4-bet and 5-bet defense frequencies

Red Chipper Posts: 9 ✭✭
in CORE
Hi everyone, loving CORE! I'm on the lesson about 4- and 5-bet ranges, and I'm confused why Adam suggests such high theoretical defense frequencies. He says:
• "We're expected to defend 55% of our 4-bet range against a 5-bet"
• "We are expected to defend slightly under half of the time against a 4-bet"

I'm curious where these numbers are coming from, even in theory. I've tried to work out some basic math and here's what I've come up with.

Starting with 100bb stacks:
Pot is 1.5bb (blinds).
UTG open-raises to 3bb.
Hero in the CO 3-bets to 9bb. everyone else folds.
UTG 4-bets to 22.5bb (standard 2.5x)

If UTG is bluffing, he needs Hero to fold 22.5/36bb=62.5% of the time to break even. Doesn’t that make Hero’s minimum-defense frequency 37.5%?
Or should this be calculated as UTG risking 19.5bb instead? Given he already put 3bb in the pot, he's now risking 19.5bb to win 36, making it 55% to break-even, and thus giving a 45% MDF to our Hero, close to what Adam is saying.

Based on my math, the same applies to defending against a 5-bet. If Hero 5-bets all-in, he’s risking 91bb to win 91+36=127bb, meaning he needs to generate folds 91/127=72% of the time for automatic profit. So UTG only needs to defend his 4-bet range 28% of the time to remain unexploitable by bluffs (not the 55% suggested in the video).

What do y'all think?

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• Posts: 3,654 -
edited May 21
I shared this post with the brains over at HQ and they took some time out from the CORE 2.0 roll out to share their thoughts. This is a summary:

Part of the issue is that two concepts are being mixed up.

-MDF (minimum defense frequency)
-Optimal range / GTO

MDF helps identify auto profit / loss but doesn't help identify correct plays in this context.

GTO (what Adam outlines in the video) is about constructing the entire range to avoid exploitation / maximize profit.

On the 5-bet portion, this gets even more muddied because his MDF simplified model ignores the fact that bluffs have all-in equity whereas the simplified model makes more sense with 4b-bluffs (although still overly simplified).
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• Red Chipper Posts: 9 ✭✭
Thank you! I appreciate y'all taking the time to look into it.

That distinction makes sense to me. I've started simultaneously making my way through Janda's Applications of NLH and it turns out he has a chapter early on where he derives very similar numbers.

It seems a lot of it comes down to these key takeaways:
• Like you said, MDF only describes auto profit/loss. And most importantly, MDF doesn't take into account the distinction between raising as a defense and calling as a defense.
• The numbers that my math comes up with apply if the strategy is to defend only by raising. Janda goes into some detail about this but convinces me that this is not optimal--we need a calling range as well.
• Having a calling range certainly expands the portion of our range with which we can defend profitably. Just how much we can expand is difficult to calculate precisely, because we don't know what our average EV is when calling (to do so, we'd need to solve the game of poker). But throwing around some reasonable estimates for average EV when calling can give us a decent sense of how much more we can expand our defense range.

Hope this helps some future numbers nerd who encounters this chapter and is also curious!

Thanks again for all your help!
• Posts: 3,654 -
Thanks for that addition, @sonchosmilax, the depth of this game even in ostensibly simple situations never fails to amaze me.
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