My normal game is $5-5 where the rake is automatically $5 if a flop is seen +$1 for the jackpot +$1 if the turn is seen.
Assume Under the gun raises to $15 and it folds around to the big blind. There is a $7 rake at CC (technically $6 but $1 more if u see a turn. I'm using $7 since we are out of position and it is far more likely that we either get bet off of our hand or see a turn than we win on the flop). This means we need to call $10 more to win $18. So we need $10/$28 ~ 35.7% equity to call.

I assumed a 7% opening range by utg.
Using poker stove I found that 35.7% equity hands equate to about 38.8% of all possible starting hands or
22+, A2s+, K9s+, Q9s+, J8s+, T8s+, 97s+, 86s+, 75s+, 64s+, 54s, 43s, A2o+, K9o+, Q9o+, J9o+, T8o+, 98o, 87o

Few questions
1. are there programs out there to help me do these types of calculations faster?
2. I'd like to do an estimation of the button/small blind/ etc using the same starting parameters or slightly modifiying them for raise size, rake, additional number of players to act who might 3bet and make me fold my equity, etc.
3. Suggestions on the way to defend other than calling. Theoretically, if I get under the gun to fold to a 3bet, I'll have more equity in the hand. I have a difficult time playing unsuited weak hands like T8o and 87o so should I be folding these or incorporating them into a 3betting range?

Depending on stack sizes hot and cold equity is probably not the best measure to determine what hands to play and you're looking for individual hand equities not how range does vs range.

I'm not sure if most of the commercial software can do preflop range estimations even just hand vs range, but there are other posters that know more about that.

You most certainly shouldn't just flat as your only defensive strategy. The quality and flaws of your opponents will better dictate how you should defend.

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It's probably better to just watch training videos or talk to winning players in your game to find out what is recommended/standard, but I would think that - if it's a full ring game - you shouldn't defend very much in the BB vs UTG. Most offsuit hands apart from AKo/AQo will be total garbage, as they will realize their equity quite poorly OOP against a very strong/tight range.
I think it was Bob that suggested that vs a 3x open, he typically defends about twice as wide as the opener's range, but that's a very general rule of thumb. So if villain is opening 7%, you might be able to play 14% of hands profitably in the BB.

P.S. I don't play live, but is the rake in that game considered very high? In highly raked games, you should usually play even tighter. Save your wide blind defence ranges for battles with late position/SB players, and vs smaller opens. Calling 3x opens by UTG could put you in a lot of -EV spots.

EDIT: I can't say how useful or relevant this is for your game, but in a 100NL full ring game where UTG opens for 3x, this is supposedly the "optimal" BB strategy according to Snowie:



There are some fairly random 3-bets in there (the numbers), but Snowie thinks only 9.5% of hands are +EV in the situation I described. P.S. Snowie's chart is based on UTG opening 7.91% of hands. You should obviously deviate according to the looseness/tightness and indeed skill level of your opponent.

Oh one thing I forgot to mention is that you might start thinking about a defend hand as "can I lose less than 1 bb by doing something other than folding?"

+1 to Arty's post.

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I was looking for a baseline from which to deviate. I certainly don't want to fold way too much as my big blind will be too easy to steal. Obv this isn't the best example since under the gun is rarely/never(?) stealing but I wanted to understand a way to extrapolate this to defending from other positions and opening ranges.

Definitely not just flatting as my only defensive strategy. Average stack sizes are probably around 60-160bb in my game.

Don't get me wrong, IMO it is a smaller mistake to under-defend the big blind to make decisions easier postflop Oop. But if we are workingwith snowie and looking for optimal solutions, shouldn't we be trying to defend the optimal amount (not saying that what I suggested was optimal) regardless of how difficult it makes our later decisions?

I am not sure where our wires got crossed but I wasn't saying you should defend less than optimally.

What line you choose to defend with (i.e. call, 3bet, etc) will largely be based on your opponents tendencies.

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Striving towards optimal play is admirable, but bear in mind that many hands in your defending range will be very close to breakeven. In other words, they won't do much better than lose 1bb even if you play "perfectly". In that sense, you can reduce variance by playing even nittier. This is particularly the case because when you're in the BB, a key route to profit is to aggressively check-raise light. If you're not comfortable making post-flop moves with weak hands against a perceived tight player, you're literally better off folding pre-flop with "breakeven" hands like 65s or QJs, because you'll rarely be able to get to showdown with the best hand by check-calling. Many of the hands you defend with will have to be bluffed at some point.
I would note that many "fish" have a habit of calling pretty wide in the BB "because of pot odds", but they just want to try and make a hand. It's pretty hard to make a hand that will beat UTG's tight range if you're passive post-flop. Endbosses will defend fairly wide in the BB because of those same pot odds, but they have a higher expectation than the fish, because the endboss won't just be a calling station post-flop. He or she is going to try and win the pot with the worst hand at least some of the time.

EDIT: When you get round to building defending ranges vs late position players, you'll soon find you can defend (and also 3-bet) much more often. A hand like QJs would no longer be marginal, because the BTN will have so many hands you're actually crushing. Against UTG's narrow range, QJs only crushes JTs. It's in pretty bad shape against almost everything else. Versus the button, however, QJs would be both a clearly profitable call or a 3-bet, and many worse queens would also be +EV.

Hi mate,

Unfortunately there are some mistakes in this thread...

You say that you "need" that equity to make the call but that's not true. You have to consider all future cards and future moves to find your final profit figure. If you were playing purely for value, you still wouldn't need that much equity because by the river there will be more money in the pot. As we're not playing purely for value, we also have to consider what we make by making the opponent fold with our current action or any future action.

That isn't as hard to consider as you may think. You don't need to consider range vs range. That's a method made popular because it helps calculate GTO. At any given time you only actually need to consider your actual hand, not ur actual range, which makes the whole sum a whole lot easier.

Once I read through it became clear that you are wanting a GTO answer, and I specialise in exploitative theory so I'm not the best man to answer this thread. But yeah, this thread is very misleading to someone who doesn't want to play GTO, and so I figured its only fair to put it straight... In a bit of a rush, but hope that all makes sense.