The probability of being dealt:
Pocket aces 220/1 (0.45%)
Any pocket pair 16/1 (5.9%)
A-K suited 331/1 (0.3%)
A-K offsuit 110/1 (0.9%)
A-K suited or offsuit 82/1 (1.2%)
Any two suited cards 3.3/1 (24%)
Max stretch suited connectors, e.g. J-T suited 46/1 (2.1%)
Max stretch connectors, e.g. J-T suited or offsuit 11/1 (8.5%)
Either pocket aces or pocket kings 110/1 (0.9%)
Either pocket aces, pocket kings or A-K 46/1 (2.1%)
Either pocket aces, pocket kings, pocket queens, A-K, A-Q or K-Q 19/1 (5%)
Any pocket pair or two cards ten or higher 4.5/1 (18%)
Any pocket pair of sevens or higher or two cards ten or higher 5.4/1 (16%)
N.B. If you take a pocket pair to the river, you have a 4.2/1 (19%) chance of making a set or better.
If you take two suited cards to the river, you have a 15/1 (6.4%) chance of making a flush in your suit by then. Your chance of making a flush in your suit by the river with two unsuited cards is 53/1 (1.8%).
The Flop
The probability of improving to:
A set or better from a pocket pair (where the pair is matched by one or more cards on the board) 7.5/1 (11.8%), which is broken down as follows:
A set 8.3/1 (10.8%)
A full house 136/1 (0.74%)
Quads 407/1 (0.25%)
A flush from two suited cards 118/1 (0.84%)
A four-flush from two suited cards 8.1/1 (10.9%)
A three-flush from two suited cards 1.4/1 (41.6%)
A four-flush from one suited card 88/1 (1.1%)
A three-flush from one suited card 6.8/1 (12.8%)
A straight from two max stretch connectors 76/1 (1.3%)
An eight outs (open-ended or double belly buster) straight draw from two max stretch connectors 8.6/1 (10.5%)
A gutshot straight draw from two max stretch connectors 3.6/1 (22%)
At least a pair (using your pocket cards) from two non-pair cards 2.1/1 (32.4%)
A pair (using one of your pocket cards) from two non-pair cards 2.5/1 (29%)
Two pair (using both of your pocket cards) from two non-pair cards 49/1 (2%)
Any two pair from two non-pair cards 24/1 (4%)
Trips (using one of your pocket cards) from two non-pair cards 73/1 (1.35%)
A full house (using both of your pocket cards) from two non-pair cards 1087/1 (0.09%)
Quads (using one of your pocket cards) from two non-pair cards 9799/1 (0.01%)
What will appear on the Three Flop Cards
Three of a kind 424/1 (0.24%)
A pair 5/1 (17%)
Three suited cards 18/1 (5.2%)
Two suited cards 0.8/1 (55%)
No suited cards (rainbow) 1.5/1 (40%)
Three cards in sequence 28/1 (3.5%)
Two cards in sequence 1.5/1 (40%)
No cards in sequence 0.8/1 (56%)
From Flop to Turn
The probability of improving to:
A full house or better from a set on the next card (7 outs) 5.7/1 (15%)
A full house from two pair on the next card (4 outs) 11/1 (9%)
A set from one pair on the next card (2 outs) 23/1 (4.3%)
A flush from a four-flush on the next card (9 outs) 4.2/1 (19%)
A straight from an open-ended straight draw on the next card (8 outs) 4.9/1 (17%)
A straight from a gutshot straight draw on the next card (4 outs) 11/1 (9%)
A pair from two non-pair cards (overcards) on the next card (6 outs) 6.8/1 (13%)
A second pair with your kicker on the next card, when you hold the same pair as your opponent but are 'outkicked' (3 outs) 15/1 (6%)
From Flop to River
The probability of improving to:
A full house or better from a set by the river 2/1 (33%)
A full house or better from two pair by the river (4 outs) 5.1/1 (17%)
A set or better from one pair by the river (2 outs) 11/1 (8.4%)
A flush from a four-flush by the river (9 outs) 1.9/1 (35%)
A flush from a three-flush by the river 23/1 (4.2%)
A straight from an open-ended straight draw by the river (8 outs) 2.2/1 (32%)
A straight from a gutshot straight draw by the river (4 outs) 5.1/1 (17%)
A pair or better from two non-pair cards (overcards) by the river (6 outs) 3.2/1 (24%)
A second pair with your kicker by the river, when you hold the same pair as your opponent but are 'outkicked' (3 outs) 7/1 (13%)
From Turn to River
The probability of improving to:
A full house or better from a set on the final card (10 outs) 3.6/1 (22%)
A full house from two pair on the final card (4 outs) 11/1 (9%)
A set from one pair on the final card (2 outs) 22/1 (4.4%)
A flush from a four-flush on the final card (9 outs) 4.1/1 (20%)
A straight from an open-ended straight draw on the final card (8 outs) 4.8/1 (17%)
A straight from a gutshot straight draw on the final card (4 outs) 11/1 (9%)
A pair from two non-pair cards (overcards) on the final card (6 outs) 6.7/1 (13%)
A second pair with your kicker on the final card, when you hold the same pair as your opponent but are 'outkicked' (3 outs) 14/1 (7%)
Before the Flop Match-Ups (Expected Value)
Pair vs. Pair
Ad-Ah vs. Kc-Ks 81.3%-18.7%
Ad-Ah vs 6c-6s 79.8%-20.2%
Pocket Rockets vs. Big Slick
Ad-Ah vs. Ac-Ks 92.6%-7.4%
Ad-Ah vs. Ac-Kc 87.9%-12.1%
Pocket Rockets vs. Connectors
Ad-Ah vs. Jc-Ts 82.0%-18.0%
Ad-Ah vs. Jc-Tc 78.3%-21.7%
Ad-Ah vs. 6c-5s 80.6%-19.4%
Ad-Ah vs. 6c-5c 76.9%-23.1%
Pair vs. Two Overcards
Td-Th vs. Ac-Ks 57.3%-42.7%
Td-Th vs. Ac-Kc 53.9%-46.1%
6d-6h vs. Ac-Ks 55.4%-44.6%
6d-6h vs. Ac-Kc 52.1%-47.9%
Jd-Td vs. 2c-2s 54.0%-46.0%
Jd-Th vs. 2c-2s 51.2%-48.8%
Pair vs. One Overcard (dominated hand)
Kd-Kh vs. Ac-Ks 70.0%-30.0%
Kd-Kh vs. Ac-Kc 65.9%-34.1%
6d-6h vs. 7c-6s 64.2%-35.8%
6d-6h vs. 7c-6c 60.5%-39.5%
Pair vs. One Overcard
Kd-Kh vs. Ac-Qs 71.6%-28.4%
Kd-Kh vs. Ac-Qc 67.9%-32.1%
Td-Th vs. Ac-2s 71.1%-28.9%
Td-Th vs. Ac-2c 67.4%-32.6%
6d-6h vs. Ac-2s 69.9%-30.1%
6d-6h vs. Ac-2c 66.2%-33.8%
Dominated Hands
Ad-Kh vs. Ac-Qs 74.0%-26.0%
Ad-Kh vs. Ac-Qc 69.7%-30.3%
Ad-Kh vs. Ac-6s 73.5%-26.5%
Ad-Kh vs. Ac-6c 69.2%-30.8%
Ad-Kh vs. Kc-Qs 74.2%-25.8%
Ad-Kh vs. Kc-Qc 69.9%-30.1%
Ad-Kh vs. Kc-7s 75.0%-25.0%
Ad-Kh vs. Kc-7c 70.7%-29.3%
Two Overcards vs. Non-Pair
Ad-Kh vs. 7c-6s 61.5%-38.5%
Ad-Kh vs. 7c-6c 57.7%-42.3%
One Overcard vs. Non-Pair
Ad-2h vs. 7c-6s 53.9%-46.1%
Ad-2h vs. 7c-6c 50.4%-49.6%