It’s been years since I last played in a cardroom, or played much holdem online at all, but I am going on a trip to San Diego, and planning on playing there. The cardroom I am thinking of visiting (Oceans 11) offers 8/16 limit (usually nothing higher) and has a $5 drop, a $1 jackpot, and another $1 taken on the river.

Using Equilab, I was going to try to figure out how such a huge rake will effect play in the BB in a raised heads-up or three-way pot. As you know a high rake should most effect play in the blinds. If you raise preflop outside the blinds, there is always a chance the blinds will fold and you will pay no rake, or that there will be many callers, diluting the effect of the rake.

In a hypothetical rake free game, to call a raise heads up in the Big Blind, you will need roughly 35% equity (rather than 50% equity) against the opener’s range because of the pre-invested BB. I know that off-suit big/little hands have RIO, and that suited connectors if played correctly can over-realize their equity. Let’s just say, for the sake of argument, you need 36% equity for some RIO type hands, and 33% for suited connectors, with a range that averages 34%. (You are out of position, but the folded SB money pads the pot a little.)

What is the best way to calculate the way in which a drop/rake changes the equity you need to call in the BB? So for example, if the drop/jackpot is $8 and the BB is $8 (as in 8/16) then do they cancel each other out? Would you now need roughly 50% equity or better to call an opener in the BB heads-up?

In a three-way pot with a $8 drop, instead of needing about 23% equity, you would need around 33% equity or better to call or raise in the BB?

Any thoughts or comments would be appreciated.

the range of the pf raiser (and that of other players who enter the pot) will also matter here

i would tighten up slightly in high-rake situations (for example i'd defend say j7o here 3ways online but likely would fold it live) but i wouldn't tweak my ranges too much

however, i don't think you need to put a ton of time into working this stuff out away from the table. it seems like it could be a lot of work for not a lot of reward

also important to keep in mind is that it's not the best approach to construct your pf ranges strictly off of hot/cold equity %s relative to the price we're getting (pot odds). playability is a much more important factor, especially in multiway situations

Thanks for your reply BigBadBabar.

I ended up spending some time working on my original question of how a high rake effects big blind defense, if on average 35% equity is needed to defend the big blind against the range of a raiser from outside of the blinds. (I realize as I mentioned in my first post that playability and other conditions will change needed equity to defend, but for the sake of this exercise I just wanted to presume 35% equity.)

I ended up doing the math on my own. I found a gold Pokerstrategy.com article (that I bought many years ago) where that very often cited 35% equity needed to defend the big blind heads up is explained mathematically.

The article provides an equation to demonstrate how the 35% is derived.

Equity = (D-1) (2*D +0.5) = 3 (2*4 +0.5) = 3/8.5 = 35%

D stands for the investment in the pot by the raiser and defender measured in small bets. The 0.5 in the above equation is the small blind dead money.

So the equation I got for the defending the BB heads up in which the rake or drop is equal to the small blind would change that equation to
Equity = (D-1) (2*D) = 3 (2*4) = 3/8 = 37.5%

You would need 37.5% equity to defend the BB against the range of a raiser outside the small blind, not taking into account playability, skillness of opponent, etc.

If the rake/drop is one full Big Blind the equation would be changed to

Equity = (D-1) (2*D - 0.5) = 3 (2*4 - 0.5) = 3/7.5 = 40%

40% equity against the raisers range is needed to defend the BB. This is actually is lower than I had originally guessed.

I realize playability will change the required equity. The Pokerstrategy.com article I mention estimates that playability changes the required equity by +/- 3.5%. You can add 3.5% to a hand like 56 suited, and you would need 3.5% more equity for something with high RIO like A2o.

Does my math for the 37.5% and 40% equity need to defend the BB heads up (in those rake conditions) seem right?

What do you think of the +/-3.5% added or taken away for playability?

You're thinking about good things. You might want to also consider how your opponents are terrible. Hot and cold equity isn't the whole story. You mentioned dominated hands. Out of position vs crushers, you suffer horribly with dominated A's, K-something offsuit, etc. Versus people who miss value bets all the time and who don't use position, those hands don't suffer as much. If you're against people who just bet when they have it and who check when they don't (who ignore RvR spots), the disadvantage is less. If they aren't showdown bound enough, you get bluffing opportunities. If they are showdown monkeys, you get tons of extra value when you hit. The worse and more predictable they are at poker, the better things go on the last 3 betting streets -- the ones ignored by a hot/cold sim.

Thanks DougL for your response.

Yes, the skill of the raiser would need to be taken into account. Let’s say, the raiser is very passive, and will not bluff or value bet the river with less than top pair, good kicker. That could save us (perhaps optimistically, but for the sake of argument) a big bet on average by allowing us to fold to a river bet or get a free showdown. That saved big bet could be plugged into the above equity equation.

So lets say we are playing a game with no rake (a time charge game) and go back to the 35% hot/cold equity needed for the average hand against an opener’s range of average skill.

Equity = (D-1) (2*D +0.5) = 3 (2*4 +0.5+1.0) = 3/9.5 = 31.57%
+0.5 for the little blind, and +1.0 for the weak player bonus.

Dominated/RIO hands would need a bit more equity (maybe 1 to 3% more) and suited connectors would need a bit less equity (maybe 1 to 3% less) against the player’s range.

I’m also thinking that as the opener’s range gets much broader that the need to discount for domination/RIO situations becomes less of an issue. By my Equilab calculation, against a 10% opener (77+,A9s+,AJo+, KTs+, KQo, QTs+) an A/big card combination will make up almost half of all the hands in his range (68 hand combinations with an Ac/Big, and 88 hand combinations without an ace). The possibility of reverse domination for an Ace/little in the Big Blind is huge.

With a 25% opener, only about a third of his hands will contain an Ace or an Ace that will dominate yours (as he is typically opening A7o, but also A2s). The equity adjustment would seem to need to be less.

Is this how you and other serious FLH players go about figuring out these situations?

I’m interested in learning how others go about making more precise modifications to the 35% baseline equity needed in this type of heads up blind defense situation?

How much equity do you add or take away for domination/RIO hands or suited connectors?

How much equity would you add or subtract for weak for strong opponents.