Thursday, June 14, 2007

Sit N Go Strategy - Equilibrium Push / Call Ranges And Why They Matter To You!

Inspired equally by Sheets' SNG Strategy videos on PxF and by EastBay's lecture on HU play in SNGPT this post will look at equilibrium points at the bubble of SNGs. I am going to assume some familliarity with ICM / $Equity and All-In or Fold Sit N Go Bubble Strategy... if you are a new reader who is not yet aware of these concepts then please take a look at the 'List of Plan3t Gong Articles' in the right hand side and check out the Bubble Play / ICM Listing.

Soooo, what are we talking about with equilibrium?? First then a mathematical example - and then a quick discussion on how this could improve your SNG bubble strategy at whatever level you play.

Here is our example, newly arrived at the bubble equal stacks of 3000 and blinds of 200/100(Ante 25)- folded to the Small Blind (SB) who estimates that the Big Blind will only call his shove with 66+ ATo+ (top 8% of hands) - what can the SB Push? Ahhah, trick question! Of course Poker ICM followers will know that this becomes an 'Any-2' shove - that is the blinds will be won so often (along with a % of showdowns) to make it profitable for the SB to push all in with any-2 here...

Now we take something important into account - the calling range of the BB player assumed that the SB was pushing a 'reasonable' range. What if the BB somehow 'knew' that the SB was pushing any-2 cards? What does this do to his potential calling range?? Well it now expands a bit - BB can profitably call with top 10% here.

But wait - if SB knows that BB knows he will push any-2 and thus call with top 10% would it still be profitable for the SB to push with junk?? No - if the BB is calling top 10% then the bottom 20% of holdings are no longer profitable to shove in this situation, the SB can still shove 80% here profitably though.... in which case what can the BB now call with?

Last time through - if the SB shoves top 80% then the BB calls with top 9%....

We could go on, what has happened is that we reached an 'equilibrium' point in the push / call dynamic. Each player adjusting their range for what they anticipated the adjustments of their opponent would be to their default range. We got to 80% / 9% here but it is easy to imagine how adjusting the numbers to suit different situations could lead to different results.

So the next question is whether this has any practical application for low and middle-limit SNG players??

Absolutely - the application is the adjustment of your pushing and calling ranges when you perceive that your opponents have an understanding of ICM / Bubble play. If you know that your opponent is pushing any-2 cards into you then you must call correctly against that range. If you call correctly against that range in one game and then meet that same opponent again there is a strong chance that your opponent will realise that you call correctly and tighten their range a little to compensate.

At the lowest limits opponents will not be thinking like this - however you can still use the same model to assess what happens to their range if you continue to push. You will find plenty of 'horrible' calls at the lowest limit SNGs - since you can not control them the only adjustment you can make is to adjust your own pushing range to have a positive expectation against their calling range.

Recommend that all serious SNG players should have an ICM calculator such as SNG wizz or SNG Power Tools - once you have learned about equity models and ICM your game can move to the next-level (which strangely enough is knowing when to ignore the guidance given by ICM). My thought is that if you ignore ICM or treat it as some mathematical nonsense you are giving up an advantage to your opponents - understand it first, learn when not to use it second.

GL at the tables, Mark

PS: Couple more articles over at SNG Planet including one on using the SAGE poker system when heads-up at the end of a SNG Satellite Qualifier... Best Poker Tournament Strategy

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