Easy to remember push/fold/callpush table/formula

Question

I've tried to generate a push fold table that's easy to remember in my head. This is what I've got so far:

Take the highest card:

A = 10
K = 8
Q = 7
J = 6
T = 5
9-2 = Face value / 2

Add the following:

4 if the next highest card is one lower than the highest card (and at least 4).
3 if the next highest card is two lower than the highest card (and at least 3).
2 if the next highest card is three lower than the highest card.
1 if the next highest card is four lower than the highest card.

Add one if suited.

Pairs are just twice the value number + 4, i.e. TT = 14.

This is pretty quick to calculate in my head.

I push in the small blind (assuming no antes) in these situations based on stack size:

2BB: 5
3BB: 6
5BB: 7
10BB: 8

I push on the button on the above, but add 3:

2BB: 8
3BB: 9
5BB: 10
10BB: 11

Cut off is one higher again:

2BB: 9
3BB: 10
5BB: 11
10BB: 12

And any other position:

2BB: 10
3BB: 11
5BB: 12
10BB: 13

I remember (8,9,10,11) for the button. Before each hand is dealt, I look at my stack size, and pick either 8,9,10,11 depending on that. I then take away 3 if I'm small blind, or add 1 if I'm cut off or 2 otherwise. That gives me a number. I can then look at my hand and quickly calculate it's number to decide whether to push or fold.

When it comes to calling pushes, I will call at 2BB based on the same conditions that an opponent would push on (assuming they're me), with 3BB I'll call if my hand is one better score than what my opponent would push on, and with 5BB or greater I'll call if my hand is two better than what my opponent would push on (always assuming they're using the same table). So if my opponent pushes from early position and I've got 10BB, they'd push on 13 so I'll only call on 15, which is JJ or AKs. The effective stack size here is based on how committed I could be to the pot, if someone pushes with a small stack but I've got a large stack AND I've got people to act after me I'm generally more cautious and push up the effective stack size depending on the stack of those after me. I also generally 1 for each flat caller, and with a few callers and late position with marginal pushing hands I'll sometimes call instead.

All these tables assume a final table situation with a 50/30/20 payout. Take away 1 if you're heads up or in the money in a three way 50/30/20 situation. Be more cautious as approaching the bubble (perhaps add 1), particularly when calling. If your opponent understands the bubble, don't be more cautious pushing, but if they don't (and are likely to call) don't push as much near the bubble.

Anyway, I know this is just a guideline, and I've made these numbers by plugin some scenarios into the Nash generator, but I've been noticing some situations where my numbers are a bit off. I was wondering if anyone else has a easy to remember and calculate during a live game push/fold/call table/formula, because I feel mine is far from perfect and there's probably one out there that's either easier to remember, more accurate or both.

I understand adjusting to your opponents is important, but I feel it's really important to have a baseline. I've made one up myself which is easy to do during a live tournament but I have a feeling I'm re-inventing the wheel and someone has probably done a better job at it than me.

Answer 1

A push/fold table can be an unexploitable strategy in short stacked heads up play. It has been solved using game theory, for example in Mathematics of Poker. There exists easy to remember approximations of the exact solution. One of them is SAGE (sit and go endgame system). A search on that will give you many good articles explaining it, but the short version goes like this: Calculate the Power Index (PI) for your starting hand.  PI = face value of top card * 2 + face value of bottom card Add 2 if suited Add 22 if pair (i.e. always push)

E.g QTo = 12*2 + 10 = 34 86s = 8*2 + 6 + 2 = 24

In the SB, if PI >= (number of BB in shortest stack + 19) then push all-in Call in the BB if you have 4 higher in PI than is needed to push in SB.

This strategy is unexploitable for stacks ~<= 8 BB, a common scenario at the end of tournaments. Unexploitable means that even if you tell your opponent that you are playing this strategy, there is nothing he can do other than play the "call if PI is 4 higher"-response. Any other strategy will have lower expected value.

Note that unexploitable does not mean best. If you have an edge over your opponent some adjusted strategy might have higher expected value, but leaves you open to exploits (e.g. your opponent plays Sage). In practice it is a good baseline strategy. Stick to it if you feel you're out of you league. Make small adjustments if you feel your opponent doesn't have clue.

As for a table driven strategy for non-short-stacked multiplayer tables, don't do it. It is exploitable and the play in those situations depends on far more factors than what can be captured in a table.