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Data from preflop solver with a 3bb RFI strategy in a 500z rake structure. Approximately 40.5% RFI range.

Link:

https://public.tableau.com/profile/z...EV?publish=yes

Really cool. Thanks!

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It's working today. Confirmed AA is a good hand.

Hello kvnd, thank you for sharing this with the class.

Could you please tell us the overall BTN bb/100 when folded to?

Awesome! How do you think the EV distribution would change with smaller open sizes, say MIN or 2.5x? Would hands like 75s, A3o, or 22 suddenly become profitable opens? Because at 3x those hands appear to be -EV (or breakeven at best).

I have that data, but it would take me about 40 minutes to put together.

For your specific example,

75s goes from an exactly 0 EV open with a 3x size to 0.02 with a 2.5x size.

A3o goes from 0 to 0.01 EV (mixed open in the 3x range)

22 goes from 0 to 0.035

The EV of big hands declines with a smaller open. Hands that are strong but not super strong such as ATs or KJs have approximately equal EVs with the 2.5 and 3x sizes. Weaker hands gain EV with smaller size.

I will edit this answer with the answer to brokenstars question in a little bit


Taking the weighted average of bb/hand, and multiplying it by the percentage of the time we open (0.41), I get about 25bb/100 which doesn't seem right. Anyway, here's the data, the calculation I did to answer this was in column E: https://docs.google.com/spreadsheets...it?usp=sharing

I used the following equation to get ~24bb/100:

[(# of combos)/1326]*ev and then just summed up the entire column. This equation makes more sense to me since it's just like:

(freq of hand)*(ev of hand) and then summation

https://docs.google.com/spreadsheets...it?usp=sharing

If you think this is correct then please share the excel file for the 2bb and 2.5bb rfi opens.

Yes I got the same answer. 24, 25, whatever. I rounded. We got the same answer

I have to manually create the dataset by typing all the info in by hand into a spreadsheet. It takes a half hour. Making the graphic only took 15 mins. Don't really feel like making any more spreadsheets

Good stuff. Shows how much variance there is in the game when with hands as strong as 99 and AQo you should be happy to steal the blinds since your EV is less that 1.5 bb.

I wonder how many hands want to get called.

That solution correlates with what I remember from Snowie. i.e. Only TT+, AK, and AQs win more than 1.5bb on the button. I think Snowie only estimated an EV of about 7.5bb for AA though, whereas this solution has it at 10bb.

Different 3 bet and 4 bet sizings both for our opponent and us can alter the EV of AA in particular. Snowie has pot sized 3 and 4 nets right? The solution I have used a 4x 3 bet size and 55% pot 4 bet (our 4 bet size)

For a 2.5x RFI, there is a like a 5% drop in our AA's EV when our opponents choose a 4x over a 4.75x 3 bet size for their range

It's crazy that so much of our EV comes from AA/KK! Less than 1% of our range make up 1/3 of our EV

AA/KK aren't paying their fair share of rake, IMO. EV inequality is a serious and rising problem in today's poker games.

I thought the most interesting thing was that suited Broadway's generate the same amount of EV as offsuit ones, despite the latter being three times more common

Also the rapid decline in EV from TT to 66 for pocket pairs

If you've got a tracker like HEM, look at your 'holecards' report.
Make a note of how much money you've made with AA, and then compare it to your overall figure. If you're like most players, the amount you've won with aces alone will be close to or even higher than your total net profit.
e.g. In my last tracked sample of 125,000 hands, I had an overall EV of 65 buyins (EV of 5bb/100). But I won more than that (73 buyins) with AA alone. i.e. The net result of all other hands added together was negative.

well yes but AA is more profitable because it's part of a wider range
it's incorrect/incomplete to look at individual EVs within a range
their ev is what it is because they are in that specific range
board coverage is important, among other things
notice how preflop solvers don't necessarily go for highest ev opens in a vacuum, but look to strength the range as a whole. take hj for example, instead of opening 55 100% of the time and folding everything below, solver opens 22-55 at 25% freq each for better board coverage and even tho it thinks opening 98s-54s is slightly losing or break even, it adds some to improve the overall ev of the range
obv, if you told it to just open AA and nothing else, the ev would take a sharp nosedive

An equilibrium strategy (which solvers attempt to approximate) will never take an action that has less EV than another action for each combo. There are no loss leaders. Hands that are breakeven at equilibrium can improve the EV of the overall strategy against the maximally exploitative counterstrategy, but offer no benefit against the equilibrium strategy.

Yes, of course, if your opponents realised that was your strategy, they would exploit the hell out of you. It's the possibility that we have AA when we open that makes hands like JTs +EV, and equally it's the case that having JTs in our range that helps the EV of AA. But if you never got dealt aces due to a flaw with the RNG (although it would be in your theoretical range and your opponents still played as if you had aces sometimes), you'd be guaranteed to lose in the long run. AA is an insanely important/profitable part of your range.