Probabilities

Poker Probabilities I

After 2,6 Million Hands the result are these stats:

Combination	Number	Probability in per cent ...
Royal Flush	4	0,00015 %
Straight Flush	36	0,00135 %
Poker / Four of A Kind	624	0,02 %
Full House	3744	0,14 %
Flush	5108	0,20 %
Straight	10200	0,39 %
Three of A Kind	54912	2,11 %
Two Pair	123552	4,75 %
Pair	1098240	42,25 %
High Card	1302540	50,13 %

Poker Probabilities II

The Probability, that you have	in percent is that...	the Odds against are...
...preflop one pair	5,88	16 : 1
...preflop suited cards	23,53	3,25 : 1
... preflop two Aces or Kings	0,90	110 : 1
... preflop AceKing	1,21	81,90 : 1
... preflop at least one Ace	14,93	5,70 : 1
... after the Flop a Flush Draw and you get the Flush	34,97	1,86 : 1
... after the Flop an open-ended Straight Flush Draw and you get the Straight Flush	8,42	10,90 : 1
... after the flop at an open-ended Straight Flush Draw you get at least a Straight	54,12	0,85 : 1
... after the flop two pairs and you get at least a Full House *	16,74	4,97 : 1
... after the flop a 3 of a kind and you get at least a Full House *	33,40	1,99 : 1
... after a hit on the flop with a builded pair you get at least one of the same cards again	8,42	10,90 : 1
... hit with a pocketpair on the flop	11,76	7,51 : 1
... hit on the flop to get one pair	32,43	2,08 : 1
... with two suited holecards two colourhits on the flop (so that you have flushdraw)	11,79	7,48 :1
... with two suited holecards til the end 3 more suited cards (but not more) of the same colour	5,77	16,3 :1
... a pocketpair and til the end you get one same card more	19,18	4,21 : 1

* Full House in all variants

Poker Probabilities III

The Probability, that you	in per cent this is	the odds against are
... flops a flush with 2 holecards of the same colour	0,84	118 :1
... flops 4 of a kind with a pocketpair	0,24	407 :1
... flops with 6-5 offsuit a Straight	1,31	75,6 :1
... flops with 7-5 offsuit a Straight	0,98	101 :1
... flops with 8-5 offsuit a Straight	0,65	152 :1
... flops with 9-5 offsuit a Straight	0,33	305 :1
... flops with 9-8 suited a Straight Flush	0,02	4.899 :1
... flops with 9-7 suited a Straight Flush	0,02	6.532 :1
... flops with 9-6 suited a Straight Flush	0,01	9.799 :1
...flops with 9-5 suited a Straight Flush	0,01	19.599 :1
... and all other ten players have no Ace or King	1,4	70,5 :1
... in a Heads-up both players have a pair of Aces	0,00*	270.724 :1
... dont get preflop an ace or a pair the next 20 hands	1,05	94,0 :1
... dont get preflop an ace or a pair the next 50 hands	0,00**	87.897 :1
... will get the next 4 hands preflop two Aces	0,00***	(2.385.443.280 :1)

* in fact 0,00037%
** in fact 0,0011%
*** in fact 0,00000004%

Poker Probabilities IV - Head's Up

Favorit-vs-underdog	Probability	Odds
Pair vs. 2 undercards	0.83	4.9 : 1
Pair vs.smaller Pair	0.82	4.5 : 1
Pair vs. 1 overcard, 1 undercard	0.71	2.5 : 1
2 overcards vs. 2 undercards	0.63	1.7 : 1
Pair vs. 2 overcards	0.55	1.2 : 1

Poker Probabilities V - Pocket Pairs

Probability to meet a higher pair at X opponents	1	2	3	4	5	6	7	8	9
KK	0.0049	0.0098	0.0147	0.0196	0.0244	0.0293	0.0342	0.0391	0.0439
QQ	0.0098	0.0195	0.0292	0.0388	0.0484	0.0579	0.0673	0.0766	0.0859
JJ	0.0147	0.0292	0.0436	0.0577	0.0717	0.0856	0.0992	0.1127	0.1259
TT	0.0196	0.0389	0.0578	0.0764	0.0946	0.1124	0.1299	0.1470	0.1637
99	0.0245	0.0484	0.0718	0.0946	0.1168	0.1384	0.1593	0.1795	0.1990
88	0.0294	0.0580	0.0857	0.1125	0.1384	0.1634	0.1873	0.2101	0.2318
77	0.0343	0.0674	0.0994	0.1301	0.1595	0.1874	0.2138	0.2387	0.2619
66	0.0392	0.0769	0.1130	0.1473	0.1799	0.2104	0.2389	0.2651	0.2890
55	0.0441	0.0862	0.1263	0.1642	0.1996	0.2324	0.2623	0.2892	0.3129
44	0.0490	0.0956	0.1395	0.1806	0.2186	0.2532	0.2841	0.3109	0.3334
33	0.0539	0.1048	0.1526	0.1967	0.2370	0.2729	0.3040	0.3300	0.3503
22	0.0588	0.1141	0.1654	0.2124	0.2546	0.2914	0.3222	0.3464	0.3633

Poker Probabilities VI - Flop

Board consists of...	on the Flop		on the Turn		on the River
	Poss.	Odds	Poss.	Odds	Poss.	Odds
3 or more Cards of same colour	0.05177	18.3 : 1	0.13522	6.40 : 1	0.23589	3.24 : 1
4 or more Cards of the same colour			0.01056	93.7 : 1	0.03394	28.5 : 1
Rainbow-flop (different colours)	0.39765	1.51 : 1	0.10550	8.48 : 1
exactly 3 consecutive Cards	0.03475	27.8 : 1	0.11820	7.46 : 1	0.25068	2.99 : 1
exactly 4 consecutive Cards for a Straight			0.03877	24.8 : 1	0.18991	4.27 : 1
3 or more consecutive Cards of the same colour	0.00217	459 : 1	0.00869	114 : 1	0.02172	45.0 : 1
exactly 3 of a kind (not FullHouse or Four of a Kind)	0.00235	424 : 1	0.00935	106 : 1	0.02128	46 : 1
exactly one pair	0.16941	4.90 : 1	0.30417	2.29 : 1	0.42450	1.36 : 1
exactly two pairs			0.01037	95.4 : 1	0.04716	20.2 : 1

Poker Probabilities VII - OverCards at a Pocket-Pair