Shoving with Ax

Remember my previous post about the Pair Principle? Here’s another one from Phil Gordon’s toolbox. It is called the A-X rule.

The rule itself is very simple:

If your ace kicker card has a higher value than the number of players that are left to act after you, you are a slight favourite.

It sounds too simple, right? It is, and in my view its use cases are limited. I would use it only in a regular paced game with less than ten blinds left in a shove or fold situation.

What’s the math?

This time we don’t need to make any calculations during a hand. We only need to convince ourselves that this might work.

I tried this with an equity calculator and this is what I found out:

Equity against one player when holding… A2o is (52%), A2s is (56%)
Equity against two players when holding… A3o is (35%), A3s is (39%)
Equity against three players when holding… A4o is (27%), A4s is (30%)
Equity against four players when holding… A5o is (20%), A5s is (25%)

Let’s increase our kicker value by one and see what happens.

Equity against one player when holding… A3o is (52%), A3s is (57%)
Equity against two players when holding… A4o is (36%), A4s is (39%)
Equity against three players when holding… A5o is (25%), A5s is (29%)
Equity against four players when holding… A6o is (20%), A6s is (23%)

Very little change to be seen. Now we kick our kicker once more.

Equity against one player when holding… A4o is (57%), A4s is (59%)
Equity against two players when holding… A5o is (35%), A5s is (38%)
Equity against three players when holding… A6o is (25%), A6s is (30%)
Equity against four players when holding… A7o is (21%), A7s is (26%)

Since we don’t know our opponents cards we simply divide the rest of the equity with the number of players left to act.
For example:
holding A3o against two opponents leaves (100-35)/2 which equals 32.5% equity for each opponent, or…
holding A5o against four opponents leaves (100-20)/4 which equals 20% equity for each. At worst it’s a coin flip.

Would I shove?

The A-X rule has some merit to it although it has been criticized around the internet for being a crude tool. I haven’t checked but a solver might give a different opinion about these shoves.

Against one or two players with just few blinds in front of me, sure I would shove. Anything more than that starts to feel tricky. A low pair could simply beat us if our luck runs out. But as always, everything in poker depends from different variables in our table which we need to take into account.


Well, Phil Gordon’s A-X rule breakdown is indeed eye-opening.
It actually sounds easy, but of what ive learned until today, poker is never that simple.
Crunching the numbers, sure, it gives us a glimpse, but relying solely on it feels like playing with fire.
I’d tread carefully, especially when there’s more than a couple of players in the mix or when stacks aren’t too deep.
For me, poker is all about adaptability, so while it’s a neat trick to have up your sleeve, I wouldn’t go all-in on it just yet.

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Fun concept! I think I would only use it when in the CO, Button, BB, or SB positions and under 10 BB stack. I like how you did the math and how little difference it really makes when you bump it up.

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I don’t think your calculations are very relevant, I have to say :slight_smile:

What matters is not our equity against a full range of random hands, but against the holdings that are likely to call our shove.

A4 is better than A3 because we are now live against 33 instead of dominated, for example.

The margins will still be slim as there really isn’t too much difference between the wheel aces, at the end of the day. But slim margins are what we’re parsing here, after all!

I’m just glad, I’m not a professional Poker Player, cuz I’d be Broke lol. But always good to hear the strategies, I always look forward to having fun with the great folks, here & gl to all!!

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Thought you chopped with an axe not shoved lol

I have to disagree with you, but it’s true the math part is not that important.
The math only shows that this works in theory.

But this is exactly the point of this tool. We can’t possibly know what players who are left to act after us might be holding. Therefore the assumption is that it could be anything, and because of that this tool takes into account the full range of hands.

But as I’ve said, it’s a crude tool and not for every occasion.

Nice rule . I think I have read about it sometimes in the past . I might try to apply it in action , see if it works , try maybe in some freerolls or very cheap games . Ofcourse the Ax with x<8 , non suited , I am afraid ti sjove even with low stack , even with two or three players . At the most important moments opponents tend to wake up with big ace at later streets to bust my ass out . Almost every time lol .

We can’t know what our opponents will have, but we can know reasonably well what they are likely to call with.

For example, including 10-3 offsuit is only marginally relevant, as most players in most configurations aren’t even considering calling an all-in with that hand (unless it’s like, 1bb type situation)

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Hi, Naforole.

It looks pretty close to GTO Charts when you are around 10BB deep.

It seems like Phil Gordon overestimates Ax off suit and underestimates Ax suited slightly.

Trying to solve things with math can of course be an interesting challenge but for most players today: just look at some push-fold charts and make a little adjustment if you think the players behind you are tighter or looser than GTO.

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Actually the rule itself doesn’t mention anything about the suites.
The difference comes when we run these through an equity calculator.

Thankfully, being useless at math, it’s reassuring to know the A-X rule, like most mathematically calculated hands, can be vulnerable to the bluff calculator?


hi folks,

i have to say that the last words by naforole are the best of this topic because i wouldnt give to much impact to this theory because every A-x combi which is also off suited and lets say A-9 and under they arent so strong as they seem like.
Naforole said it by himself a weak pair could beat us holding this hand, i also recommend against 2-4 villains dont play it too aggressive because 1 or 2 could also hold an A with a better kicker than you.


Yep only if I have to, lol:)

I must respectfully disagree with this rule. I really don’t like it at all.

Personally, I think that today there are many available tools and resources to understand why we are shoving some hands or not. For example, any basic sit and go or tournament course will explain mathematically why we can shove a lot of hands from small blind vs. big blind, or why it is better to shove some hands from certain position while would be bad to shove others.

While Phil Gordon may have had all the good intentions doing these shortcuts, they should not be taken that seriously. Better study and understand the theory. Let these shortcuts be just a piece of poker history.

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I agree with what some others said.

Poker is way way complicated as a game to follow rules set in stone. Yes, they have their place in your arsenal, but I think we should see each spot on its own and act accordingly. Also I don’t know if Phil Gordon’s rules are relevant in today’s online poker arena. But for complete beginners, this rule is a good base. And always try to apply some reading to your opponents. If someone is very tight, then the A4o or the A3o aren’t so good.

I agree with everything except the last part - if the question is where we can shove profitably, our downstream (in position) opponents being very tight makes it MORE profitable to shove a weak ace, not less. They’re more likely to fold.

I dont know about this rule. The last time i heard of phil gordon was long long time ago. Actually the first poker book i had and read “beginner strategies for poker players” was from him. That was like 15 years ago.

Sure its an interesting concept with around 10BB but in sone cases im shoving my ace anyway, no matter if there are 3, 4 or 5 opponents to act behind me.

This rule is interesting, it helps a lot… But in fact, it is not decisive for winning a hand. Maybe manage to steal the blinds.

Less than 10bb and in some positions from CO I find it more interesting to use. Hope no one pays with better hands :grinning: