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Flawless Poker

Universal Law 01

THE BIG BANG

The deck and the deal

Fifty-two cards, two at a time. That is the whole starting universe, and the classes players name are not dealt equally often.

Fifty-two cards, two at a time.

Order does not matter, so the count of starting hands is 52 × 51 ÷ 2. Players then collapse those 1,326 combinations into 169 classes: 13 pairs, 78 suited hands, and 78 offsuit hands. A class is a name. The deck deals combinations, and an offsuit hand has three times as many as a suited hand.

The size of the starting universe.
FactValue
Distinct two-card starting hands1,326 (52 × 51 ÷ 2)
Strategic hand classes169 (13 pairs + 78 suited + 78 offsuit)
Combos of one pocket pair6
Combos of one suited hand4
Combos of one offsuit hand12
Possible flops after your two cards19,600
Possible five-card boards after your two cards2,118,760
Boards in a heads-up all-in, four cards known1,712,304

How often the deck offers a hand.

These are chances per hand dealt to you, before anyone acts. Pocket aces twice in a row is 1 in 221, squared: 1 in 48,841.

Starting-hand frequency, from the 1,326 combinations.
HandCombosChancePlain English
Any pocket pair785.88%1 in 17
One specific pair, such as aces60.45%1 in 221
Ace-king, either suit pattern161.21%1 in 83
Ace-king suited40.30%1 in 332
Ace-king offsuit120.90%1 in 110.5
Any suited hand31223.53%1 in 4.3
Any hand with an ace19814.93%1 in 6.7
Queens or better, or ace-king342.56%1 in 39
Jacks or better, or ace-king403.02%1 in 33
Tens or better, or ace-queen624.68%1 in 21
Two broadway cards, ten through ace, pairs included19014.33%1 in 7.0
Suited connectors, 32s through AKs483.62%1 in 28

Pairs 5.9% Suited 23.5% Offsuit 70.6%

Is there a bigger pair out there?

You look down at a pocket pair. This is the chance that at least one other seat at a full table holds a higher pocket pair. Kings can only be outrun by aces. Queens can be outrun by aces or kings. The count runs over every way the remaining cards can reach the other seats.

Chance at least one opponent holds a higher pocket pair.
Your pair6-max, five opponents9-max, eight opponents
Kings2.44%, about 1 in 413.91%, about 1 in 26
Queens4.84%, about 1 in 217.67%, about 1 in 13
Jacks7.18%, about 1 in 1411.29%, about 1 in 8.9
Tens9.47%, about 1 in 1114.77%, about 1 in 6.8

At a full 9-handed table, at least one player is dealt a pocket pair about 41.9% of the time. That figure is a simulation of 500,000 deals, not a closed-form count.

The same two cards are still a different decision from a different seat.

The button acts last on the flop, turn, and river. Early position has more players left to act. The color grid below is one fixed example for about 100 big blinds. It is not an opening law for every chair, stack, or table. The selectivity picture is a coaching sketch of the same idea: most hands are folded, and a full ring folds more than a six-max game.

FLAWLESS POKER / STUDY CHART

How often you get a premium hand

Premium-hand frequency: pocket aces once in 221 hands, aces or kings once in 111, ace-king once in 83, queens or better or ace-king once in 39, and any pair once in 17.
Exact counts from 1,326 starting-hand combinations. The live-play times assume about 30 hands an hour. They describe how often the cards arrive, not whether to play them. Open full-size chart ↗
FLAWLESS POKER / STUDY CHART

Starting-hand selectivity by table size

Illustrative proportions of hands played in six-max and full-ring cash games, with most starting hands folded.
Broad illustrative starting-hand frequencies, not a measured rule or a guarantee of winning. Position, rake, table style, stack depth, and opponents change a sensible VPIP; selecting hands is only one part of sound play. Open full-size chart ↗
FLAWLESS POKER / STUDY CHART

One starting-hand strength map

Color-coded example starting-hand grid grouping premium, strong, playable, speculative, and folded hands.
A fixed educational example for approximately 100-big-blind play, not a universal opening range. Position, action before you, rake, stack depth, and opponent tendencies change which hands are worth playing. Do not treat the color groups as an all-position prescription. Open full-size chart ↗

These counts are for study and post-session review. Where a row comes from a simulation, the caption names how many deals were run. Where a stack or a pot is made up, the caption says so. None of these figures is an instruction for a live pot.