EV stats and max winrate questions/observations.

[OrianasDaad]

I've been doing some figuring on the EV numbers over at the pokerroom website, and have found, according to their EV stats, the maximum winrate.

Here's how I got it:

I figured that if each hand had an EV, then it should follow that multiplying that EV amount in BB by the probability of getting that hand will provide an EV/100 hands.

Proabilites:
Pocket pairs: .4525
Suited: .1508
Offsuit Non-Pair: .6033

For instance, KQs is listed with an EV of 0.39. You'll get this hand .15% of the time. .39 * .15 = .0588. That's how much this hand is worth towards the theoretical "maximum" winrate.

This magical theoretical figure, by-the-way is about 4.87 BB/100.

My questions are:

- How reliable are the numbers at pokerroom?
- Even if the stats are only close to a "true" EV for each hand, the total theoretical winrate can't be much different can it?
- Did I even do this right?
- These stats at pokerroom do include the blinds, correct?
- Assuming these number do not include the blinds and they are theoretically correct, doesn't that make this game unbeatable? I personally believe that if this is the case, then limit HE is unbeatable. Thankfully, I'm fairly certain that pokerroom's EV calculations have included the blinds.
- Since I didn't do each of these hands by position (just overall), will this winrate change signifigantly when I only include hands when they are profitable at a certain position?
- I noticed that some offsuit hands that have less EV are worth more to the overall BB/100 than suited hands, due to frequency. Just an interesting observation.
- Adding the frequency of hands that are either +EV or null EV, it comes to a mere 13.25%. Does this mean that players who have a higher VPIP than this (outside the blinds) are either "tricky", playing hands for their relative and/or positional value?

Answer any or all. Please discuss.

[pzhon]

[ QUOTE ]

Proabilites:
Pocket pairs: .4525
Suited: .1508
Offsuit Non-Pair: .6033


[/ QUOTE ]
Each offsuit hand has 12 possibilities out of 1326 = 2/221 = 1/100 * 0.9050.
Each suited hand has 4 possibilities out of 1326 = 2/663 = 1/100 * 0.3017.

[ QUOTE ]

For instance, KQs is listed with an EV of 0.39. You'll get this hand .15% of the time. .39 * .15 = .0588. That's how much this hand is worth towards the theoretical "maximum" winrate.


[/ QUOTE ]
I see no connection between the theoretical maximum win rate and the PokerRoom stats. PokerRoom averages the results over all of the players dealt that hand. Some called 3 cold with A4o; some folded. Some overlimped with KK. If you wouldn't do those, the numbers may not be accurate for you. If it isn't theoretically correct to make those plays, the numbers will not tell you much about optimal play.

[ QUOTE ]
This magical theoretical figure, by-the-way is about 4.87 BB/100.

[/ QUOTE ]
I suspect you are adding up all of the positive numbers without subtracting the negative numbers. This would be wrong. If you got this figure another way, please explain your method.

[ QUOTE ]
- How reliable are the numbers at pokerroom?

[/ QUOTE ]
The values for the hands in particular levels and particular positions are pretty noisy, perhaps with errors of 0.05 in common limits, and much more in less common limits. When you average over all positions and limits, the noise is reduced, but you no longer have a figure that is valid for any limit or position.

In addition to the noise, there are systematic errors.

[ QUOTE ]
- These stats at pokerroom do include the blinds, correct?

[/ QUOTE ]
Yes.

[uuDevil]

[ QUOTE ]

Proabilites:
Pocket pairs: .4525
Suited: .1508
Offsuit Non-Pair: .6033


[/ QUOTE ]

These add up to more than 1 (can't be). I think the numbers are

Pairs 0.0588
Offsuit 0.706
Suited 0.235

!Edit: these numbers are for hands grouped by type. [img]/images/graemlins/blush.gif[/img]
!See pzhon's post for the probability per hand.

[ QUOTE ]

This magical theoretical figure, by-the-way is about 4.87 BB/100.

[/ QUOTE ]

Can you be more specific as to how you got that? By adding up the weighted EV of all the hands with positive expectation?

Remember these numbers represent the performance of an average player. An expert can get more +EV from good hands than an average player and turn some of what are slightly -EV hands for average players to +EV hands. He also won't lose as much with bad hands. (Though it probably doesn't make much difference at the extremes-- the expert can't do much better w/ AA or 32o than the average player.)

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- How reliable are the numbers at pokerroom?

[/ QUOTE ]

I don't see any reason to doubt them.

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- Even if the stats are only close to a "true" EV for each hand, the total theoretical winrate can't be much different can it?

[/ QUOTE ]

The EV is "true" in the sense that it reflects the actual performance of average players. I would expect the EV of many hands, for an expert, to be somewhat different from what it is for the average player.

[ QUOTE ]
- These stats at pokerroom do include the blinds, correct?

[/ QUOTE ]

Yes, as far as I can tell.

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- Assuming these number do not include the blinds and they are theoretically correct, doesn't that make this game unbeatable? I personally believe that if this is the case, then limit HE is unbeatable. Thankfully, I'm fairly certain that pokerroom's EV calculations have included the blinds.


[/ QUOTE ]

Trust me, if I can beat it, it's VERY beatable.

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- Since I didn't do each of these hands by position (just overall), will this winrate change signifigantly when I only include hands when they are profitable at a certain position?

[/ QUOTE ]

If I understand what you're doing, definitely.

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- Adding the frequency of hands that are either +EV or null EV, it comes to a mere 13.25%. Does this mean that players who have a higher VPIP than this (outside the blinds) are either "tricky", playing hands for their relative and/or positional value?

[/ QUOTE ]

However they are doing it, experts can definitely extract more value from more hands than the average player. But this isn't all THAT hard-- the average player is losing ~3 BB/100 hands according to those stats.