Average Hands

[AlienBoy]

People often refer to Q7 as the "computer hand" - the legend goes that someone analyzed it and found it to be the mean (or was it median?) hand in terms of EV - though Poker Stove does not seem to think so. In fact Q7s is a favorite against 8 other random hands, and Q7o is a definite dog against 8 other random hands.


Just out of interest, I began a trial and error run of specific hands against 8 random hands (9 hands total). These are the hands that are very close to "even" with the random bunch. If it is farther than .1% from the average, that is indicated by "slight favorite" or "slight dog":


Pocket Pairs:

44


Suited Aces, kings, and queens:

None - all suited aces and suited kings have an equity advantage over 8 other random hands. Q2s is nearly even with the 8 random hands, but still a slight favorite.


Suited Jacks and tens:

J4s

T5s (slight dog)

Other suited hands: See suited connectors



Offsuit Aces, Kings, Queens:

A8o (incidentally, all other offsuit non-connectors (except A9o) are substantial dogs) A9o is the only offsuit non-connector with an equity advantage.

K9o and Q9o (slight favorites)


Suited connectors:

Zero gap:

43s (slight dog)


One Gap:

53s (slight favorite)


Two gap:

74s (slight dog)


Three gap:

95s (slight dog)



Offsuit connectors:

Zero Gap:

T9o is a favorite, 98o is a dog - the average in right between them.

One Gap:

J9o (slight favorite)

Two Gap and Three Gap: Same as offsuit kings and queens.




I don't know that any of this is useful, but I found it interesting that there were *many* hands that were right at the average against 8 other random hands.

Basically, there are three hands that are a dead heat against 8 other random hands: 44, J4s, and A8o.




AB

[Gonso]

I believe you're think of a HU scenario, where Q7o is reasonably close to 50-50 vs a single random hand (it's actually slightly better than that). Alos I believe you're referring to Harrington's SHAL chapter.

Q5o is closer to 50-50 btw

[PantsOnFire]

Q7 is used as the median hand in a heads up battle against a random hand. In other words, if you are the SB and it's just you and the BB, you can move all in and it will be a +EV play.

A good example is a tourney when it gets down to heads up. You should move in on the button with Q7 or better. This is generally true if villain is equal or better skill. If you have much better skill, then you can fold or see a flop for a limp. Or you can raise a tight villain if that's your edge. You want to seek big edges rather than slight edges against weak opponents.

[DrVanNostrin]

[ QUOTE ]
Q7 is used as the median hand in a heads up battle against a random hand. In other words, if you are the SB and it's just you and the BB, you can move all in and it will be a +EV play.

[/ QUOTE ]
This would only be true if your opponent was not allowed to look at his cards. There is a table in NLHTaP that has the S-C numbers, which tell you at what stack sizes it is +EV to move all-in with each starting hand (assuming 1/2 blinds and your only options are all-in or fold).

[PantsOnFire]

[ QUOTE ]
[ QUOTE ]
Q7 is used as the median hand in a heads up battle against a random hand. In other words, if you are the SB and it's just you and the BB, you can move all in and it will be a +EV play.

[/ QUOTE ]
This would only be true if your opponent was not allowed to look at his cards. There is a table in NLHTaP that has the S-C numbers, which tell you at what stack sizes it is +EV to move all-in with each starting hand (assuming 1/2 blinds and your only options are all-in or fold).

[/ QUOTE ]
With respect to that table, obviously if your stack size in relation to blinds is smaller, you can open shove with a wider range because of the pot odds.

However, the uniqueness of Q7 is that since it is 50% against a random hand, you can move in with any stack size (against one other random hand) since the blinds will always give you slightly better than 1:1 odds.

If I am wrong here, I would be gracious if somebody could point out my error.

[trojanrabbit]

[ QUOTE ]
However, the uniqueness of Q7 is that since it is 50% against a random hand, you can move in with any stack size (against one other random hand) since the blinds will always give you slightly better than 1:1 odds.

If I am wrong here, I would be gracious if somebody could point out my error.

[/ QUOTE ]
It's wrong since your opponent isn't calling with a random hand. When he has a bad hand, he folds and you win a small pot. When he has a good hand, you'll be worse than 50/50 and will likely lose a big pot. Those "slightly more than 1:1 odds" are irrelevant.

Tysen

[Gonso]

The jam/fold tables in MoP will do it, lol I was just translating the table to numbers based around pot size (as opposed to blinds) as I read this

[LarryLaughs]

Trojan rabbit, I agree.

That is what the S-C numbers mean. They mean that since the opponent is not calling with a truly random hand, you can still move in if your stack is equal or smaller than the S-C number.

[PantsOnFire]

[ QUOTE ]
[ QUOTE ]
However, the uniqueness of Q7 is that since it is 50% against a random hand, you can move in with any stack size (against one other random hand) since the blinds will always give you slightly better than 1:1 odds.

If I am wrong here, I would be gracious if somebody could point out my error.

[/ QUOTE ]
It's wrong since your opponent isn't calling with a random hand. When he has a bad hand, he folds and you win a small pot. When he has a good hand, you'll be worse than 50/50 and will likely lose a big pot. Those "slightly more than 1:1 odds" are irrelevant.

Tysen

[/ QUOTE ]
Let me rephrase this.

Let's say it is heads up, I always have the SB (i.e. button) and I am always dealt Q7. Say it is a cash game and I have an adequate bankroll to buy-in many times.

My strategy with my Q7 is to move all-in every time. Is there any strategy BB can employ such that I will not win in this situation in the long run?

[jay_shark]

Pantsonfire , your goal is to be the favorite when "called" .

You're the favorite against a random hand , but you're not necessarily the favorite when called .

By the way , q-5 is a coin flip heads up and q-7 is more on the plus side .

Watch what happens when the BB restricts his calling range to the top 40% of hands when you have 20 bb's (he has you covered) .

EV(sb) = 1.5*0.6 +0.4*[20.5*.3723 - 19.5*0.6277 ]
= -0.9432

So shoving with q-7 with 20 bb's is negative EV against the BB who calls with the top 40% of hands .