Defending our opens UTG, interesting results.

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Defending our opens UTG, interesting results.

'Okay so I'll briefly explain it from UTG.
We open a reasonable range of; 66+,ATs+,A5s-A2s,KJs+,QJs,J9s+,T9s,98s,87s,AJo+,KQo
which is 12.5%.

Someone 3bets us to 9x (we open 3x). They are risking 9 to win 3 (our bet) + 1.50 (the blinds).
This means they have that if we fold 9/(9+4.5) or 63%, they automatically profit with any two cards. Which is bad for us, it means they are exploiting us.

So we set about defending roughly 37% of our 12.5% opening range. This is 0.37*12.5, 4.625%.

Right, now we'll assume that when the 3bettor 5bets all in he has roughly 30% equity with his bluffs. He invested 91bb extra to 5bet bluff, so his net loss when he 5bet bluffs and we call is (approx) 91-60=-31

We 4bet to 20, then he 5bets he is risking 31(the amount he loses when we call) to win 20 (our bet)+9 (his 3bet) +1.50 (the blinds). This means if we fold more than 31/100+20+9+1.50, 24%, he auto profits. So we need to 4bet with a 76% value, 24% bluff ratio.
0.76*4.625=3.515. This actually equates to AQs, JJ+, AKo roughly.
We then balance this with 24% bluffs 1.11%, roughly A2s, AJs, ATs, KQs.

and yada yada your range is protected perfectly.'

I recently wrote this for someone, and having never actually done the maths myself (lazy I know) was fairly suprised by the results. Basically all the articles I read in the past were fairly dated and based their ranges on bigger 4bets and 3bets. The implications of a smaller 3bet are fairly dramatic, especially when people 3bet to 8 or 7.5 even IP nowdays.

Could someone check my working, and also would anyone reccomend a different strategy, maybe involving calling? Basically would appreciate some opinions because I was pretty shocked we have to value shove AQs to protect a 12.5% opening range really.
Thanks and gl.

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