# Theory - BTN vs Blind Defense (Dynamic GTO)

Scenario:
BTN raise to 2.5x, SB folds, BB 3-bets to 9x...

Stats on BB:
Fold in BB vs BTN steal = 79%
3-Bet in BB vs BTN steal = 8%
Call in BB vs BTN steal = 13%

Stats on SB:
Fold in SB vs BTN steal = 82%
3-Bet in SB vs BTN steal = 18%
Call in SB vs BTN steal = 0%

Given that blinds are folding more than 62.5%, we are raising any two cards.

To keep things realistic and simple, let's pretend that villain sees a 50% BTN steal in his HUD (merged across all situations) and he doesn't realize that Hero is actually opening any two in this particular situation.

If villain's 3-bet gets a fold more than 67% of the time, then he can get away with 3-betting any two cards. So based on GTO, we should be defending 33.3% to protect ourselves. Given that we'll be flatting some 3-bets and 4-betting, let's bump that number up to 40% as villain will get to realize some equity with his bluffs when we flat his 3-bet.

40% of 50% is 20% of hands.

Now, in practice, I feel like this is sub-optimal (pun intended) as we'd be defending very wide against a very narrow 3-bet range.

Discussion point 1 - In my mind, it makes no sense to defend this wide against such a tight player. Even though he could 3-bet bluff us profitably with any 2 cards in a vacuum, in the long run he's simply folding way too often and letting us steal very profitably. So when he does 3-bet us, I think that we should design a 4-bet range and a flatting range while ignoring that according to GTO play, we should be defending 40% of the time (or 20% of hands). In essence, it makes more sense to me to view this as a new "game". Game 1 was stealing the blind. When he 3-bets 8% of the time and we have a weak hand, he wins that game. However, we know that it is +EV for us to keep playing this game as often as possible. Now that he 3-bet us, Game 1 is over and we're on to Game 2. Game 2 is now finding a balanced defense strategy against an 8% 3-bet range from BB vs BTN. Thoughts?

So if we assign him a 3-bet range as such:

So from here, I'm getting back to GTO because it makes sense to me here (but not earlier). If we 4-bet to 21bb, that means that we are risking 18.5bb more to win a 12bb pot, so if villain folds more than ~60% of the time, we can 4-bet any two cards, so that means villain's MDF against a 4-bet is to 5-bet at least 40%.

0.40 x 8% 3-bet range = 3.2% range ~{JJ+, AK, AQs}

The only hands with +50% equity against that range is KK+. So for our 4-bet value range we include KK+ which is 12 combos. I include 12 combos of AJo as 4-bet bluffs to reach a 1:1 value:bluff ratio.

So we have a very narrow 4-betting range of KK+, AJo. In other words, we're 4-betting 4% of the time we get 3-bet. Now, onto the 3-bet flatting range.

Discussion point 2 - This is where I'm having trouble and where I'm second guessing myself. I included a potential 3-bet flatting range and I'm curious to get some opinions on it. What hands would you include that I didn't? What hands would you exclude that I included?

We are getting 6.5 : 12 on a call (we need 35% equity). The weakest hand in our flatting range is KQs, which has about 43.85% equity against that 3-bet range. hands like 66-55 have more equity but I feel they have playability issues as we'll have trouble getting to the river and showing our hand down most of the time we don't hit a set.

Thoughts?

P.S. Are there any recommended videos specifically on flatting 3-bets after stealing from the BTN/SB? New to RIO so would appreciate some recommendations on this topic.