Blind defence maths question

• Bronze
Joined: 29.01.2010
Playing NL25sh sb v bb

sb is a 24/20 40bb reg

steal: 38% (co: 38%, btn: 39%, sb: 38%)

vs 3bet: 47% fold, 26% call, 29% 4bet

He raises sb 65c to 75c (sb = 10c).

How many hands do we need to defend?

He needs us to fold >65% for it to be profitable {65/(65+35)}

=> we need to defend at least 35%. But because he's not opening every hand am I correct in thinking that we need to defend at least 13.3% (38 x .35)?

I'm unsure how to combine two...
• 9 replies
• Bronze
Joined: 06.06.2012
How many hands do we have on the reg? How accurate are your stats?
• Super Moderator
Super Moderator
Joined: 02.09.2010
Originally posted by holmeboy
He needs us to fold >65% for it to be profitable {65/(65+35)}
Since he raises 3 bb to gain 1.5 bb
He gets 1.5 bb profit every time you fold.

He is totally break-even if you fold 1/3 of the time, even if he gives up on the flop 100% of the time you call, and folds to your 3Bet 100%.

3 * 1/3 == 1 wins if you fold
1.5 * 2/3 == 1 loses if you call or raise

If you call or raise, then the hand equities come into the equation

For the fun of it, I put villain's 38% steal range into Equilab.
It looks like this:
44+,A2s+,K3s+,Q5s+,J7s+,T7s+,97s+,87s,A3o+,K7o+,Q8o+,J9o+,T9o

If you then use the hand range calculator tool, you find the range that gives you > 50% equity is something like this:

Equity     Win     Tie
SB     41.37%  39.48%   1.89% { 44+, A2s+, K3s+, Q5s+, J7s+, T7s+, 97s+, 87s, A3o+, K7o+, Q8o+, J9o+, T9o }
BB     58.63%  56.73%   1.89% { 55+, A5s+, KTs+, A7o+, KJo+ }

But there is more to it that that.
He plays w/ a 40bb stack. You don't have much in the way of implied odds.

But since he only needs you to fold 33% of the time, you can call or raise w/ the top 66% of hands (well, not really, but let's look at it for fun)

Equity     Win     Tie
SB     55.50%  53.79%   1.72% { 44+, A2s+, K3s+, Q5s+, J7s+, T7s+, 97s+, 87s, A3o+, K7o+, Q8o+, J9o+, T9o }
BB     44.50%  42.78%   1.72% { 22+, A2s+, K2s+, Q2s+, J2s+, T2s+, 94s+, 84s+, 74s+, 64s+, 54s, A2o+, K2o+, Q4o+, J6o+, T6o+, 97o+, 86o+, 76o }

Even with such a wide range, we're almost a flip vs a 38% opening range.
AND we have position.

If you drop your call 3Bet range to closer to his you get the added benefit that we won't steal so often, but at the cost that when he DOES steal it will be with better hands.
• Bronze
Joined: 29.01.2010
Suck at multi quoting so bare with me lol

Originally posted by elchipriota
How many hands do we have on the reg? How accurate are your stats?

Originally posted by VorpalF2F
Originally posted by holmeboy
He needs us to fold >65% for it to be profitable {65/(65+35)}
Since he raises 3 bb to gain 1.5 bb
He gets 1.5 bb profit every time you fold.

He is totally break-even if you fold 1/3 of the time, even if he gives up on the flop 100% of the time you call, and folds to your 3Bet 100%.
He's risking 0.65 to win 0.35. So if we play 100 hands and we fold 33 times he gets:

0.35x33 = +\$11.50

He's fit or fold so gives up and loses 0.65 once we call/3b.

0.65x66 = -\$42.9

He loses a lot.

But if we fold 66 times under the same conditions:

0.35x66 = +\$23.1

0.65x33 = -\$21.45

Therefore he needs us to fold 66%, not 33%. Right?
• Bronze
Joined: 29.01.2010
But that's if he's opening 100% of hands, which he is not.

So I know we can defend tighter and in doing so exploit his low steal frequencies. I'm wondering if I'm correct in saying I can defend ~13.3% for it to be a breakeven steal for him (preflop)?

And I know frequencies change. I'm using this as an isolated example to make sure I understand it properly
• Super Moderator
Super Moderator
Joined: 02.09.2010
Originally posted by holmeboy

Originally posted by VorpalF2F
Since he raises 3 bb to gain 1.5 bb
He gets 1.5 bb profit every time you fold.

He is totally break-even if you fold 1/3 of the time, even if he gives up on the flop 100% of the time you call, and folds to your 3Bet 100%.
He's risking 0.65 to win 0.35. So if we play 100 hands and we fold 33 times he gets:

0.35x33 = +\$11.50

He's fit or fold so gives up and loses 0.65 once we call/3b.

0.65x66 = -\$42.9

He loses a lot.

But if we fold 66 times under the same conditions:

0.35x66 = +\$23.1

0.65x33 = -\$21.45

Therefore he needs us to fold 66%, not 33%. Right?
Hmmmm,
OK, I mis-calculated.a bit (well, a lot ), but let me try again.
In the pot at the start are 1.4 bb = \$0.35
His bet is 3 bb = \$0.75

So he is risking 3 bb to win 1.4
that is, he is risking \$0.75 to win \$0.35
In your calculation, you say he is risking \$0.65.
It looks like you may be taking his original \$0.10 out of the mix.
It is already gone, so it is part of the winnings .

So if he is risking 3 bb to win 1.4
Then...
If you fold 68% of the time he has won:
0.68 * \$0.35 = \$0.24
and lost
0.32 * \$0.75 = \$0.24

Interestingly, if he drops his bet to 2.5 bb then you only have to fold 64% of the time.

I have a spreadsheet that calculates fold equity for semi-bluffs, and I tried to use that in this case, but it doesn't work quite the same, since SB is risking MORE than he hopes to gain.

So the conclusion is that if BB folds to steal > 68%, then it is instant profit, even if SB never plays back when 3Bet, and always loses when called.

And I just re-read your original post, and I'm a bit confused.
If he does indeed put in a bit of \$0.65, then your original calculation was exactly correct.

If he bets 3bb -- \$0.75 , then my corrected one is correct.

So what do you plan to do against this guy?
• Bronze
Joined: 12.10.2011
[QUOTE] So he is risking 3 bb to win 1.4 [/quote]He is actually risking 2.6bb because he has already put in the 0.4bb for the small bind. Since he already put this in the pot we do not count this towards the money he is putting in.

Just a small nitpick
• Super Moderator
Super Moderator
Joined: 02.09.2010
[quote]Originally posted by TinoLaan
[QUOTE] So he is risking 3 bb to win 1.4 [/quote]He is actually risking 2.6bb because he has already put in the 0.4bb for the small bind. Since he already put this in the pot we do not count this towards the money he is putting in.

Just a small nitpick [/quote]Once the money is in the middle it isn't his to "risk".
It is already gone, so if he wins, he wins it too.

If you subtract it from his "risk" amount, you must subtract it from his "win" amount, since if you consider it his while it is in the pot, then he is not winning it.

I actually put on my algebra hat, and worked out this equation:
W = P / (B + P)
W is the required win percentage to break even
P is the pot
B it the bet.

After doing all that, I realized the op had that exact formula in it.

There is a strategy article on this too -- one that I must admit I wasn't bothered to look up.

It is a gold article:
http://www.pokerstrategy.com/strategy/bss/1725/1/

All of their calculations include hand equity though.

Aha!
This is the article I wanted:
http://www.pokerstrategy.com/strategy/fixed-limit/1219/1/

EV = (possible winnings) * (probability of winning) - (possible losses) * (probability of losing)

So if you include the original SB amount in one category or the other, the result (should) come out the same.

I find it easier to think of the money as gone as soon as it is in the middle.
• Bronze
Joined: 12.10.2011
Exactly. Once it's in the middle, it's gone. That's essentially what I said

But you said he is risking \$0.75, but because of the SB that he posted, he's only risking \$0.65. That's what I said in my post. Whereas it's true, that his total bet is \$0.75, he is actually only betting \$0.65, because he already posted a \$0.10 SB.

But like I said, it's just a nitpick. Otherwise your calculation is perfect!
• Bronze
Joined: 29.01.2010
Awesome, glad to see a few people involved!

Originally posted by VorpalF2F
So what do you plan to do against this guy?
Once we work out how much we need to defend was hoping to get a few people involved it working out a range.

Off the top of my head I'm defending most broadways and maybe 3betting some hands like K4/K5s as bluffs w/blockers.