Friday, October 08, 2004


Short-Stacked Mathematical Approach (2)

OK. Using a computer program to simulate the calculation below for various hands, positions and stacks, we can put together a table to help us determine whether to commit our chips in any short-stacked situation. Let me clarify that these results apply to the situation where everyone in front of you has folded their hand. Even if someone has just called the blind, that's different, and we'll deal with that later on.

Here are the four categories of hand we are going to consider in our first table :

- A good Ace : A7, KQ
- Any Ace : A2, KT
- A good King : K8
- Any King : K2, QT

The maximum stack size you need to commit in various positions is as follows :

Players yet to act

A7, KQ.............> 20 SBs............> 20................14...................10
A2, KT.............> 20...................14................10....................7
K2, QT...............10....................7.................7....................7

It's vital to remember the correct sense. If you have K8 with 3 players behind you, you can commit with 10 SBs or less. If you have more than 10, you should fold.

Notice how if you fold, then next hand you will need a hand that is one "level" stronger. With 10 SBs in front of you, on the button you need K2/QT. If you don't find it, next hand you need one level up, K8. Next hand again you need A2/KT. If you find yourself "in between", just adjust accordingly. For example, with 12 SBs on the button you need something halfway between K8 and K2 = K5 (or QJ).

Points to remember :

- A2 is about equal to KT. It's better than any smaller King. If you can commit with K8, you can also commit with any Ace
- Being suited is worth adding on 1 or 2 SBs (to the maximum requirement) - basically it might swing a close decision towards committing
- Any pair is basically good to commit from any position with 15 SBs or less. Smaller pairs in early position are a little marginal, and can be passed if you like, but there's nothing wrong with moving in with any pair when first to act with 15 SBs or less. AT or better is also good from any position (albeit slightly marginal with 14-15 SBs in early position)
- Committing can mean going all-in if you like, in fact that's probably best if you're not sure. If you prefer, you can move about half your stack in with the intention of calling/betting the flop irrespective. On some tables this might work better (if any opponent(s) might make a bad fold on the flop). But if you have less than 12 SBs, just go all in, you don't have enough chips to get fancy. And DO NOT get half way in and then fold the flop. If you think you might be tempted to do this on certain flops, then avoid the problem by once again going all-in pre-flop
- With less than 8 SBs, you must try to play a hand before taking the blinds. Now any pair, Ace, King, Q8, Q5s, J9, even small suited connectors are good. Position is less important now - in late position you have fewer potential callers, but in early position you have less time to make your stand, and these pretty much cancel out
- In the small blind, any above-average hand is good, which is the same range of hands as in the previous point. The small blind is the best position to bet half your chips instead of all of them, because you get to act first on the flop, and you can bet out. If I have 10-15 SBs in the small blind and I'm going to play, this is what I'll do. Obviously you call if you are reraised pre-flop.
- If you have 13 SBs in the small blind, or 10 SBs in any other position, or less, then you can raise with any 2 cards if there is at least a 50% chance all your remaining opponents will fold. The calculation is similar. Even with rags you are usually only a 2-1 dog when called (sometimes 5-2 and only occasionally in trouble against an overpair).
- If you prefer, you can apply the short-stack rules with up to 20 SBs. This might be a good idea if you are surrounded by tougher opponents. A2 on the button and A7/KQ with three players to act are ok with anything up to 22 SBs. Small pairs and AT should be passed in early position, but 77/AJ are good from anywhere with 20 SBs or less.
- These are guidelines. If you can pick up any tells on the player(s) behind you, factor those in. If someone is obviously going to pass, you can reduce the number of players to act by one. If someone's obviously going to play, you have to tighten up quite a bit, and basically use your common sense.
- I nearly forgot about antes. If there are antes in play, you can basically add them to the requirement in the table. If the antes total 2 SBs, then a "7 SB" hand in the table becomes a "9 SB" hand. In practice I prefer to use the antes as a "tiebreaker" in a close situation. If it would be close without the antes, I'll go for it. Antes also need keeping an eye on if you are close to "must-move" time. You might have more than 8 SBs now, but if the antes will reduce that to less than 8 SBs by the time the blinds arrive, you must try to move this round
- Similarly, if the blinds are about to go up, this can throw a spanner in the works. It's sometimes better to figure that you need at least 5 SBs next time you're on the button after taking the blinds. I can't cover all eventualities so just be aware when the blinds are going to increase, and to what.

I must stress again all the above only applies when no one has entered the pot in front of you. That's probably the most important point to remember. And that's about it. Everything else follows on from this basic strategy.

Might I suggest you retitle this post "A tribute to Paul Samuel"? Whilst the substance of yours is far better the form is disturbingly similar - I got lost in the tabulations and figures. Perhaps you could summarise your results and provide a link to the maths to make for easier reading? Casual observers might be less deterred. OTOH perhaps unlike me you actually have better things to do with your time.

Aifter awwl, Ah's jus' a doggon simple farmhand a learnin' this here card game that ma pappy lawst the rainch awwn. Ah needs some straight tawlking, boy!

Redneck regards,
Richard (who just proved his point on having nothing whatever to do)
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