A few folks collaborated on this, inc LIMITPOKER and BURR..
One of the many things I love about poker is that its so situational and theres almost as many opinions about plays as there is scenarios...
Odds are a useful tool in deciding what move to make, in cash games they are one of the most important. I play mainly MTTs and STTs where (thankfully as Im not the most mathematically minded) other factors play arguably as important role if not more so..
Game type
Amount of players at table and in the hand:
(2nd pair, no draws aint likely to be best or get a re-re-raise past 2 or 3 other players)
Position
What stage of the hand you're at:
(pre-flop; flop; turn; river)
What you intend to do with your knowledge of the odds:
(float with view of possible bluff next bet
call for showdown value, hopefully hitting best hand
raise semi-bluff with draws)
Implied odds.. will you stack him if you hit?..
Your table image
(tight
loose
passive
aggressive)
Your notes on the other players in the hand
(are they capable of folding even top pair
will they respect your raises
do they bluff
how do they bet draws or made hands)
What do you think you need to beat honestly (if thats how you want to beat it)
Prizes
and many more variables..
One of the most valuable tools Ive learned is this:
On the flop (so 2 cards to come) every out = 4%
On the turn (1 card to come) every out =2%
eg:
6 handed im dealt 6s7s in the Big Blind (my stack is 1860, Blinds 30 & 60 in 6 seater STT; 3 paid and 4 left in it - 2 knocked out already.. kinda tells ye what type of game its been so far;)
Under The Gun calls
Small Blind raises to 80 (pot size -I know hes a fairly TAG player and has a hand; his stack = 1810)
I call
UTG folds.. to the flop two handed..
Js3s4d
quite a flop for my hand with gutshot str8 and flush draws
SB bets 210 into the pot of 190 making the pot now 400..
I have 12 outs (9 spades & three 5s <the five of spades already counted in flush>) as long as he aint semibluffing a better flush draw..
Using the above guide that means Im gonna win this hand honestly about 48% of the time from here... IF it goes to showdown....
...WHAT WOULD YOU DO????
Heres a table of pure mathmatical odds to be used with caution:
Pair preflop - 6%; 1 in 17
Suited cards preflop - 24%; 1 in 4.2
Suited Connectors - 4%; 1 in 25
AA or KK preflop - .9%; 1 in 111
AK preflop - 1.2%; 1 in 83
AKs preflop - .3%; 1 in 332
A in hand preflop - 16%; 1 in 6.25
AA, KK, QQ, JJ - 1.8%; 1 in 56
AA versus KK preflop (heads up) - .004%; 1 in 22560
AK dealt preflop and hitting an A or K by the river: 50%; 1 in 2
Four flush completing (AdQd eg: Flop 10d8d6s Turn 6c River 7d) 39%; 1 in 2.6
Open Ended Straight-Flush completing to flush/straight by river 54% 1 in 1.85
Open Ended Straight completing (eg (98 Flop 10.7.4 Turn K River 6) 34% 1 in 2.9
Two Pair on flop Improving to Full House 17% 1 in 5.8
Three of a kind (set) on flop improving to Full House or Quads 37% 1 in 2.7
Pocket pair improving to three of a kind on flop 12% 1 in 8
No pair hand preflop improving to a pair on the flop 32% 1 in 3.125
One pair on flop improving to two pair or three of a kind by river 22% 1 in 4.7
Pocket pair improving to three of a kind after flop 9% 1 in 11
Two over cards improving to a pair by river 26% 1 in 3.9
Two over cards and a gutshot improving to pair or straight 43% 1 in 2.3
Gutshot straight draw hitting by river 17% 1 in 6
Gutshot and pair improving to two pair or better 39% 1 in 2.6
2 players on flop, that someone has an A when one is on board 23% 1 in 4.3
2 players in with board paired, chance of one of them having it 17% 1 in 5.8
Nice question and hope scenarios can get battered out here
Odds of being dealt certain starting hands
Hand Probability Odds
A-Ks (or any specific suited cards) 0.00302 331-1
A-A (or any specific pair) 0.00453 220-1
A-Ks, K-Qs, Q-Js, or J-10s (suited cards) 0.0121 81.9-1
A-K (or any specific non-pair, incl. suited) 0.0121 81.9-1
A-A, K-K, or Q-Q 0.0136 72.7-1
A-A, K-K, Q-Q, or J-J 0.0181 54.3-1
Suited cards, jack or better 0.0181 54.3-1
A-A, K-K, Q-Q, J-J, or 10-10 0.0226 43.2-1
Suited cards, 10 or better 0.0302 32.2-1
Suited connectors 0.0392 24.5-1
Connected cards, 10 or better 0.0483 19.7-1
Any two cards with rank at least queen 0.0498 19.1-1
Any pocket pair 0.0588 16-1
Any two cards with rank at least jack 0.0905 10.1-1
Any two cards with rank at least 10 0.143 5.98-1
Connected cards (cards of consecutive rank) 0.157 5.38-1
Any two cards with rank at least 9 0.208 3.81-1
Neither connected nor suited, at least one 2-9 0.534 0.873-1
Odds of making a hand with certain number of outs
Example drawing to Outs Make on turn Make on river Make on turn or river
Prob. Odds Prob. Odds Prob. Odds
Inside straight flush;
Four of a kind 1 0.0213 46.0-1 0.0217 45.0-1 0.0426 22.5-1
Open-ended straight flush;
Three of a kind 2 0.0426 22.5-1 0.0435 22.0-1 0.0842 10.9-1
High pair 3 0.0638 14.7-1 0.0652 14.3-1 0.1249 7.01-1
Inside straight;
Full house 4 0.0851 10.8-1 0.0870 10.5-1 0.1647 5.07-1
Three of a kind or two pair 5 0.1064 8.40-1 0.1087 8.20-1 0.2035 3.91-1
Either pair 6 0.1277 6.83-1 0.1304 6.67-1 0.2414 3.14-1
Full house or four of a kind; (see note)
Inside straight or high pair 7 0.1489 5.71-1 0.1522 5.57-1 0.2784 2.59-1
Open-ended straight 8 0.1702 4.88-1 0.1739 4.75-1 0.3145 2.18-1
Flush 9 0.1915 4.22-1 0.1957 4.11-1 0.3497 1.86-1
Inside straight or pair 10 0.2128 3.70-1 0.2174 3.60-1 0.3839 1.60-1
Open-ended straight or high pair 11 0.2340 3.27-1 0.2391 3.18-1 0.4172 1.40-1
Inside straight or flush;
Flush or high pair 12 0.2553 2.92-1 0.2609 2.83-1 0.4496 1.22-1
13 0.2766 2.62-1 0.2826 2.54-1 0.4810 1.08-1
Open-ended straight or pair 14 0.2979 2.36-1 0.3043 2.29-1 0.5116 0.955-1
Open-ended straight or flush;
Flush or pair; Inside straight,
flush or high pair 15 0.3191 2.13-1 0.3261 2.07-1 0.5412 0.848-1
16 0.3404 1.94-1 0.3478 1.88-1 0.5698 0.755-1
17 0.3617 1.76-1 0.3696 1.71-1 0.5976 0.673-1
Inside straight or flush or pair;
Open-ended straight, flush or high pair 18 0.3830 1.61-1 0.3913 1.56-1 0.6244 0.601-1
19 0.4043 1.47-1 0.4130 1.42-1 0.6503 0.538-1
20 0.4255 1.35-1 0.4348 1.30-1 0.6753 0.481-1
Open-ended straight, flush or pair 21 0.4468 1.24-1 0.4565 1.19-1 0.6994 0.430-1
Odds Against Flopping
Hand Odds Percent
A flush 118-1 0.8%
A straight when holding any two connecting cards J-10 through 5-4 76-1 1.3%
Three of a kind when holding a pocket pair 7.5-1 11.8%
A pair (matching one of your holecards) 2.45-1 29.0%
Odds of two hands versus each other preflop (approximated)
Situation Hands Odds Percent
Higher pair vs. lower pair Js Jc vs. 7h 7d 4.09-1 80.3% vs. 19.7%
Pair vs. two higher cards 7s 7c vs. Ah Jd 1.23-1 55.1% vs. 44.9%
Pair vs. two lower card Qs Qc vs. 9h 7d 4.77-1 82.7% vs. 17.3%
Pair vs. a higher and a lower card Js Jc vs. Ah 7d 2.50-1 71.4% vs. 28.6%
Two higher cards vs. two lower cards Qs Jc vs. 6h 5d 1.70-1 62.9% vs. 37.1%
A higher and a lower card vs.
two middle cards As 6c vs. Jh 9d 1.27-1 55.9% vs. 44.1%
Highest and third highest card vs.
second highest and lowest card As 6c vs. Jh 2d 1.73-1 63.3% vs. 36.7%
Highest and common card vs. lowest and common card As Jc vs. Jh 9d 2.74-1 73.3% vs. 26.7%
Choice of an overcard hitting the board when holding a pocket pair
Hand Overcard on Flop Overcard on Complete Board
2-2 100% 100%
3-3 99.9% 99.9997%
4-4 99.4% 99.988%
5-5 98.1% 99.91%
6-6 95.8% 99.6%
7-7 92.1% 98.8%
8-8 86.7% 96.9%
9-9 79.3% 93.3%
10-10 69.5% 86.9%
J-J 57% 76.3%
Q-Q 41.4% 59.9%
K-K 22.6% 35.3%
A-A 0% 0%
Probability of facing a larger pair when holding...
Hand Against 1 Against 2 Against 3 Against 4 Against 5 Against 6 Against 7 Against 8 Against 9
K-K 0.0049 0.0098 0.0147 0.0196 0.0244 0.0293 0.0342 0.0391 0.0439
Q-Q 0.0098 0.0195 0.0292 0.0388 0.0484 0.0579 0.0673 0.0766 0.0859
J-J 0.0147 0.0292 0.0436 0.0577 0.0717 0.0856 0.0992 0.1127 0.1259
10-10 0.0196 0.0389 0.0578 0.0764 0.0946 0.1124 0.1299 0.1470 0.1637
9-9 0.0245 0.0484 0.0718 0.0946 0.1168 0.1384 0.1593 0.1795 0.1990
8-8 0.0294 0.0580 0.0857 0.1125 0.1384 0.1634 0.1873 0.2101 0.2318
7-7 0.0343 0.0674 0.0994 0.1301 0.1595 0.1874 0.2138 0.2387 0.2619
6-6 0.0392 0.0769 0.1130 0.1473 0.1799 0.2104 0.2389 0.2651 0.2890
5-5 0.0441 0.0862 0.1263 0.1642 0.1996 0.2324 0.2623 0.2892 0.3129
4-4 0.0490 0.0956 0.1395 0.1806 0.2186 0.2532 0.2841 0.3109 0.3334
3-3 0.0539 0.1048 0.1526 0.1967 0.2370 0.2729 0.3040 0.3300 0.3503
2-2 0.0588 0.1141 0.1654 0.2124 0.2546 0.2914 0.3222 0.3464 0.3633
Probability of facing multiple larger pairs when holding...
Hand Against 1 Against 2 Against 3 Against 4 Against 5 Against 6 Against 7 Against 9
K-K < 0.00001 0.00001 0.00003 0.00004 0.00007 0.00009 0.00012 0.00016
Q-Q 0.00006 0.00018 0.00037 0.00061 0.00091 0.00128 0.00171 0.00220
J-J 0.00017 0.00051 0.00102 0.00171 0.00257 0.00360 0.00482 0.00621
10-10 0.00033 0.00099 0.00200 0.00335 0.00504 0.00709 0.00950 0.01226
9-9 0.00054 0.00164 0.00330 0.00553 0.00836 0.01177 0.01580 0.02045
8-8 0.00081 0.00244 0.00493 0.00828 0.01253 0.01769 0.02378 0.03084
7-7 0.00112 0.00341 0.00689 0.01160 0.01758 0.02487 0.03351 0.04353
6-6 0.00149 0.00454 0.00918 0.01550 0.02353 0.03335 0.04503 0.05861
5-5 0.00191 0.00583 0.01182 0.01998 0.03040 0.04318 0.05840 0.07619
4-4 0.00239 0.00728 0.01480 0.02506 0.03821 0.05438 0.07371 0.09635
3-3 0.00291 0.00890 0.01812 0.03075 0.04698 0.06699 0.09099 0.11919
2-2 0.00349 0.01068 0.02180 0.03706 0.05673 0.08107 0.11034 0.14484
Probability of facing an ace with large kicker when holding...
Hand Against 1 Against 2 Against 3 Against 4 Against 5 Against 6 Against 7 Against 8 Against 9
AK 0.00245 0.00489 0.00733 0.00976 0.01219 0.01460 0.01702 0.01942 0.02183
AQ 0.01224 0.02434 0.03629 0.04809 0.05974 0.07126 0.08263 0.09386 0.10496
AJ 0.02204 0.04360 0.06468 0.08529 0.10545 0.12517 0.14445 0.16331 0.18175
AT 0.03184 0.06266 0.09250 0.12139 0.14937 0.17645 0.20267 0.22805 0.25263
A9 0.04163 0.08153 0.11977 0.15642 0.19154 0.22520 0.25745 0.28837 0.31799
A8 0.05143 0.10021 0.14649 0.19038 0.23202 0.27152 0.30898 0.34452 0.37823
A7 0.06122 0.11870 0.17266 0.22331 0.27086 0.31550 0.35741 0.39675 0.43369
A6 0.07102 0.13700 0.19829 0.25523 0.30812 0.35726 0.40291 0.44531 0.48471
A5 0.08082 0.15510 0.22338 0.28615 0.34384 0.39687 0.44561 0.49041 0.53160
A4 0.09061 0.17301 0.24795 0.31609 0.37806 0.43442 0.48567 0.53227 0.57465
A3 0.10041 0.19073 0.27199 0.34509 0.41085 0.47000 0.52322 0.57109 0.61416
A2 0.11020 0.20826 0.29552 0.37315 0.44223 0.50370 0.55840 0.60706 0.65037
A board being dealt consisting of...
Board Texture Making on flop Making by turn Making by river
Prob. Odds Prob. Odds Prob. Odds
Three or more of same suit 0.05177 18.3-1 0.13522 6.40-1 0.23589 3.24-1
Four or more of same suit 0.01056 93.7-1 0.03394 28.5-1
Rainbow flop (all different suits) 0.39765 1.51-1 0.10550 8.48-1
Three cards of consecutive rank
(but not four consecutive) 0.03475 27.8-1 0.11820 7.46-1 0.25068 2.99-1
Four cards to a straight (but not five) 0.03877 24.8-1 0.18991 4.27-1
Three or more cards of
consecutive rank and same suit 0.00217 459-1 0.00869 114-1 0.02172 45.0-1
Three of a kind
(but not a full house or four of a kind) 0.00235 424-1 0.00935 106-1 0.02128 46-1
A pair
(but not two pair or three or
four of a kind) 0.16941 4.90-1 0.30417 2.29-1 0.42450 1.36-1
Two pair (but not a full house) 0.01037 95.4-1 0.04716 20.2-1
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