Presentation by Lee Jones at 2005 WPPC
Copyright © 2005 Lee H. Jones
Note to organizer: each primary numbered entry should be the title of a single Power
Point slide. Lettered sub-entries should be bullets on that slide.
Heads-up Strategy for No-Limit Hold’em Tournaments
1. An Equilibrium Heads-up Strategy for No-limit Hold’em
a. Developed by James Kittock of Mission College, California, with
assistance from Lee Jones
b. All information here Copyright © 2005 James Kittock and Lee Jones
2. The Scenario
a. You are the last two players in a no-limit hold’em tournament.
b. The button has the small blind and acts first.
c. The ratio of stack sizes to the big blind has gotten relatively small (less
a. Every chip has identical value. That is, there is no extra bonus for winning
your opponent’s last chip, and no extra penalty for losing your last chip.
b. The small blind is one-half of the big blind.
c. Because the blinds are large compared to the stacks, the only viable
strategy for the button is to move all-in (“jam”) or fold. This is true
almost always in sit-and-go’s and smaller tournaments. In major events,
the stack:blind ratios are often much bigger than 10:1 (at least initially).
d. If the button jams, then (by definition) the big blind can only call or fold.
4. What is an equilibrium strategy (ES)?
a. This strategy can not be exploited. If you play this strategy, your
opponent must play the equivalent strategy, or his EV will go down.
b. If either player deviates from the strategy, his results will suffer.
5. How was the strategy determined?
a. Take all 169 possible starting hold’em hands (e.g. KK, QJo, 85s) and rank
them (from AA down to 32o) by determining how each does against a
random hand, taking into account the relative likelihood of various
matchups (e.g., AA vs. AKs is relatively uncommon compared to 85s vs
b. Determine the EV of each against all the others.
c. Plug these numbers into a model that calculates the expected change in the
small blind’s stack size (“delta SB”).
d. Use game theory (specifically, the “minimax” technique) to determine the
ES for each player, for various stack-to-blind ratios.
6. The results – a qualitative view
a. Most players do not adjust correctly for changing hand values as the
number of players goes down.
b. This lack of adjustment becomes egregious at heads-up play.
c. Most players jam from the button/small-blind far less than they should.
d. Most players, in the big blind, call a jam by the button/small-blind far less
than they should.
e. The equilibrium strategy will clobber most opponents playing by the seat
of their pants.
7. The results – quantitative
Optimal Top % and Cutoff Hands
SB (jam) BB (call)
Delta SB (in BB
1 89% 62s 100% 32o 0.010
2 79% 64s 89% 62s 0.051
3 74% 95o 70% 75s 0.061
4 71% T4o 60% J5o 0.047
5 68% 96o 53% 97s 0.026
6 64% 76s 48% Q2s 0.002
7 61% T4s 42% Q7o -0.018
8 58% J2s 39% K2s -0.042
9 55% 98o 36% 33 -0.063
8. The “Sit And Go Endgame” System (SAGE)
a. Copyright © 2005 by James Kittock and Lee Jones
b. Developed by James Kittock as an easy-to-remember approximation to the
equilibrium strategy (ES).
c. Gives up virtually no advantage to an ES player. And (like the ES)
crushes most players – even experts.
d. Far easier to compute than looking up than the top N percent of hands in a
9. SAGE: Computing a Power Index (PI)
a. The “power number” of each card is its rank. J=11, Q=12, K=13, A=15
(don’t forget the ace is 15!)
b. Take the power number for your higher card and double it.
c. Add the power number of your lower card.
d. If it’s a pocket pair, add 22.
e. If they’re suited, add 2.
f. The sum is the Power Index (PI) of your hand.
10. SAGE: Using the PI
a. Compute the ratio (R) of the shortest stack to the big blind.
b. Look up the necessary PI for that value of R.
c. If the PI of your hand is greater than or equal to that value, then jam (if
you’re the button/small-blind) or call (if you’re the big blind).
11. The SAGE Numbers
12. SAGE Example 1
a. Blinds are 500/1000. After the blinds are taken, the SB has 5635 chips
and the BB has 2865 chips.
b. The SB has pocket 3’s. PI = (2 x 3) + 3 + 22 = 31
c. BB has J4s. PI = (2 x 11) + 4 + 2 = 28
d. The value of R is the smaller stack (2865) divided by 1000 ≈ 3.
e. Looking at the table, the SB should jam, and the BB should call, since
both have PIs higher than the respective entry in the table (22 for the SB
and 24 for the BB).
13. SAGE Example 2
a. Same circumstance, but the blinds are 200 and 400.
b. Now R is 2865 divided by 400 ≈ 7.
c. The SB should still jam (his PI of 31 is greater than the necessary 26).
d. If the SB jams, the BB should now fold, since his PI (28) is smaller than
the corresponding entry (30).
14. Why should we give this away?
a. It improves the game of poker. A field of study can only advance if its
participants discuss, argue, and (in this case) prove what is true and what
b. It’s not fair that just a few people have this. If you think we’re the first
people to do this, you’re wrong. If you find yourself heads-up with Greg
Raymer or Chris Ferguson, don’t think for a moment that they are without
c. Don’t think this will make the games terrible. Look what Brunson did
with Super/System. Look what Sklansky did with Theory of Poker. Look
R Jam (SB) Call (BB)
1 17 any
2 21 17
3 22 24
4 23 26
5 24 28
6 25 29
7 26 30
what Harrington is doing with the Harrington on Hold’em books. The
games continue to be great.
d. It’s fun to make a big splash in the swimming pool.
15. [entire slide should be this quote]
“In poker, as in every other area of human endeavor, the considered opinions of a
collection of the world’s best practitioners might be right, but it might also be quite
wrong. The consensus of what is considered true seems obvious and inevitable until
some brave soul comes along and says ‘No, the truth is really like this.’”
-Dan Harrington, Harrington on Hold’em, Volume II, p. 162