. The general formula for the required odds to call is:

Pot odds = (Stack + 1BB)/(Stack - 1BB)

where Stack is the stack of the small blind before posting the small blind.

If there is more interest in this topic, please let me know and I will calculate what hands in the big blind can call profitably a small blind desperation push as a function of small blind stack.

Please note that the above is valid only if the big blind has a big stack so that decisions are made solely on cEV. If the big blind had, say, twice the stack of the small blind, it would be incorrect to call so liberally because the $EV comes into play. If the big blind loses, it will become desperate and its $EV would be much worse with a tiny stack.

Bentheman87 said:

What I mean is how small your M has to be before it's mathematically correct to call your all in even with 7 2 offsuit. So just ignore his stack size and the point of the tournament. Say he somehow knows you have King 4 offsuit and he has a 8 5 offsuit. How small does your M have to be before its correct for him to call given his pot odds?

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Let's calculate it.

First of all, let me point out that 27o is not the worst hand against a random hand. 23o is the worst.

Here is the pot equity against a random hand:

• 23o: 32.303%
• 27o: 34.584%

The reason is that the high card value of 27o is more important against a random hand than the str8 potential of 23o.

Just to illustrate that there is no mistery, here is how these hands fare against a "good" hand, say AQ:

• 23o: 33.535%
• 27o: 31.613%

As you can see, 27o proudly reclaims its mythological status as "worst hand". The reason is that the high value of 27o over 23o is now no longer relevant and the str8 potential of 23o puts it over the top.

Next time someone asks you what the worst poker hand is, answer them: It depends!


Let's now calculate the maximum small blind stack that we can call profitably with anything, including 23o. As I pointed out in my previous post, we are assuming that the big blind has a substantial stack so that losing the race will not be a significant event for it.

The required pot equity to call profitably a random hand with 23o is:

pe = 32.303%

The corresponding pot odds are:

pot_odds = (100%-pe)/pe = 2.0957

The relation to stack size is given by:

pot_odds = (Stack + 1BB)/(Stack - 1BB)

where Stack is the stack of the small blind before posting the small blind.

Inverting this equation for Stack gives us what we need:

Stack = 1BB*(pot_odds + 1)/(pot_odds - 1)

in our case this is:

Stack = 1BB * 3.0957 / 1.0957 = 2.8 BB

Stack(after posting the small blind) = 2.3 BB

If there are antes, we get even better pot odds and thus can call bigger stacks, everything else being equal.

Example: Blinds are 50/100, no antes. Small blind has 210 left after posting the small blind. We are in the big blind with 1,500 stack. If the small blind pushes and we are sure it is a desperation push, we call without even looking at our cards because their stack is 2.1BB which is less than the required maximum of 2.3BB. Should the small blind make the mistake to just complete, we push without looking at our cards because we get the same pot odds, but have some FE as well.

Of course with hands better than 23o we can call bigger stacks since our equity goes up.

Bentheman87 said:

Wow, that's very suprising that you guys have the same hand requirments with an M of 5 as you do with an M of 3.

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When M goes from 3 to 5, it is true that we have more time and can therefore wait for a better hand. This implies that we should tighten up. However, there is an opposing force that dictates that we should play looser, especially in late position and unopened pot. That is stealing the blinds from late position is a profitable play and necessary for survival. We don't get enough premium hands to sustain our short stack without stealing.

The effects of stealing can be viewed in this thread:
https://www.cardschat.com/forum/tournament-hand-analysis-51/stealing-button-high-blinds-98634/
Even though that thread deals with one specific hand and position, the trends are the same for other hands and positions.

The bottom line is that even though we are dog when called, we pick up the blinds far more often than we are called, assuming our stack is not tiny. The cEV for one caller is:

cEV = (% they fold)*1.5BB + (% one call)*((% we win)*(1.5BB + Stack) - (% we lose)*Stack)

When we are called, the 2nd term is negative since we are usually dog. However, we win far more often the blinds to make this profitable. The tighter the players left to act, the better it is since the first term is where we make our money.

Because of these two opposing forces (wait more with a bigger stack, but steal more as well), the playing range for M=3 and M=5 can be very similar.


Let me now comment why we can play loosely with M<3. If we look at the equation for cEV, the first term is almost zero since it is not likely people will fold to our tiny stack push. The second term is negative. The looser we are(and we have to be since we are desperate), the more negative our cEV is. How can then be proftibale to play like that with a tiny stack?

The answer lies in the fact that $EV is what dominates desperation play. As some players know, marginal chip values are not constant. For example, if we had a stack of 1,000 when blinds are 5/10, losing 500 is much worse than winning 500. More extreme, losing 1,000 is much worse than doubling up. That means that our first 1,000 chips are more valuable than our next 1,000 chips.

An easy way to see this is to consider $EV which is the driving force in tournaments. If we lose our stack of 1,000, our $EV goes from whatever it was to zero. On the other hand, doubling up doesn't double up our $EV. So a coin flip all-in early in a tourney has -$EV. Even if we are slightly favorite, it is still -$EV.

In most cases, additional chips have less value than what we already have. However, this is not always true. One situation when this is reversed is when our stack is way too small. When our stack is that small, we have lost all FE so we cannot steal. If we wait, we will be blinded out so waiting has zero $EV. That means that the chips we have are less valuable than the chips we can get if we double up. So even though our super-short stack play has -cEV, we are still playing +$EV since waiting will surely mean we will not make the money.

There is an obvious exception to this if we are close to a bubble and can make it by folding.

Steveg1976 said:

You are absolutely correct and I apologize for my incorrect post. I will be double checking everything from here on out, and leaving the math to AG and Cheetah for a while.

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Steve, don't let this deter you from trying to do this yourself. Everyone makes mistakes. If you make another mistake, I am sure someone will notice. And if no one notices, then it wasn't important anyway.

Cheetah said:

Steve, don't let this deter you from trying to do this yourself. Everyone makes mistakes. If you make another mistake, I am sure someone will notice. And if no one notices, then it wasn't important anyway.

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I am going to make a point of over the next few months really focusing on the Math, I am sure there is value there that I am missing. I don't mind mistakes, and I don't mind being questioned, when you blow something you won't forget it in the future that is for sure.

How can I help?

Bentheman87 said:

Also here's another question to think about. How small does your M have to be before it's correct for the big blind to call your all in with any two cards, assuming he knows that you don't have a big pair like AA KK QQ or JJ since it's so unlikely given your desperate situation.

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The short answer to this is the rule of ten:deal: . If the big blind or any one else for that matter has ten times more chips than you they should call you with any two cards..............:vroam: