assuming you only shove or fold to the 4bet (although flatting seems like reasonable option though, folding on flops where you don't hit a pair or a draw) :

folding = 188.46 - 9.50 => 178.96

5b/call = (188.46-107.5)(x) + (188.46+107.5)(1-x) = 178.96
where x is the % of the time you lose
x = .544
so you need 45.6% equity to stack off

assume he is 4betting linear
you have the right equity when he gets to 4betting wider than the top 11%
how wide should we assume he is 4betting?
think this might be a good situation to use Bayes theorem.

since the main hand you are worried about running into is AA (because you have 49% vs top 11% excluding AA and only 31% vs AA) we look at bayes theorem in reguards to AA.

imputs:
- if he is opening 50% and you hold an A he has 3.5% AA hands prior to 4betting
- he has 4b 2/6 time
- we will assume he is always 4betting when he has AA
output:

Probability of holding AA after opening then 4betting = (1 * .035) / .33
=> 11%

The 11% range that you need him to have to stack of profitably has AA 20 % of the time (23% when you don't block an A) almost double as often as we now assume he actually has AA.
Note: Villain having an observed 4b % of 18% would put him at the 20% AA threshold

So we should be alright to stack off !!!

https://en.wikipedia.org/wiki/Bayesian_inference

Yeah this is a shove. Don't think it's close. You block AA and KK and dominate all the stuff that is relatively overweighted as a result.

Also I trust steds math tho I only skimmed it :)

Thanks sted, thanks Tom, that's the beauty of this site, you post a hand, you have Mr Chambers or Mr Galfond commenting on your hand :) And you have subscribers performing in-depth analysis. I'll have to read carefully the math you perform, but Anyways, real added-value from both of you guys, thanks a lot :-)

One beginner question here : when we hold an A, a K, or both blockers, how much do we reduce the likelihood that villain holds AA and KK?

Opponent is dealt pocket pair 2.5% of the time (technically 2.57% if you count trips and quads). If you do not have one, his dealt frequency shifts to just under 3.0%. If you do have one it shifts to 1.5%. Same works for flopped cards (so dealt frequency of a set, ignoring pre-flop weighting of the various pocket pairs, is 1.5%. In practice, % of range that is AAA-QQQ is much higher for a raiser, as well as KKK-QQQ for a caller). Both in our hand and on the board, or two in hand or two on board, reduces dealt frequency to 0.5%. Again pre-flop range weighting applies.

Interesting,

It's basically similar to Holdem then : holding a blocker reduces by c. 50% the frequency of our opponent holding the pair that we block.

So am I correct to say that :
- when we hold no Ace no King (ex: 9876) our opponent has 6% total chance of holding AA* or KK*,

• when we have one A (Axxx) he has 4.5% of holding AAxx or KKxx (1.5% AA and 3.0% KK)

• when he have both A and K he has 3.0% chance of holding AA or KK (1.5% each)?

If I understand it right, when we don't know any card of the deck (52 unknowns), any pair (ex: AA) probability is 2.57%, and when we assume to know 4cards (ex: our cards, and we want to assess Villain's probability) the probability of Villain holding any pair (ex: AA) is 3.0% (48 unknown cards)?

This are probably very basics combinatorics questions, but I'm learning the game, so it helps.

I'll study with very deep focus your combinatorics section :)

yes you are right on all those.

fwiw I always use the 2.50% number, not 2.57%. AAAx is occasionally playable but no other trips hands ar so it's better to just drop them.

hang on. I'm a little off here. Well. Some clarity is needed.

If all we know is the flop, and it has an ace, AA** is 1.49%. With no ace it is 2.89%
If all we know is our hand, and we have an A (so this is for pre-flop blocker 3b/4b decisions), it's 1.55%. And 3.01% with no A in our hand.

But for all practical purposes both are ~1.50%/3.00% and that is a really convenient trio of numbers to rmember (1.5/2.5/3.0)

If we know hand and flop and there are 2/1/0 known aces it's actually 0.61%/1.76%/3.41%

All these are based off the 2.57 number.. once we add a blocker that added trips frequency goes way down, from .07% to like .01-.02. With no blocker it's more like .1, so it does matter. If all we know is the ace-less flop I think his non trips AAA is like 2.80.

In all cases, again, you need to adjust for preflop range weighting!

Thanks Tom for that much detail, it made me work again on combinatorics. This might be "obvious" for some players, but I just want to say that to me (and probably to other players as well), the real added value of training sites like Runitonce not only comes from pro's videos, but also a lot from Pro's commenting user's histories and adding input. Again, I do think it matters a lot. So again, thanks for the input Tom.

Thanks Bluechip. I like being part of the community and try to respond as many places as I can. Plus I just like doing it/poker. I actually have a handful of threads noted where longer answers are needed that I keep meaning to come back to.

fwiw RIO leadership told me off the bat that part of the job was participating in our video threads and the forums. I think that's part of why you see so many pros posting.