Nash Equilibrium Pushbot And Call Charts for Poker Tournaments

Nash Equilibrium Pushbot And Call Charts for Poker Tournaments

Powerful poker tools and mathematical models have have enabled poker players to develop and implement game-theory based unexploitable and optimal poker strategies and plays in specific, key situations.

One concept which is highly applicable to poker tournaments and SNGs is “Nash Equilibrium”.

For heads-up play (e.g. blind vs blind hands) it’s possible to calculate game-theory optimal (GTO) shove and calls ranges which are profitable in the long run, based on your stack size, and cards / those of your opponents.

Poker Pushbot charts can answer important questions quickly- for heads-up situations, for example:

Can I go all in with this hand profitably?
Which hands can I profitably call a shove with vs my opponents stack size, when they go all in for X big-blinds?

Equilibrium rankings are meant as a guide to help you to develop an idea of which hands and hand ranges are good enough to warrant an all-in and which hands are good enough to call an all-in vs an aggressive opponent.

It folds to you in the small-blind. You have 12 big-blinds and Queen ten offsuit. What’s your play? Can you profitably and unexploitably go all in, or do you wait for a better sport?

You can Shove (go “all in”) profitably if:

If you are in the small blind,
everyone before you has folded,
your effective stack (the smallest of the stack sizes of you vs your opponent in blinds blinds) is smaller than the number given in the table below for your specific hand

in this spot when you have 12 big-blinds.. From the pushbot chart below, we can see that QTo is a profitable SHOVE (as is Q9, and Q8, but NOT Q7o)

*Pro Tip: the push chart can also be used when you’re short-stacked and interested in jamming “all in” from the button. In this case account for the extra player that you’ll be shoving into (the Small Blind) by dividing all the stack size numbers in the chart by 2. Similarly you could divide by 4 for stack size for a protiable cutoff jam.

Nash Equilibrium pushbot chart for going all-in from the small-blind (SB)

Suited Cards

O
f
f
s
u
i
t

C
a
r
d
s

AA50
AKs50
AQs50
AJs50
ATs50
A9s50
A8s50
A7s50
A6s50
A5s50
A4s50
A3s50
A2s48

AKo50
KK50
KQs50
KJs50
KTs50
K9s50
K8s50
K7s49
K6s36
K5s32
K4s26
K3s20
K2s19

AQo50
KQo50
QQ50
QJs50
QTs50
Q9s50
Q8s50
Q7s20
Q6s29
Q5s24
Q4s16
Q3s14
Q2s13

AJo50
KJo50
QJo50
JJ50
JTs50
J9s50
J8s50
J7s32
J6s19
J5s16
J4s14
J3s11
J2s8.8

ATo50
KTo50
QTo45
JTo46
TT50
T9s50
T8s50
T7s36
T6s25
T5s12
T4s11
T3s7.7
T2s6.5

A9o45
K9o24
Q9o24
J9o29
T9o32
9950
98s50
97s36
96s27
95s14
94s6.9
93s4.9
92s3.7

A8o43
K8o19
Q8o13
J8o14
T8o18
98o21
8850
87s43
86s31
85s19
84s10
83s2.7
82s2.5

A7o41
K7o16
Q7o10
J7o8.5
T7o9.9
97o11
87o16
7750
76s36
75s24
74s14
73s2.5
72s2.1

A6o35
K6o15
Q6o9.8
J6o6.5
T6o5.7
96o5.2
86o7.1
76o11
6650
65s29
64s16
63s7.1
62s2

A5o37
K5o14
Q5o8.9
J5o6
T5o4.1
95o3.5
85o3
75o2.6
65o2.4
5550
54s24
53s13
52s2

A4o35
K4o13
Q4o8.3
J4o5.4
T4o3.8
94o2.7
84o2.3
74o2.1
64o2
54o2.1
4450
43s10
42s1.8

A3o32
K3o13
Q3o7.5
J3o5
T3o3.4
93o2.5
83o1.9
73o1.8
63o1.7
53o1.8
43o1.6
3350
32s1.7

A2o29
K2o12
Q2o7
J2o4.6
T2o3
92o2.2
82o1.8
72o1.6
62o1.5
52o1.5
42o1.4
32o1.4
2250

Nash Equilibrium chart for calling an all-in in the big blind

The action folds to the small-blind who goes “all in” for 15 BBs – half of your 30bb Stack. You look down at King Queen Suited.

Can you call the all-in profitably?

If you are in the big blind (BB)
everyone before the small blind has folded,
The SB moved all-in,
and your effective stack (in BBs) is smaller than the number specified in the table above.

Looking at the chart we can see that we can profitably call with QKO, as well as KJo, KTo and K9o

Suited Cards

O
f
f
s
u
i
t

C
a
r
d
s

AA50
AKs50
AQs50
AJs50
ATs50
A9s47
A8s41
A7s36
A6s31
A5s30
A4s26
A3s25
A2s23

AKo50
KK50
KQs50
KJs45
KTs32
K9s24
K8s18
K7s15
K6s14
K5s13
K4s12
K3s11
K2s11

AQo50
KQo46
QQ50
QJs29
QTs24
Q9s16
Q8s13
Q7s11
Q6s10
Q5s8.9
Q4s8.5
Q3s7.8
Q2s7.2

AJo50
KJo27
QJo20
JJ50
JTs18
J9s14
J8s11
J7s8.8
J6s7.1
J5s6.9
J4s6.2
J3s5.8
J2s5.6

ATo50
KTo24
QTo16
JTo13
TT50
T9s12
T8s9.3
T7s7.4
T6s6.3
T5s5.2
T4s5.2
T3s4.8
T2s4.5

A9o40
K9o18
Q9o12
J9o9.9
T9o8.5
9950
98s8.3
97s7
96s5.8
95s5
94s4.3
93s4.1
92s3.9

A8o35
K8o14
Q8o9.8
J8o7.7
T8o6.7
98o6.1
8850
87s6.5
86s5.6
85s4.8
84s4.1
83s3.6
82s3.5

A7o29
K7o13
Q7o8
J7o6.4
T7o5.5
97o5
87o4.7
7750
76s5.4
75s4.8
74s4.1
73s3.6
72s3.3

A6o22
K6o11
Q6o7.4
J6o5.4
T6o4.7
96o4.2
86o4.1
76o4
6650
65s4.9
64s4.3
63s3.8
62s3.3

A5o21
K5o10
Q5o6.8
J5o5.1
T5o4
95o3.7
85o3.6
75o3.6
65o3.7
5543
54s4.6
53s4
52s3.6

A4o19
K4o9.2
Q4o6.3
J4o4.8
T4o3.8
94o3.3
84o3.2
74o3.2
64o3.3
54o3.5
4432
43s3.8
42s3.4

A3o17
K3o8.8
Q3o5.9
J3o4.5
T3o3.6
93o3.1
83o2.9
73o2.9
63o3
53o3.1
43o3
3322
32s3.3

A2o16
K2o8.3
Q2o5.6
J2o4.2
T2o3.5
92o3
82o2.8
72o2.6
62o2.7
52o2.8
42o2.7
32o2.6
2215

* The maximum stack size considered in this model is 50 BBs

Data Source: Mathematics of Poker (2006) by Bill Chen

Author: Brandy Lawrence