Poker Starting Hand Odds Calculator

The 1,326 starting hand math

A standard 52-card deck dealt 2 cards to a player produces C(52,2) = 1,326 possible starting hand combinations. Texas Hold’em uses these as the foundation of all subsequent decisions.

The 1,326 combinations reduce to 169 unique hand “types” by ignoring suit symmetry (suited vs offsuit matters; specific suits don’t). Of these 169:

• 13 pocket pairs (AA, KK, QQ, …, 22)
• 78 suited combinations (AKs, AQs, …, 32s)
• 78 offsuit combinations (AKo, AQo, …, 32o)

The exact number of combinations for each hand type:

Those last two are worth checking rather than trusting. There are 1,326 hands and 1,128 of them contain no ace, which is C(48,2), so 198 do. Broadway is twenty cards, T through A in four suits, and C(20,2) is 190.

You’ll get a pocket pair every 17 hands on average. Pocket aces specifically come about once every 221 hands, so in a 100-hand session, you’re more likely than not to never see them.

Sklansky’s groupings, the classic starting hand rankings

David Sklansky’s Theory of Poker (1987) grouped the 169 hands into 8 categories:

Modern poker has moved beyond strict Sklansky groups (with deeper position-based analysis), but the framework remains a useful teaching tool.

Heads-up win rates (preflop, all-in)

When two hands run out to showdown, expected win rates (no further skill involved):

Three matchups worth knowing by heart, because they come up constantly and people get the first one backwards:

• JJ vs AKs: the pair is the favourite, about 54% to 46%. The overcards need to pair up or make a straight or flush; the jacks only need the board to miss.
• 22 vs AK offsuit: about 52% to the deuces. Even the worst pair in the deck is ahead of the best unpaired hand.
• QQ vs 87 suited: about 80% to the queens.

The first two are what poker calls a “race”, and the honest summary is that a pair against two overcards is a coin flip that leans a couple of points toward the pair, not toward the overcards. If you find yourself hoping AK is ahead of a pair preflop, it is not.

Multi-way pots dramatically reduce winning hand expectations

In a 6-handed all-in situation:

Even pocket aces win less than half the time against five opponents, because every one of them has some chance to outdraw you. That is the whole argument for raising hard before the flop with a premium hand: the point is not to build a pot, it is to get the field down to one or two players where the edge is real.

Read the bottom row before the top one. A random hand against five opponents wins one time in six, because somebody has to win and there are six of you. No hand can do worse than its share of that, which sounds obvious and is exactly the constraint most published multi-way tables violate.

Post-flop hand equity (drawing hands)

After the flop, certain hands have specific equity to improve:

The “rule of 4 and 2”: multiply outs by 4 on the flop (for turn+river combined), by 2 on the turn (for river only). It’s accurate to within 1-2% for most hands.

Pot odds, the second pillar of poker math

Pot odds tell you whether a call is profitable:

Pot odds = Amount to call ÷ (Pot + Amount to call)

If you face a $20 bet into a $40 pot, pot odds = $20 ÷ $60 = 33%. You need at least 33% equity to call profitably.

A flush draw (35% equity by river) facing a 33% pot odds is a slight call. Facing 40% pot odds is a fold.

Implied odds, the deeper consideration

Pot odds assume the rest of the hand plays passively. Implied odds account for additional money you can win if you hit your draw. A draw with 25% equity facing 33% pot odds is unprofitable on pot odds alone, but if you’ll win another $50 on later streets when you hit, the implied odds make it profitable.

This is why deep stacks, meaning stacks that are large relative to the pot, favour implied-odds hands like suited connectors and small pairs you can set-mine with. There is money left behind to win when you hit. Short stacks kill implied odds entirely, because there is nothing left to extract, so short stacks favour raw equity: big pairs and ace-king.

Position is enormously valuable

Two identical hands have very different EV depending on position. From later positions, you have:

• More information about opponents’ decisions
• Better bluffing opportunities
• Pot control on later streets
• Bigger bluffs that fold out marginal hands

The same 88 from UTG (under the gun, first to act) loses money on average; from button (last to act), it’s profitable. Modern poker theory weights position almost as heavily as raw hand strength.

Hand reading and ranges

Skilled players do not ask what hand the opponent has. They ask what range of hands the opponent could have here: something like the top 20% of starting hands, plus a few suited connectors, plus the occasional bluff. Then they narrow it as the betting goes on.

GTO (Game Theory Optimal) solvers, run on modern computers, generate near-optimal ranges for every situation. Top players study these to refine their decisions, though the useful skill is not memorising solver output. It is noticing when an opponent has drifted a long way from it.