Poker Equity & OddsEquity against a range
Short answer
Your equity against a range is the average of your equity against each hand in it, weighted by how many ways the villain can hold each hand. It is the number a real decision needs, because nobody knows the exact hand. The range grid in Poker Equity & Odds does the counting; this page shows the counting.
One hand is a guess, a range is a plan
A♠ Q♥ against a shoving range of TT+,AKs,AKo,AQs,AQo,AJs,KQs. Each row is one hand in the range, how many ways villain can hold it once your cards are out, and your equity against it.
| Villain holds | Combos | AQ has |
|---|---|---|
| AA | 3 | 7.3% |
| AJs | 3 | 69.7% |
| AKo | 9 | 25.6% |
| AKs | 3 | 24.6% |
| AQo | 7 | 50.0% |
| AQs | 2 | 47.5% |
| JJ | 6 | 43.1% |
| KK | 6 | 28.2% |
| KQs | 3 | 70.4% |
| 3 | 30.3% | |
| TT | 6 | 43.1% |
| The whole range, weighted by combos | 51 | 38.6% |
Against the pairs AQ is a dog, against AJ and KQ it is a big favourite, and against AK it is crushed. The weighted average, 38.6%, is the one number you can act on.
Count combos first
The weights are combos: a pair has 6, a suited hand 4, an offsuit hand 12, before you remove the ones that use a card you can see. With an ace and a queen in your hand, AA is down to 3 combos and AK to 12. The combos guide does the counting.
Narrow the range as the hand goes on
Preflop: the whole range on the grid, painted or picked from a preset.
On the flop: the same range, now with the combos the board took out, and your equity against what is left.
A range gets narrower with every action. A player who calls a raise and then calls a flop bet has fewer hands than a player who only called the raise. The grid shows the combos still live after each street, and your equity moves with them.
AQ against a shove
tight shove: QQ+,AKs,AKo
24 combos. The call needs 28.6% (100 to call into 150). Fold.
wider shove: TT+,AKs,AKo,AQs,AQo,AJs,KQs
51 combos. Still behind, and still a call: 38.6% clears 28.6%.
Same hand, same bet, two answers. The range is the decision. Lesson 4.6 of the course, AQ against a shove, is this spot; for comparison, JJ against the tight range has 36.2%.
Paint the range, read the number
Drag across the 13x13 grid or start from a preset, then run your hand against it. Range vs range is metered on the free tier and unlimited on Premium.
Questions
What does equity against a range mean?
Your equity against each hand the villain could hold, weighted by how many ways they can hold it. AQ against TT+,AKs,AKo,AQs,AQo,AJs,KQs comes out at 38.6%: a weighted average over 51 combos.
How do I put someone on a range?
Start from what they did: a shove from a short stack is one range, a raise from early position another. Then take out the hands they would have played differently. The app has presets by position and action.
Can I call a shove with AQ?
Against a tight shove (QQ+,AKs,AKo) AQ has 24.4% and the call needs 28.6%: fold. Against the wider shove above it has 38.6%: a call, while behind.
Is a range calculation exact?
Yes when it fits on the phone: every hand in the range, every board. Very wide range against range spots are sampled, and the app prints the margin of error.
Where the numbers come from. Every figure on this page comes from the app's own engine, the code that runs on your phone. Outs come from the Outs & Odds tool, hit chances are exact counts, and equities count every runout with no sampling. Engine build 18a5e00d. More worked numbers: flush draw odds and the pot odds cheat sheet.