Best Poker Bets

Odds and Sods - Probabilities and Odds for Best Poker Bets

Frequency of Both Start Cards being Dealt

[6,7,8,9,10,J,Q,K,A]

>5    1:2
>6    2:5 [7,8,9,10,J,Q,K,A] 8 of 13 cards
>7    1:3
>8    1:5
>9    1:6
>10    1:11 [J,Q,K,A]

Basic Probabilities

Probability of being dealt:

• Any pocket pair: 16 to 1 (5.9%)
• Two suited cards: 3.25 to 1 (23.5%)
• A-K (Big slick – suited or offsuit): 81.9 to 1 (0.9%)
• Any single ace: 5.7 to 1 (15%)
• Pocket Aces: 220 to 1 (0.5%)
• Pocket Aces or Kings: 110 to 1 (1%)
• A paired flop occurs every 1/6 times a flop is dealt
• A paired turn card every 1/5 times a turn is dealt
• A paired river card every 1/4 times a river is dealt

Odds of connecting with the Flop in Hold’em

• Hitting another kind of your pocket pair (making a set): 7.5 to 1 (11.8%)
• You will pair at least one of your unpaired hole cards: 2.1 to 1 (32.4%)
• Hitting two or more of your suit when you hold suited cards: 7.5 to 1 (11.8%)
• Hitting a flush on the flop with suited hole cards: 118 to 1 (0.8%)
• You will hit two pair on the flop with unpaired hole cards: 49 to 1 (2%)

Flush Statistics

Probability of there being a flop with 3 Suited cards

Your first card can be anything. So you have 52 choices out of 52 cards (because no matter what card you draw you can get a full hand of the same suite). Your second card, has to be the same suit as your first card, so probability of that is 1251 because there are 13 of each suite and you have to subtract 1 for the one card you have drawn. Your third card has to be the same suite as the first and the second, notice there are only 11 cards left of that suite, so selecting that specific card will be 11/50

Giving a total probability of:

(52/52)×(12/51)×(11/50) = 0.05 => 1 in 20

Completing the Flush

With 4 suited cards (various combos) => you have 9 outs to make your hand on the turn or river (There are 13 cards per suit and you have 4 of them). So you have 9 outs out of 47 total unknown cards (52 cards in the deck – your 2 cards and – 3 more on the flop) => 9/47 => 1 in 5 chance to hit your flush after the turn or the river. The odds can get better late in the game as fewer cards remain in the pack BUT some of your suited cards may have been buried.

With 3 suited cards after the flop, you have 10 outs to make your hand after the turn and river but you need to score twice (both times) => Your chance of hitting the flush on the turn is 9/47 = 19.15% (about 1 in 5). If you don't hit on the turn, your change of hitting the river is 9/46 = 19.57%. Your overall chances are 19.15% + (19.57% * (1-0.1915)) = almost exactly 35%.

Odds On the Flop in Texas Hold’em

Outs

This is especially where “outs” come into your line of thinking and how all of these Texas Hold’em odds are generated. For example, if you have 4 cards to a flush you have 9 outs to make your hand on the turn. There are 13 cards per suit and you have 4 of them.

There are 9 unknown cards left that could complete your flush so you have 9 outs out of 47 total unknown cards (52 cards in the deck – your 2 cards and – 3 more on the flop). This is how Texas Hold’em odds are calculated. 9/47 = 19.1, or a 19.1% chance to hit your flush on the turn.

Straight and Flush Draw Odds

Drawing to open-ended straights and flushes, or fear of your opponents doing so, is one of the most common scenarios in Hold’em.

On the flop, when you have:

• Four cards to a flush, you will complete it on the turn: 4.2 to 1 (19.1%)
• An open-ended straight, you will complete it on the turn: 4.9 to 1 (17.9%)
• A set, you will complete a Full House or Four of a Kind on the turn: 5.7 to 1 (14.9%)
• Two pair, you will complete a Full House on the turn: 10.8 to 1 (8.5%)

Note that the figures above also apply on the turn to calculate odds for the river since you have the same 1 card to come.

Odds of hitting a hand by the river from the flop

The following set of odds is the likelihood to complete these hands by the river on the flop, so with 2 cards to come.

On the flop, when you have:

• Four cards to a flush, you will complete it by the river: 1.9 to 1 (35%)
• An open-ended straight, you will complete it by the river: 2.2 to 1 (32%)
• A gutshot straight draw, you will complete it by the river: 5.1 to 1 (17%)
• Two pair, you will complete at least a Full House by the river: 5 to 1 (17.7%)
• Three of a kind, you will complete at least a Full House by the river: 2 to 1 (33.4%)
• One pair, you will complete at least three of a kind by the river: 10.9 to 1 (8.4%)
• An open-ended straight flush draw, you will complete at least a straight by the river: 0.9 to 1 (54.1%)
• An open-ended straight flush draw, you will complete it by the river: 10.9 to 1 (8.4%)

All-in One-on-One in Texas Hold’em

Preflop matchups when played to showdown:

• Larger pocket pair vs. smaller pocket pair (AA vs. KK): Larger pair is at least an 80% favorite
• Pocket Aces vs. unpaired cards (AA vs. KQ): Pocket Aces are at least an 80% favorite
• Pocket Pair vs. overcards (QQ vs. AK): Pocket pair is at least a 52% favorite (commonly referred to as a coin flip)
• Pocket Pair vs. one overcard (JJ vs. A10): Pocket pair is at least a 66% favorite
• Overcards vs. Undercards (AK vs. Q10): Overcards are at least a 57% favorite
• One overcard (A3 vs. J10): Overcard is at least a 50% favorite
• Better kicker (AK vs. AJ): Better kicker is at least a 70% favorite

Extra Texas Hold’em odds

• The odds are 70.5 to 1 (1.4%) that no one at the table has an Ace or a King at a 10-handed table.

EXTRA ODDS

Pairs - chance overcard in flop	.
KK	22%
QQ	41%
JJ	56%
TT	69%
99	80%
88	86%
77	92%
66	96%
55	98%
higher pair beats lower pair	82%
lower pair beats higher pair	18%
KK same chance as 33 or 22 against AA	18%
Pair beats 2 higher cards (22 vs AJ)	55%
Pair beats 2 lower cards (QQ vs T6)	86%
Pair beats 2 lower cards (suited or connected)	70%
Pair beats cards 1 higher/1 lower (QQ vs A7)	71%
Pair flops a set or better	11.8%
Pair flops a set	11%
Pair flops a full house	1%
Pair flops 4 of a kind 1	0.25%
Matched Pair to trip	8%
Have 2 pairs after flop => full house	16%
Odds get an A	15%
Odds get an A or a pair	21%
Dealt an A, probability of no one else having one:	.
2 players	88%
3 players	77%
4 players	67%
5 players	58%
6 players	50%
7 players	43%
8 players	36%
9 players	30%
That is if you have an A with 9 other players,	.
there’s a 70% chance that at least one other player also has an A!	.
.	.
Straights - chance to complete	.
3 card straight after flop the chance of completing	30%
2 connected cards to complete straight	2%
J-10 is the best of the connectors in one way – because these are the only cards that make 4 straights and each straight is the nuts! nuts.	.
.	.
Trips	.
Trips on the flop chance of full house or better	33%
.	.
Flushes	.
If you start with any 2 suited cards:	.
to flop a flush	1%
to flop a four card flush	11%
to complete a flush with four cards flushed	35%
with any 2 suited cards get a complet flush	4%
.
AK	.
AK unsuited vs small suited connectors	7:5.
AK suited vs small unsuited connectors	9:5.
AK unsuited vs a pair	10:11.
AK suited vs a pair	1:1
.	.
Other odds	.
Any 2 cards vs any 2 lower cards (e.g. AK vs 7-2)	63%
Two higher cards vs a pair (e.g. KQ vs 9-9)	45%
Two suited higher cards vs a pair (e.g. KQs vs 9-9)	50%
One card higher and one lower than a pair (e.g. K-10 vs QQ)	40%
One card higher and one in between Villain’s 2 cards (e.g. AJ vs K9)	150%
One card higher and one lower than Villain’s 2 cards (e.g. A-2 vs J-4)	56%
One card the same as Villain’s, the other higher (e.g. A-10 vs A-9)	71%
No pair in card improving to at least a pair	27%
.	.
Other insights	.
Most flops miss pairing most hands! (Indeed, if you hold AK, you won’t pair either card on the flop 68% of the time).	.
The probability that your opponent is bluffing is a least 10%	.
Any time you have an A in your hand and you are getting a little over 2:1 pot odds to call, you pretty much have to call. It’s only against AA that your chances are markedly worse.	.

OUTS & ODDS

Extra Probabilities