Which hands should the small blind shove at 3bb?
At 3bb the small blind shoves 78.0% of hands, 1,034 of 1,326 combos, and the rest fold without a fight.
In shorthand the shoving range is 22+, A2s+, K2s+, Q2s+, J2s+, T2s+, 92s+, 84s+, 74s+, 64s+, 54s, A2o+, K2o+, Q2o+, J2o+, T3o+, 95o+, 85o+, 76o. By equity against a random hand, 64s is the lowest-ranked hand that still shoves and T2o is the highest-ranked hand that folds. T2o mixes between shoving and folding at this stack, which marks the edge of the range: either choice is close to break-even.
Small blind shove chart at 3 big blinds heads-up. Shoves: 22+, A2s+, K2s+, Q2s+, J2s+, T2s+, 92s+, 84s+, 74s+, 64s+, 54s, A2o+, K2o+, Q2o+, J2o+, T3o+, 95o+, 85o+, 76o.
- Shove
- Mixes
- Fold
- Under 50% equity
Which hands should the big blind call with at 3bb?
The big blind's side of the 3bb chart: call with 92.3% of hands (1,224 combos) and fold the rest.
In shorthand the calling range is 22+, A2s+, K2s+, Q2s+, J2s+, T2s+, 92s+, 82s+, 72s+, 62s+, 52s+, 42s+, 32s, A2o+, K2o+, Q2o+, J2o+, T2o+, 92o+, 84o+, 74o+, 64o+, 53o+, 43o. By equity against a random hand, 43o is the lowest-ranked hand that still calls and 83o is the highest-ranked hand that folds. 63o mixes between calling and folding at this stack, which marks the edge of the range: either choice is close to break-even.
Big blind call chart at 3 big blinds heads-up. Calls: 22+, A2s+, K2s+, Q2s+, J2s+, T2s+, 92s+, 82s+, 72s+, 62s+, 52s+, 42s+, 32s, A2o+, K2o+, Q2o+, J2o+, T2o+, 92o+, 84o+, 74o+, 64o+, 53o+, 43o.
- Call
- Mixes
- Fold
- Under 50% equity
Which kinds of hands make up the 3bb ranges?
Pairs, suited hands and offsuit hands thin out at different speeds as the stack grows. The table counts the hands of each kind that act at 3bb, out of the 13 pairs and the 78 suited and 78 offsuit hands, and the share of each kind's specific combos that act once mixed hands are weighted by how often they act.
| Kind | Small blind shoves | Share of combos | Big blind calls | Share of combos |
|---|---|---|---|---|
| Pairs | 13 of 13 | 100.0% | 13 of 13 | 100.0% |
| Suited hands | 67 of 78 | 85.9% | 78 of 78 | 100.0% |
| Offsuit hands | 57 of 78 | 73.5% | 69 of 78 | 89.1% |
Which decisions are closest at 3bb?
At 3bb the tightest decisions are the hands whose edge over folding is smallest. Folding costs -0.500 for the small blind and -1.000 for the big blind, and every figure below is in big blinds.
| Hand | Rank of 169 | Shove EV | Fold EV | Edge | Equity when called | Chart |
|---|---|---|---|---|---|---|
| 85o | 137 | -0.500 | -0.500 | +0.000 | 39.6% | Shove |
| 64s | 138 | -0.466 | -0.500 | +0.034 | 40.2% | Shove |
| 92s | 132 | -0.458 | -0.500 | +0.042 | 40.6% | Shove |
| T2o | 135 | -0.500 | -0.500 | +0.000 | 39.8% | Fold |
| 75o | 141 | -0.532 | -0.500 | -0.032 | 39.0% | Fold |
| 83s | 139 | -0.533 | -0.500 | -0.033 | 39.2% | Fold |
| Hand | Rank of 169 | Call EV | Fold EV | Edge | Equity vs shoves | Chart |
|---|---|---|---|---|---|---|
| 43o | 164 | -0.984 | -1.000 | +0.016 | 33.6% | Call |
| 92o | 149 | -0.957 | -1.000 | +0.043 | 34.1% | Call |
| 53o | 161 | -0.947 | -1.000 | +0.053 | 34.2% | Call |
| 63o | 162 | -1.000 | -1.000 | +0.000 | 33.3% | Fold |
| 73o | 160 | -1.026 | -1.000 | -0.026 | 32.9% | Fold |
| 83o | 157 | -1.032 | -1.000 | -0.032 | 32.8% | Fold |
Which seat is ahead at 3bb?
At 3bb the small blind's seat is worth +0.052 big blinds per hand dealt, so the shove range steals enough blinds to come out ahead of the big blind's seat. The small blind stays ahead until the stack reaches 8bb, where the value per hand turns negative. Value per hand dealt counts folds, shoves and calls together, from the start of the hand before the blinds go in.
How does the chart change around 3bb?
| Stack | Small blind shoves | Big blind calls | Small blind value per hand |
|---|---|---|---|
| 1bb | 100.0% | 100.0% | +0.000 |
| 2bb | 89.4% | 100.0% | +0.010 |
| 3bb | 78.0% | 92.3% | +0.052 |
| 4bb | 73.8% | 74.1% | +0.066 |
| 5bb | 71.5% | 62.1% | +0.056 |
Going from 2bb to 3bb, T2o, 83s, 94o, 75o, 82s and 14 more leave the small blind's shoving range; 83o, 82o, 73o, 63o, 72o and 4 more leave the big blind's calling range.
The biggest single move for the small blind between 2bb and 3bb is 83s, which goes from shoving 100% of the time to 0%. For the big blind it is 83o, from calling 100% of the time to 0%.
The stack is the effective stack, the smaller of the two, because only that many chips can change hands. At 3bb it is 3 big blinds even if the other player has more.
Where can I check one hand or a different stack?
Hands near the edge of the 3bb ranges have pages of their own, and the calculator answers any hand at any stack from 1 to 20 big blinds. For tournament prize money, see the ICM examples.
How was this chart computed?
The game has two players, blinds of 0.5 and 1, no ante and one effective stack. Every one of the 169 starting-hand classes is dealt in proportion to the card-compatible pairs of specific hands, and a showdown is settled with the exact equity from our preflop table. Each side keeps answering the other's average strategy until neither can gain, then the borderline hands are solved exactly. Exploitability is the most the two players could gain together by switching to a best response, in big blinds per hand. At 3bb the published strategies have an exploitability of under 0.000001 big blinds per hand, against a limit of 0.001.
Source: GeorgeLiPoker's own heads-up solver, run on its exact preflop equity table.
Questions
- What is the push or fold range at 3bb heads-up?
- The small blind shoves 22+, A2s+, K2s+, Q2s+, J2s+, T2s+, 92s+, 84s+, 74s+, 64s+, 54s, A2o+, K2o+, Q2o+, J2o+, T3o+, 95o+, 85o+, 76o, which is 78.0% of hands. The big blind calls 22+, A2s+, K2s+, Q2s+, J2s+, T2s+, 92s+, 82s+, 72s+, 62s+, 52s+, 42s+, 32s, A2o+, K2o+, Q2o+, J2o+, T2o+, 92o+, 84o+, 74o+, 64o+, 53o+, 43o, which is 92.3% of hands. Both ranges are for a chips-only game with blinds of 0.5 and 1 and no ante.
- Is 85o a shove at 3bb?
- 85o is one of the closest decisions on the small blind chart. Shoving is worth -0.500 big blinds against -0.500 for folding, so the chart shoves it, and it is rank 137 of 169 by equity against a random hand.
- Should the big blind call with 63o at 3bb?
- The chart folds it, narrowly. Calling is worth -1.000 big blinds against -1.000 for folding, and its equity against the shoving range is 33.3%.