Texas Hold ‘Em Odds from 1 to 52

[SS] Stan the Stat loved lists almost as much as he loved numbers. His favorite Go-Go’s song? “Girl of 100 Lists”.1 Slacker. Stan had created that many by the time he was seven years old. So it was no surprise when he proudly unveiled his latest list of numbers, Texas Hold ‘Em Odds from 1 to 52. “One for each card in the deck”, Stan boasted. “Of course, I had several choices for many of the odds, so I tried for variety. By coincidence, the last one stumped me the longest time.”

A♠ 1 to 1 Odds of finishing with a pair on the river with unpaired hole cards 1.08 to 1 48.15%
A♥ 2 to 1 Odds of improving from 3-of-a-kind to a full house or quads on the turn or river 1.99 to 1 33.40%
A♦ 3 to 1 Odds of being dealt suited cards 3.25 to 1 23.53%
A♣ 4 to 1 Odds of hitting a flush draw on the river 4.11 to 1 19.57%
K♠ 5 to 1 Odds of being dealt connectors 5.38 to 1 15.69%
K♥ 6 to 1 Odds of being dealt at least one Ace 5.70 to 1 14.93%
K♦ 7 to 1 Odds of hitting a 3-outer on the turn or river 7.01 to 1 12.49%
K♣ 8 to 1 Odds of flopping a flush draw with suited cards 8.14 to 1 10.94%
Q♠ 9 to 1 Odds of flopping an 8-out straight draw from max connectors (JT-54) 8.57 to 1 10.45%
Q♥ 10 to 1 Odds of being dealt two cards that are Jacks or higher 10.05 to 1 9.05%
Q♦ 11 to 1 Odds of filling an inside straight draw on the turn 10.75 to 1 8.51%
Q♣ 12 to 1 Odds of not flopping an overcard with pocket Sevens 11.73 to 1 7.86%
J♠ 13 to 1 Odds of being dealt 2-gappers 12.81 to 1 7.24%
J♥ 14 to 1 Odds of hitting a 3-outer on the river 14.33 to 1 6.52%
J♦ 15 to 1 Odds of completing a flush by the river with suited cards 14.63 to 1 6.40%
J♣ 16 to 1 Odds of being dealt a pocket pair 16.00 to 1 5.88%
10♠ 17 to 1 Odds of being dealt unsuited 2-gappers (e.g., 85o) 17.42 to 1 5.43%
10♥ 18 to 1 Odds of a monochromatic flop 18.32 to 1 5.18%
10♦ 19 to 1 Odds of beating KK with K2 offsuit (suit dominated, the worst all-in preflop matchup) 18.69 to 1 5.08%
10♣ 20 to 1 Odds of being dealt connected cards, 10 or higher 19.72 to 1 4.83%
9♠ 21 to 1 Odds of being dealt a pair of Fives or better 21.10 to 1 4.52%
9♥ 22 to 1 Odds of hitting a backdoor straight (e.g., from 876) 21.52 to 1 4.44%
9♦ 23 to 1 Odds of hitting a backdoor flush 23.02 to 1 4.16%
9♣ 24 to 1 Odds of a single opponent with random hole cards having quads on a 3-of-a-kind flop 24.00 to 1 4.00%
8♠ 25 to 1 Odds of being dealt any suited connectors 24.50 to 1 3.92%
8♥ 26 to 1 Odds of making a straight or better on the turn with random hole cards 26.15 to 1 3.68%
8♦ 27 to 1 Odds of making 3-of-a-kind by the turn with random hole cards 26.81 to 1 3.60%
8♣ 28 to 1 Odds of a 3-card straight flop 27.78 to 1 3.48%
7♠ 29 to 1 Odds of being dealt suited 2-gappers 29.14 to 1 3.32%
7♥ 30 to 1 Odds of the board having no overcards by the turn with pocket Sevens 30.48 to 1 3.18%
7♦ 31 to 1 Odds of the board having no overcards by the river with pocket Eights 31.21 to 1 3.10%
7♣ 32 to 1 Odds of being dealt suited cards Tens or higher 32.15 to 1 3.02%
6♠ 33 to 1 Odds of hitting a backdoor half-inside straight (e.g., 976) 32.78 to 1 2.96%
6♥ 34 to 1 Odds of hitting a backdoor flush to chop the pot when your opponent flops the worst flush (e.g., holding 32s) 34.36 to 1 2.83%
6♦ 35 to 1 Odds of making a full house or better on the river with random hole cards 34.71 to 1 2.80%
6♣ 36 to 1 Odds of nobody holding an Ace, King, or Queen at a 6-handed table 35.94 to 1 2.71%
5♠ 37 to 1 Odds of flopping an 8-out straight draw from 3-gappers 37.28 to 1 2.61%
5♥ 38 to 1 Odds of making a full house on the river with random hole cards 37.52 to 1 2.60%
5♦ 39 to 1 Odds of improving a pair to a full house on the turn and river 39.04 to 1 2.50%
5♣ 40 to 1 Odds of being dealt a weak suited Ace (A9s-A2s) 40.44 to 1 2.41%
4♠ 41 to 1 Odds of hitting a 1-outer on the river when three players are all-in (e.g., QQ vs. KK vs. AA on AKQ2 board) 41.00 to 1 2.38%
4♥ 42 to 1 Odds of making exactly Jack high on the turn with random hole cards 42.28 to 1 2.31%
4♦ 43 to 1 Odds of being dealt a pair of Tens or better 43.20 to 1 2.26%
4♣ 44 to 1 Odds of flopping a four flush holding unsuited cards 43.55 to 1 2.24%
3♠ 45 to 1 Odds of hitting an inside straight flush draw on the river 45.00 to 1 2.17%
3♥ 46 to 1 Odds of being dealt max stretch suited connectors (JT-54) 46.36 to 1 2.11%
3♦ 47 to 1 Odds of hitting a runner-runner 1-gap straight flush or a full house/quads missing three board outs (e.g., 8d8h vs. Ad5d + Jd9d2d [Jh, 9h, 2h mucked]) 46.83 to 1 2.09%
3♣ 48 to 1 Odds of flopping two pairs using both unpaired hole cards 48.49 to 1 2.02%
2♠ 49 to 1 Odds of at least one player holding 4-of-a-kind or better if 10 players make it to the river 49.21 to 1 1.99%
2♥ 50 to 1 Odds of an opponent holding a pair of Aces when you have an Ace at a 9-handed table 50.04 to 1 1.96%
2♦ 51 to 1 Odds of making a flush or better by the turn with random hole cards 51.43 to 1 1.91%
2♣ 52 to 1 Odds of hitting a runner-runner full house or quads missing one hole out (e.g., 88 vs. A7s vs. + QT2s [8 mucked])2 51.56 to 1 1.90%

[SS] “Plenty of Google hits for ’52 to 1′ too.”

[RR] “But they all really meant ‘1 in 52′, or ’51 to 1’?” Roderick the Rock surmised.

[SS] “Exactly right. I almost gave up and changed the list to go from ‘1 in 1’ to ‘1 in 52’, but I hated having the pointless ‘1 in 1’ (‘Odds of there being an error in this list’?). I ended up calculating dozens of runner-runner outs until I found one that worked.”

Footnotes:

  1. Track three on the Go-Go’s 1982 album Vacation was somehow never released as a single ;-). Jane Wiedlen’s lists included: “things I love”, “what shall I wear”, “who have I kissed”, and “things I must get done today”.
  2. Added missing 52 to 1 odds on July 7, 2014.

{ The Hold ‘Em at Home blog is brought to you by THETA Poker Pro, the strongest, fastest, and most configurable Texas Hold ‘Em game for iPhone, iPad, iPod touch, and Apple TV. }

Tags:
Categories:

6 thoughts on “Texas Hold ‘Em Odds from 1 to 52”

  1. Odds of beating two pair or getting trips aces, with ace in the hole and getting runner runner aces (turn and river)? Thanks.

  2. Steve, “If you give a man a fish…”.

    Please read this article on calculating odds — http://www.thetapoker.com/outs.html — do the math twice (three outs on the turn and two outs on the river) and multiply the results.

    Hint: the answer is very small (under 3 in a thousand).

  3. I realise I’m super late to the party here, but I was trying to figure out some of these for myself and I’m stumped on the two backdoor straights, I’m getting exactly half of what you have here…

    You have #22 listed as 4.44% with 876. I figure you can complete 876 with 45, 59 and 9T. My calculation comes out as “((4/47)*(4/46)) + ((4/47)*(4/46)) + ((4/47)*(4/46))” which results as 2.22%, which as you can see is exactly half. I have pretty much the same problem problem with #33 as well.

    Could you please help me figure out where I’ve gone wrong here? Thanks. 🙂

  4. I figured it out right as I posted this. The first card drawn has 8 outs not 4. I’m getting the correct answer now. 🙂

    Sorry for the spam! You can delete my previous post if you like.

  5. Sorry I wasn’t able to reply in the four-minute window I had ;-). I’m glad you were able to figure it out though, since being able to work through the calculations is much more important than memorizing the answers.

    Thanks for reading!

Leave a Reply

Your email address will not be published. Required fields are marked *