You mixed it up. BTN is risking 2.25 to win (0.1 + 0.25 + 0.75) = 1.10. Now we ignore BTN´s equity (i.e. when called) and treat the situation as such that BTN only wins when we fold.

=> That is called auto-profit, when we fold often enough that BTN could 3bet with two blank cards - what we strive to prevent.

So we need to calculate the break-even-point where BTN makes autoprofit. As mentioned, BTN risks 2.25 to win 1.10. His odds are 1.10:2.25 or 0.48:1. That means BTN needs a fold in 1 / (1+0.48) = 67%. You want to prevent that so you have to fold less than 67% = defend more than 1 - 0.67 = 33%.

Considering that the blinds take a small share of the defense as well you can even defend slightly tighter. But as BTN regularly has equity with his bluffs you have to defend wider again.

I hope, I didnt confuse you. :)

Thanks a lot for clarifying this one for me.

To be honest ur way (=the right one) of calculations was my first version, but then for whatever reason i changed my mind and did the wrong one.
again.

I just wonder, why are we calculating 1.1 / 2.25?

since he's risking 2.25 to win 1.1 shouldn't we use the opposite one ?  2.25/1.1 = 2,045

A = 2,045 / (1 + 2,045) = 67%, so (1-A)% = 33% - ours MDF

hmm i guess since i've got the same results those ways are the same :o

BigFiszh is correct so far.

We can improve a little bit from his answer by making the following assumptions:

1. The CO opens a fraction N of hands.

2. Each player will defend with the top D (fraction) of hands, this range is the same for every player.

3. The are no card removal effect on the top D (fraction) of hands.

4. After one or more players defend, the BTN will always lose the pot.

Then the probability that neither player will defend, given D is:

1-F = P(SB folds, BB folds, CO folds) = P(SB folds) P(BB folds) P(CO folds) =

(1-D) (1-D) (N-D)/N

Hence F = 1 - (1-D) (1-D) (N-D)/N

Where is the frequency with which at least one player will defend.

For instance when the defense range is the top 5% (D=0.05) and we open 20% (N=0.20), then in total the three players will defend 32%. Which is very close to the 33% that we need, 5.1% will be enough.

If we open wider, 30% for instance, if we solve for F=0.33 with N=0.30 as a constant, we get D=0.068. Hence if we open 30% we need to defend the top 6.8% of hands.

Of course the assumptions are not very realistic. For instance it is likely that the CO will defend a wider range than the SB and the BB, since he has better pot odds and position.