SAGE – Sit And Go Endgame

[SS] “Iggy, for heads-up, short-stack, push or fold decisions, I use SAGE”, Stan the Stat declared.

[II] “What’s that?” Iggy the Improver inquired.

[SS] “Sit And Go Endgame, Copyright ©2005 by James Kittock and Lee Jones. They produced a very simple formula based on your hole cards and your stack size, which I’ve adapted to use M1 instead of big blinds. It only applies when the lower of your two Ms (after deducting the blinds and antes) is 5 or less.”2

[II] “That’s pretty much Dan Harrington’s Red Zone.”

[SS] “Right. And his Dead Zone when you’re shoving any two cards.”

[SS] “To use SAGE, all you need to do is a simple calculation and a table lookup.

  • Step One: Calculate the Power Index of your hole cards:
    • Deuces through Kings are worth 2 through 13 respectively, and Aces are worth 15; your higher card counts double
    • Pairs are worth 22 points
    • Being suited is worth 2 points

    Power Index = HighCard*2 + LowCard + Pair*22 + Suited*2

  • Step Two: In the following modified table, look up the lower M and your situation (in the small blind first to act or in the big blind after the button has shoved). If your Power Index is at or above the value listed, move all-in, otherwise fold:
    M Jam (SB) Call (BB)
    <1 any any
    1 19 any
    2 22 24
    3 24 27
    4 25 29
    5 26 31

SAGE doesn’t specify what you should do in the big blind if the button limps, but you can start with the Jam column’s values and adjust up or down according to what you think the limp represents. The same adjustment applies to calling.”

[SS] “Some examples:

  • In the small blind with a lower M of 1, holding 5♦4♣: 5*2 + 4 + 0 + 0 = 14. Table value is 19, so fold.
  • In the big blind with a lower M of 2, holding Q♣J♣ after a shove: 12*2 + 11 + 0 + 2 = 37. Table value is 24, so call the all-in.
  • In the big blind with a lower M of 4, holding K♣2♥ after a shove: 13*2 + 2 + 0 + 0 = 28. Table value is 29, so fold (borderline case).
  • In the small blind with a lower M of 5, holding 4♠4♣: 4*2 + 4 + 22 + 0 = 34. Table value is 26, so move all-in.
  • In the big blind with a lower M of 5, holding A♠3♦ after a shove: 15*2 + 3 + 0 + 0 = 33. Table value is 31, so call the all-in.
  • In the big blind with a lower M of 7, holding A♥K♥ after a shove: not a Jam or Fold situation because M is too high. Pretty easy call here though.”

[SS] “Here’s a version of the chart with hand ranges and percentages, but it’s really only so you can get a better feel for SAGE:”

Adjusted SAGE Jam/Call as Ranges

M Jam (SB) Call (BB)
<1 any
100.0%
any
100.0%
1 AA-22
Axs-8xs,76s-73s,65s
Axo-9xo,87o-83o,76o-75o
84.3%
any
100.0%
2 AA-22
Axs-9xs,87s-84s,76s
Axo-Txo,98o-94o,87o-86o
76.2%
AA-22
Axs-Txs,98s-94s,87s-86s
Axo-Jxo,T9o-T4o,98o-96o
69.2%
3 AA-22
Axs-Txs,98s-94s,87s-86s
Axo-Jxo,T9o-T4o,98o-96o
69.2%
AA-22
Axs-Qxs,JTs-J3s,T9s-T5s,98s-97s
Axo-Kxo,QJo-Q3o,JTo-J5o,T9o-T7o
57.5%
4 AA-22
Axs-Jxs,T9s-T3s,98s-95s,87s
Axo-Qxo,JTo-J3o,T9o-T5o,98o-97o
65.6%
AA-33
Axs-Kxs,QJs-Q3s,JTs-J5s,T9s-T7s
Axo,KQo-K3o,QJo-Q5o,JTo-J7o,T9o
48.6%
5 AA-22
Axs-Jxs,T9s-T4s,98s-96s
Axo-Qxo,JTo-J4o,T9o-T6o,98o
62.0%
AA-33
Axs,KQs-K3s,QJs-Q5s,JTs-J7s
Axo,KQo-K5o,QJo-Q7o,JTo-J9o
40.1%

[II] “Oh, that helps a lot. I can now see that you don’t even need the Ace or pair part of the formula, since you’re always shoving with those.”

[SS] “There are two borderline exceptions with a pair of Twos, but yes, close enough. That simplifies the Power Index calculation to your low card plus double your high card plus two if suited.”

Footnotes:

  1. See M and Q if you aren’t familiar with M.
  2. Kittock and Jones use multiples of the big blind, but that unnecessarily ignores antes.

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