6-max blind defense
 

Cross posted in hush, thought you folks might find this interesting.

Was crunching some numbers in PokerStove and thought I'd share my results.

Let's assume an opponent on the button who will raise according to MEbenhoe's starting hands chart. This comes to about 34.5% of starting hands from the button and looks like:

22+,A2s+,K8s+,Q8s+,J8s+,T8s+,98s,87s,76s,A2o+,K9o+ ,Q9o+,J9o+,T9o

How do we determine which hands should be reraised and which we should call with (or fold?). We're getting 1:3.5 immediate odds, but realistically some hands we should just fold right now (as they will cost too much if we catch a piece of the flop and we will have to check/fold very often).

If we assume we'd only like to play hands that are at least 40% to win (the same % argument used when talking about folding AQ to a tight UTG raise in higher stakes), that means we should be playing the following hands:

22+ (22 has 45% equity)

A2s+ (47%+ equity)
K2s+ (40.5%+ equity)
Q7s+ (40%+ equity)
J8s+ (40%+ equity)
T9s has 41% equity

A2o+ (44%+ equity)
K8o+ (40.5%+ equity)
Q9o+ (40.5%+ equity)
JTo has 41.5% equity

Interestingly, this results in exactly 34.5% of hands (the same number the button is raising with, but a slightly different set of hands (more suited kings, fewer little suited connectors). Running these two ranges against each other in pokerstove showed the button with 49.85% equity and the BB with 50.15%. With the positional disadvantage, button is still probably a slight favorite.

If we assume we'd also like to reraise if we are likely a favorite by 10% or more (55%+ equity), that means we should be reraising these hands:

AA - 85%
KK - 76.5%
QQ - 73%
JJ - 69%
TT - 65.5%
99 - 61%
88 - 57.5%
77 - 55%

AKs - 65%
AQs - 63%
AJs - 61%
ATs - 59%
A9s - 55.7%

AKo - 63.5%
AQo - 61.5%
AJo - 59%
ATo - 57%

If we want to add in hands which are only 5% favorites, we can put in:

66 - 53.5%
A8s - 53%
A9o - 53%
KQs - 52.6%

Interestingly, big kings do not fare well against the button's range and mostly should not be reraised (from an equity standpoint).

Of course all of this is assuming no reads and that you and your opponent play equally well postflop which of course is not usually the case.

Let me know if you have any comments or corrections (or if this has already been done to death )!

Thanks,
D5

Re: 6-max blind defense
 

Nice post.
First off, just for clarification you are talking about the villian opening on the button, not just raising. Incase someone gets confused. [img]/images/graemlins/grin.gif[/img]

A lot of this is read based, or depends on the limits you play at. Most of the .50/1 players probably don't loosen up their button opens too much, so its harder to put them on a range.

Also, I have been playing 2/4 lately and some tables are extremely tight, and I notice more pfr that are AK+, where as in 1/2 pfr would start lower than that.

Again all this is saying is, that you must have some type of read, or numbers on someone before attempting to limit their hands to this range.

Re: 6-max blind defense
 

All of your points are valid and clearly some players will raise more/less than this range. But we have to start somewhere.

There are also some players who will play scared on the flop after you 3-bet from the BB, so we'd want to raise more in that case, possibly even most hands we play.

Re: 6-max blind defense
 

This is a very nice post dude.

Re: 6-max blind defense
 

Thanks [img]/images/graemlins/smile.gif[/img]

Re: 6-max blind defense
 

[ QUOTE ]
All of your points are valid and clearly some players will raise more/less than this range. But we have to start somewhere.

There are also some players who will play scared on the flop after you 3-bet from the BB, so we'd want to raise more in that case, possibly even most hands we play.

[/ QUOTE ]

agreed, and I think it is a good post.

I'd saying seeing someone open with A5s or something from the button once or twice is enough to base a read on that he knows how to loosen up his standards. So, reraising him has a lot of merit. Like you said, it generally slows them down, and if they don't cap, I always lead the flop. If they miss, you will take it down a good portion of the time.

Re: 6-max blind defense
 

i PM'd Wookie about this question and i believe deception, you're referring to blind defense as BIG BLIND and not SMALL BLIND- right?

anyway, i asked Wookie about what to do in SB against this raise and here is his "brief" answer- hopefully maybe he'll chime in here:

[ QUOTE ]
Anyway, here are some thoughts about SB defense. As I mentioned in passing in the 6 Max Stats FAQ, pretty much anything you want to defend in the SB against a single open-raiser you have to 3bet. You would much prefer to fold the BB and be OOP against one opponent rather than OOP against two. Cool calling the raise just offers the BB 5:1 to call, which are pretty tempting odds for a lot of hands, especially in the effective middle position. What hands you chose to 3bet, however, depends strongly on you and your opponent. Is your opponent even the type to steal with a marginal hand? What is his range of hands? How confident are you in your play? How often does he fold to aggression? Are you willing to give up when you think you're beaten, or will you continue to aggressively bluff? Do you give up too easily? You're going to be choosing your defense hands from roughly the top 25% of hands, but how low you go on that list of hands depends strongly on your answers to the above questions.

The other thing to think about is when you're up against a CO/BT open limp. You're now getting 5:1 on completing, and you're up against a hand that the limper likes a little bit, but not a lot (barring the rare dude getting cute w/ AA), and a random hand. That's pretty juicy for a lot of hands. You can play some pretty marginal hands such as 97o for pair strength and come out firing. If you pair up on the flop and lead, you offer your opponents a mere 4:1, making it pretty incorrect to draw with just about anything that doesn't have 8 or more outs. Some of the veteran HUSH posters dip even lower than 97o, like, 65o+. You may not want to go quite that low to start, but try it out with T8o and see what you think. As you recognize more profitable situations, you can add a few more hands.

[/ QUOTE ]
maybe if you want to work up thoughts/equity and what not with that range of hands, that would be interesting too.

and here is a link to a 6-max blind defense (long) post by droolie- just to fill out more of this discussion and incase people missed it.

Re: 6-max blind defense
 

Yes this is the big blind only and assumes the small blind has folded.

The small blind situation is more difficult for a few reasons:

1.) It is almost never correct to just call a button raise because you are offering the BB great odds to play.
2.) There are several different blind structures. For 1/2 you might defend with a lot more than in a 1/3 or 2/5 structure. In a 2/3 structure you might defend almost as liberally as in the BB.
3.) You are not closing the action and so must consider the big blind.

Re: 6-max blind defense
 

excellent points. thinking blind defense in SB is more difficult (IMO) because of these points. as Wookie pointed out, if you're gonna play, you gotta 3-bet.

what i was hoping you could do (since i'm unclear about it) is work up the numbers like you did for BB defense and adapt them to SB defense. so there are 3 points we have to start with:

1. he's raising 35% of the hands
2. we're HAVE to 3-bet if we're going to play.
3. this, in turn, makes the flop much more difficult as it, IMO, commits us to betting out (unless BB cold calls our 3-bet and/or Button doesn't cap- then i think we could check/call or check/fold dependent).

so from there we can figure if we're HU, Button doesn't cap, and we're leading out the flop: putting in 3.5SBs to win 4.5SBs (figuring worst case, Button folds to our flop bet)-

that seems like a heck of a lot of $$ to put in to win very little worth the risk, but maybe i'm not looking at that right as that would mean we'd need a hand with a 75% equity edge [img]/images/graemlins/shocked.gif[/img] - that' can't be right! [img]/images/graemlins/mad.gif[/img]. could someone take it from there....

Re: 6-max blind defense
 

Why do we need 40% equity if we're gettng 3.5:1?

Re: 6-max blind defense
 

D5, this completely rocks. Thanks for posting it. I have appended this to MEBenhoe's original chart on the right-hand side. I've also formatted it to print on one page and changed the colors to look OK on a black and white printer. If anyone is interested and can tell me how to post the file here, let me know.

Re: 6-max blind defense
 

[ QUOTE ]
Why do we need 40% equity if we're gettng 3.5:1?

[/ QUOTE ]

40% is not necessarily the correct number, but I believe it's pretty close. I could have sworn I saw it referenced in the AQ test but I can't find it now so I can't use that argument. [img]/images/graemlins/smile.gif[/img]

Essentially the problem here is if you are going in as too much of an underdog with a hand like T7s (a 35% equity hand) you are going to be hitting a lot of second/third pairs and will throw away a lot of money. 1/6 of the time an ace flops and you will often have to throw your hand away (even if you hit a T or a 7).

You'll be out of position for the entire hand and nearly 2/3 of the time you will miss the flop completely and basically have to check/fold throwing away 1BB more than you had to.

Re: 6-max blind defense
 

[ QUOTE ]
Essentially the problem here is if you are going in as too much of an underdog with a hand like T7s (a 35% equity hand) you are going to be hitting a lot of second/third pairs and will throw away a lot of money. 1/6 of the time an ace flops and you will often have to throw your hand away (even if you hit a T or a 7).

[/ QUOTE ]
Throwing away a hand like T8 on a ATx flop seems a little weak and bad play, in general. T7 against the assumed range of stealing hands pre-flop on that flop is a 55/45 dog, and you are risking 2.5 BB to win 7 BB, which means you would have to have at least 35% of a chance to make some sort of profit. Of course, if your opponent is predictable (ie: will not raise this flop w/o a hand that beats second pair, [censored] kicker) then you can dump it for less.

(However, your equity is much greater on a KTx flop (~60%) than a ATx flop, for obvious reasons).

-K

Re: 6-max blind defense
 

I'd be interested in seeing this in table format. Couple points I'd be interested in knowing:

- Is this valid only against a button raise (ie defending with 40% equity hands)? How bout HU vs CO, UTG+2, etc? Obviously need to tighten up here but how much?

- Need to continue the SB defense conversation and at least start with some hand ranges as d5 has done here.

And d5, thanks for the cool post!

Re: 6-max blind defense
 

First off you are absolutely correct that you have a great hand on a king high flop if you hit a T.

As far as the ace high flop, when you are way behind, you will lose 2.5BB more (3BB total). This is nearly half the time (around 15.8%/34.5% you are against Ax/AA/TT/22 (using 2 as the x on the ATx flop)).

6.5%/34.5% You will be against KK/QQ/JJ/KTo/QTo/JTo/KTs/QTs/JTs/T9s/T8s/T9o. If the opponent will check behind on the river you'll only lose 1.5BB more (2BB total). If the opponent will value bet the river you'll lose 3BB here.

The rest of the time (11.9%/34.5%) you are against 99-33 (not including 22, the other set on the flop)/KQs/KJs/K9s/K8s/QJs/Q9s/Q8s/J9s/J8s/98s/87s/KQo/KJo/K9o/QJo/Q9o/J9o. At best you will get 1.5BB out of these hands which completely miss (and many players would check behind on the turn and fold the river with these). So you'd win 7.5BB here (2BB which you put in voluntarily, so 5.5 profit).

I think your best EV looks like:

-15.8/34.5*3
-6.5/34.5*2
+11.9/34.5*5.5

= .1475.

So it could potentially be a positive situation. But many opponents would value bet KK/QQ/JJ/Tx on the river and most would be capable of folding something like 98s/87s/J8s/J9s/J9o/Q9o/Q8s/Q9s/QJs when it didn't improve (we'll even assume he'll call a river bet after checking behind on the turn or bet the turn and check behind on the river with 99-33/any king).

-15.8/34.5*3
-6.5/34.5*3
7.1/34.5*5.5
4.8/34.5*4.5

=-.181

Still against most players it would probably be ok to call down here.

Re: 6-max blind defense
 

[ QUOTE ]
D5, this completely rocks. Thanks for posting it. I have appended this to MEBenhoe's original chart on the right-hand side. I've also formatted it to print on one page and changed the colors to look OK on a black and white printer. If anyone is interested and can tell me how to post the file here, let me know.

[/ QUOTE ]

New chart hosted here.

Re: 6-max blind defense
 

Looking at this chart it becomes rather obvious, that this is a pretty predictable strategy. If our hero is calling from the blinds, you always know that he doesn't have a premium hand.

Too bad Abdul Jalib isn't here anymore to provide more insight on pre-flop ballancing.

Re: 6-max blind defense
 

Balancing is all well and good - IF you're going to be playing a lot with the same players. Given the high turnover of low stakes online play, though, making the theoretically most +EV play in a vacuum is virtually always, well, the theoretically most +EV play.