Best Poker Bets

ACES

Probability that one or more players will have an Ace dealt to them with 9, 8, 7, 6, 5, 4, 3, 2 players
 
9: 83%
8: 72%,
7: 67%,
6: 62%,
5: 55%,
4: 47%,
3: 38%,
2: 27%,

If you are dealt an Ace, what is the probability that one or more of the other 8, 7, 6, 5, 4, 3, 2, 1 players will be dealt an A

8: 47%,
7: 42%,
6: 38%,
5: 32%,
4: 27%,
3: 21%,
2: 15%,
1: 7%,

AX rule => Will it be beaten by remaining players

Probability of facing an ace with larger kicker when holding AX
AX	Against 1	Against 2	Against 3	Against 4	Against 5	Against 6	Against 7	Against 8	Against 9
A2	11.0%	20.8%	29.6%	37.3%	44.2%	50.4%	55.8%	60.7%	65.0%
A3	10.0%	19.1%	27.2%	34.5%	41.1%	47.0%	52.3%	57.1%	61.4%
A4	9.1%	17.3%	24.8%	31.6%	37.8%	43.4%	48.6%	53.2%	57.5%
A5	8.1%	15.5%	22.3%	28.6%	34.4%	39.7%	44.6%	49.0%	53.2%
A6	7.1%	13.7%	19.8%	25.5%	30.8%	35.7%	40.3%	44.5%	48.5%
A7	6.1%	11.9%	17.3%	22.3%	27.1%	31.6%	35.7%	39.7%	43.4%
A8	5.1%	10.0%	14.6%	19.0%	23.2%	27.2%	30.9%	34.5%	37.8%
A9	4.2%	8.2%	12.0%	15.6%	19.2%	22.5%	25.7%	28.8%	31.8%
AT	3.2%	6.3%	9.3%	12.1%	14.9%	17.6%	20.3%	22.8%	25.3%
AJ	2.2%	4.4%	6.5%	8.5%	10.5%	12.5%	14.4%	16.3%	18.2%
AQ	1.2%	2.4%	3.6%	4.8%	6.0%	7.1%	8.3%	9.4%	10.5%
AK	0.2%	0.5%	0.7%	1.0%	1.2%	1.5%	1.7%	1.9%	2.2%
Better than 1 in 3 chance no better AX in the hand (3 opponents is the key)

Outs and Probabilities

Type of draw	Hand	The flop	Specific outs	# Outs	Flop to turn	Turn to river	Turn & River
Pocket pair to set	22	Q49	22	2	4.3%(22-1)	4.3% (22-1)	8.4% (11-1)
One overcard	A8	952	AAA	3	6.4% (14-1)	6.5%(14-1)	12.5% (7-1)
Inside straight draw	J9	Q84	10	4	8.5% (11-1)	8.7% (11-1)	16.5% (5-1)
Two pair to full house	KQ	KQ5	KKQQ	4	8.5% (11-1)	8.7% (11-1)	16.5% (5-1)
One pair to two pair or trips	AQ	A 103	AAQQQ	5	10.6% (8-1)	10.9% (8-1)	20.3% (4-1)
No pair to pair	97	23J	999777	6	12.8% (13-2)	13% (13-2)	24.1% (3-1)
Two overcards to overpair	AJ	10 8 2	AAAJJJ	6	12.8% (13-2)	13% (13-2)	24.1% (3-1)
Set to full house/ four of a kind	66	67J	6777JJJ	7	14.9% (11-2)	15.2% (11-2)	27.8% (5-2)
Open-ended straight draw	98	7103	J6	8	17% (5-1)	17.4% (5-1)	31.5% (2-1)
Flush draw	KJ	A68	2345789107	9	19.1% (4-1)	19.6% (4-1)	35% (2-1)
Inside straight draw and two overcards	AK	10 2	JAAAKKK	10	21.3% (4-1)	21.7% (4-1)	38.4% (3-2)
Inside straight and flush draw	AK	JQ3	102456789Q	12	25.5% (3-1)	26.1% (3-1)	45% (5-4)
Open-ended Straight and Flush Draw	KQ	10 J 4	9A235678J	15	31.9% (2-1)	32.6% (2-1)	54.1% (5-6)

Rule of Thumb

The “ win probavility formula” looks like this:
(OUTS X 2) + 1 = % of getting a card you need
That formula works anytime you have between three and eleven outs.
If you have FEWER than three outs, it doesn’t really matter… since you should fold anyway.
For example, let’s say you pick up an open-ended straight draw and have eight outs.
(8 outs x 2) + 1 = 17%

"Rule of Four and Two". With two cards to come, the percent chance of hitting x outs is about (Outs X 4 (%); With one car to come its Outs X 2 (%)
Outs	Make on turn or river	Make on river
1	4.2%	2.2%
2	8.4%	4.3%
3	12.5%	6.5%
4	16.5%	8.7%
5	20.3%	10.9%
6	24.1%	13.0%
7	27.8%	15.2%
8	31.4%	17.4%
9	34.9%	19.5%
10	38.4%	21.7%
11	41.7%	23.9%
12	44.9%	26.1%
13	48.1%	28.2%
14	51.1%	30.4%
15	54.1%	32.6%
16	56.9%	34.8%
17	59.8%	36.9%
18	62.4%	39.1%
19	65.0%	41.3%
20	67.5%	43.4%
21	69.9%	45.6%
22	72.2%	47.8%
23	74.5%	50.0%
Better than 30%

Win rate for Suited and Unsuited 4 players

Common Odds When Holding Three Gapped Connectors From A5 To AT:
flopping a straight (including the slight chance of a straight flush in some cases)	0.3%
flopping an 8 out straight draw*	2.6%
Common Odds When Holding One Gapped Connectors From 53 To QT:
flopping a straight (including the slight chance of a straight flush in some cases)	1.0%
flopping an 8 out straight draw*	8.0%
Common Odds When Holding Connectors From 54 To JT:
flopping a straight (including the slight chance of a straight flush in some cases)	1.0%
flopping an 8 out straight draw*	10.0%
Common Odds When Holding Two Suited Cards:
flopping a flush (including the slight chance of a straight flush in some cases)	0.8%
flopping a four flush	10.9%
Common Odds When Holding Two Unsuited Cards:
flopping a four flush	2.2%
Common Odds When Holding Paired Hole Cards:
flopping EXACTLY two pair by pairing the board	16.1%
flopping EXACTLY trips by flopping a set for your pocket pair	10.8%
flopping EXACTLY a full house, a set to your hole pair and pairing the board	0.7%
flopping EXACTLY a full house, by the board tripping up	0.3%
flopping EXACTLY four of a kind, two cards to your hole pair	0.3%
Common Odds When Holding Unpaired Hole Cards:
flopping EXACTLY one pair by pairing a hole card	26.9%
flopping EXACTLY two pair by pairing a hole card AND pairing on the board	2.0%
flopping EXACTLY two pair by pairing EACH of your hole cards	2.0%
flopping EXACTLY trips by flopping two cards to one hole card	1.3%
flopping EXACTLY a full house, trips of one hole card and pairing the other	0.1%
flopping EXACTLY four of a kind, three cards to one of your hole cards	0.1%

Simplified Odds

With 4 cards of the same suit after the flop there is a 38.3% chance of completing the flush by the river.

With 3 cards of the same suit after the flop, there is a 32.6% chance of completing the flush by the river.

With 2 cards of the same suit after the flop, there is a 29.8% chance of completing the flush by the river.

With 4 connected cards after the flop, there is a 34.8% chance of completing a 5-card straight by the river.

With 2 connected cards after the flop, there is an 8.7% chance of completing a 5-card straight by the river.

With 3 connected cards after the flop, there is a 17% chance of completing a 5-card straight by the river.

With A-K-Q after the flop, you have approximately a 17.0% chance of completing a 5-card straight by the river.

Probability of Completing Hand - Flop => River
No. of Outs	Percent	No. of Outs	Percent
20	68	10	38
19	65	9	35
18	62	8	31
17	60	7	28
16	57	6	24
15	54	5	20
14	51	4	16
13	48	3	12
12	45	2	8
11	42	1	4
Straight Flush Draw
Inside Straight Draw => 4
Flush Draw => 9
two pair or gunshot draw
Pair to Set of 3 => 2
Two pair to Full House => 4
Open Ended Straight Draw => 8

Poker Odds Chart
Odds and outs
Outs	Odds: Flop-Turn / Turn-River	Odds: Flop-River	Example
1	46:1	22.5:1	Backdoor flush draw
2	22.5:1	11:1	Pocket pair to set
4	11:1	5:1	Gunshot straight
5	8:1	4:1	Two pair/trips
8	5:1	2:1	Open-ended straight draw
9	4:1	2:1	Flush draw
12	3:1	1:1	Flush draw + gutshot
13	2.5:1	1:1	OESD + pair
14	2.5:1	1:1	Flush draw + pair
15	2:1	1:1	Flush draw + OESD

Flush

• suited cards make a flush 0.82 %
• odds hitting four flush on flop 11 %
• odds making a completed flush by river is 6.25 %
• with four suited cards in flop chance of completing flush by river is 35%
• when there are three suited cards on the flop the odds of completing a 5-card flush by the river is approximately 37%.

Straight

• odds from open ended straight draw flop to complete straight by the river 31 %
• odds of completing a 5-card straight by the river with a gutshot straight draw is approximately 16%.

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