[pzhon]

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Come up with relevant calculations which support your side, or give up.

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First of all, too many nits play tight and get blinded away waiting for big pairs,


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Who cares? That's not something I have advocated, so why bring it up? That's not what we are talking about at all.

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That being said, why wait for ace – x to jam, as the % increase is de minimus.

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No one said to wait for Ax to push when you are short-stacked. In fact, people are going too far in the opposite direction, saying they would panic and open-push any two cards, while pushing with 32o is massively -EV in many situations, such as when your M=2 and the big blind will call you with any two. The question is whether you would prefer to have a hand like 98o or a hand like A7o when you push, or, if one of those is marginal, is the other a clear fold or a clear push? The answer is that A7o is much stronger, and it is correct to push A7o at times when it is correct to fold 98o, and the reverse is almost never true. If you favor 98o over A7o, your intuition is wrong by a lot.

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Let’s take the two jamming ranges, and compare them to 2 calling ranges.
A2-a7 vs. pairs 5s or better, and ANY combo of face cards (loose). This is a likely calling range for a larger (not massive) stack.
A7o-A2o vs. 55+, ATs+, KTs+, QTs+, JTs, ATo+, KTo+, QTo+, JTo 40.693%
98s, 87s, 76s, 98o, 87o, 76o is 33.863%

So ace rag is 7% better.


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A better way to look at it is that getting called with Axo is only about 57% as expensive as getting called with you have 98o. Again, you have overlooked that Axo will be called less frequently.

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But let’s look at a more reasonable calling range, assume stacks are more even. Drop all face cards other than pairs 55+ and Ace – 10.


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That's not more reasonable at all. Most of the time, KQ preflop is about as strong as AJ, unless you assume someone has a range extremely heavily weighted toward Ax and not hands like KJ, KT, QJ, or QT. Yet you are using a range which throws away KQs but plays ATo. That appears to be designed to favor 98o over Axo.

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98s, 87s, 76s, 98o, 87o, 76o drops to 31.999%
BUT A2 – A7 drop to 27.967%,


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I get different figures from Pokerstove.
76s-98s, 76o-98o against 55+, ATo+, ATs+ has 32.066% equity.
A2s-A7s, A2o-A7o against 55+ ATo+,ATs+ has 29.216% equity.

However, even in this contrived example, it is still better to push with A7o (29.0% when called) than with 98o (32.4% when called). That's because A7o gets called only 102/1225 ~ 8.3% of the time instead of 118/1225 ~ 9.6%. While A7o loses slightly more when called, getting called less frequently outweighs this (with stacks less than 12.7 BB) even against this contrived range. So even when you tried to stack the deck in favor of a connector, A7o was still slightly better. Against a more normal range, such as the first one you tried, A7o does much better than 98o.

In cash games, if you want to balance your 4-bets with AK, KK and AA with a few weaker hands, it is often better to add hands like A7s to your 4-betting range rather than 98s. A7s is very slightly worse when called by a range like QQ+, AQs+, AKo, but it blocks many of those hands, giving you a lot more folding equity, while 98s blocks nothing.