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The SAGE System in Heads Up Poker

Say you manage to get to the final table of a large field MTT and get into a heads up situation. It can be a pretty difficult situation to master especially when your stack is only 10BBs deep.

But what if I told about a system that allowed you to play HU in a mathematically un-exploitable way? Well, introducing…the SAGE system!

(SAGE stands for Sit and Go End Game System).

The SAGE system was introduced in Lee Jones’ ‘Winning Low Limit Holdem’. It outlines how to play HU poker with less than 10BBs in a mathematically un-exploitable way. It uses power rankings on the cards that you’re dealt, letting you know when to push/shove.

First, let’s look over the conditions for when the SAGE System can be used:

• Heads Up at the end of a No-Limit Holdem MTT or SNG
• One prize
• Average stack-size is less than 10BBs
• The SB shoves all-in from the button. We have to make a decision whether to call or fold.

So, what is this SAGE System?

If there are any economists reading this than you should be familiar. The SAGE system is an “equilibrium strategy” for Game Systems, which means that if either opponent were to deviate from the SAGE strategy their expectation will go down (thus the others would go up). What this means for you is that no matter whether you’re playing the Dan Harrington or Chris Ferguson, it puts you in a level playing field effectively making it a coin-toss situation (subject to differences in chip stacks). Thus, it’s a great system for when you’re up against a much better opponent than you. It brings the odds more into your favour.

The SAGE system ranks each of the possible 169 starting hands in Texas Holdem according to their Power Rankings in Heads Up situations. AA is the best; 32 off suit is the worst etc…

Optimal Top Percentage and Cutoff Hands

How to interpret the above table:

• The “R” column is the ratio of the short stack to the big blind, after the blinds have been paid. So if the short stack is 10,000 and the big blind is 2,000, R=5.
• The “SB Top%” is the percentage of hands that you should call all-in from the SB.
• The “BB Top%” is the same thing but for BB.
• The “SB Cutoff Hand” and “BB Cutoff Hand” is the worst hand in that criterion.
• “SB Edge” is the expected amount that SB can win, in terms of big blinds, if both players follow this system.

Simplified Version for Live Games

As interesting as these nerdy calculations are, it’s not the sort as practical in a live tournament setting. SAGE System simplifies the entire process into two steps, computing a Power Index (PI) and then using PI to know when to call.

How to Work Out PI

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• Take the “power number” of each card in its rank (e.g. 10 = 10, J = 11, Q = 12, etc..).
• Take the power number for your highest card and double it.
• Add the power number to your lowest card.
• For Pocket Pairs, add 22.
• For suited connectors, add 2.
• The sum is the Power Index of your hand!.

Once you know the PI value of your hand, you can use the SAGE table below to know when to jam an opponent’s shove from SB or BB according to R. This strategy can be used for any HU situations such as SNGs, MTTs or especially satellite tournaments when there’s only one prize.

The SAGE Table

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Here I Look At The S.A.G.E Poker System
And Ask Whether S.A.G.E Heads-Up Poker Strategy Is Suitable For SNG Satellite Qualifiers.

Update: This article was written with satellite qualifiers in mind, though I wanted to point out that it works just great for any high-blind heads-up poker situation. For example, when you are down to the last 2 in a tournament you are both guaranteed at least the 2nd place prize money. Effectively you are heads up for the difference between first and second place cash. In this situation the unexploitable SAGE will make sure you win your fair share based on chips, once you get the experience of these situations you can deviate from the basic strategy in order to properly exploit your opponent's weaknesses.

When you are heads-up at the end of a SNG Tournament with just one prize on offer the SAGE poker system can be used to ensure that your play is ‘mathematically un-exploitable’. The system itself is very simple – it involves assigning ‘power rankings’ to hands and comparing them with a table showing your optimal push / fold ranges. SAGE works best with less than 10 Big Blind stacks, with more than this you have some room to play poker.

Before we get into the math and discuss whether using SAGE would be a good option a quick note on copyright. This is © 2005 Lee Jones and James Kittock. Lee Jones is former PokerStars card-room manager and author of the best selling book ‘Winning Low Limit Holdem’.

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SAGE Poker System - Works For Satellite, SNG And MTT Heads-Up Situations.

While this article is part of the Poker Satellites section here, it can also be used for high blind play in normal 1-table tournaments. Sage works with a single prize, when you are heads up at the end of a SNG you are guaranteed 2nd prize as a minimum. You can thus think of SAGE as being for the difference between 2nd and 1st (usually an additional 20% of the prize pool). Adding a 3rd player would add complexity to this simple system – we point readers to our ICM articles for more information on this.

SAGE Poker System - Introducing The 'Power Index' Score

The SAGE system’s benefit is simplicity. There are 2 key factors, both of which are very easy to work out – then a simple chart for deciding on your action. The keys factors are ‘PI’ which stands for the ‘Power Index’ of your current cards and ‘R’ which is the ratio of the smallest stack to the big blind. For each ‘R’ there are then numbers given for the SB to push all in and the BB to call based on PI.

Working out PI is done like this: Each card is given a ‘power number’ based on its rank. Ace= 15 / King = 13 / Queen = 12 / Jack = 11 and the others at face value. To get the PI of your hand take the highest card’s power number, double it – then add the number of the smaller card. For example – Queen-Eight would be (12*2)+8 = 30.

For suited cards you add 2 points to the total and for pairs you add 22 points. So the highest PI is for Ace-Ace (15*2) + (15+22) = 67 and the lowest PI is for 3-2 off-suit (3*2) +2 = 8.

So, based on the value of ‘R’ here is a list of what PI you can push and call with.

SAGE Poker System - From Unexploitable To Exploitative Strategy

Well that is the system, simple and mathematically un-exploitable – meaning that you can not lose an edge playing this system. However there is always a difference between mathematically un-exploitable play and ‘optimal play’. The question that we need to ask is how we can adjust to individual opponents?

If an opponent is playing looser than the SAGE system should indicate the logically we will not be giving up anything by following the rules outlined above. Our optimal strategy becomes the same as the Unexploitable strategy.

If an opponent is playing tighter then it would appear to follow that we should push slightly wider and call slightly tighter ourselves. The logical outcome of a tight opponent is that we are getting more ‘walks’ from the BB and taking the blind uncontested more often when we are pushing all-in from the SB… this would more than make up for the times we fold the BB ‘too tight’ giving our opponent credit for a good hand.

Good luck using SAGE at those online poker tables!

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Further Reading:

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