Poker, like life, is all about probabilities.

Every day you weigh up the risks of doing something against the benefits. It can vary from:

“Do I walk across this dance floor and ask that girl to dance?”

Risk: Humiliation! Reward: She might say yes!

Or, “Do I cross this road?”

Risk: Being hit by a car. Reward: Getting to the other side. And so on.

Poker is very much a probability-based game and so playing a strategy that follows correct poker probabilities (or odds) will increase your chances of success.

What follows are some of our favourite odds – and what they mean for you:

  • If you disregard sets, there are 169 different possible two-card hands.
  • There are 16 ways (chances) of getting AK (4 of which are AK suited), but only 6 of getting AA (or 9-9, for that matter).

Pairs

  • AA (or KK, etc.) occurs once in every 221 hands (0.45%). I.e. you can expect one of AA, KK or QQ every 74 hands – or at least one of AA, KK, QQ or AK suited once every 60 hands.
  • Hence, you can expect to pick up AA, KK, QQ or AKs about once every 7-8 rounds in an 8-handed game.
  • If you have a pair before the flop

– the chance of the deck flopping ‘overcards’ (cards higher than yours):

      • if you hold KK is 22%
      • if you hold QQ is 41%
      • if you hold JJ is 56%
      • if you hold 10-10 is 69%
      • if you hold 9-9 is 80%; 8-8 is 86%; 7-7 is 92%; 6-6 is 96%, 5-5 is 98%
    • a pair has about an 82% chance against a lower pair;
    • a pair has an 18% chance against a higher pair – indeed KK is about the same chance against AA as is 2-2! (Hence any pair is a good bet when you are getting pot odds of better than 4:1 (see our strategy guide on ‘Pot Odds & Implied Odds’);
    • a pair is 55% (11:10) against 2 higher cards (i.e. 2-2 vs A-10, or 2-2 vs 4-9) and about 50/50 if the higher cards are suited or connected;
    • a pair is 86% against 2 lower cards (i.e. QQ vs 10-6) – but less if they are suited and less again if they are suited and connected;
    • a pair is 5:2 (71.5%) against 1 card higher and 1 lower – e.g. QQ vs A-7;
    • a pair will flop a set or better 11.8% of the time – i.e. 1 in 8.5 (or odds of 7.5:1);
    • a pair will flop a set 10.8% of time – i.e. once in 9 or odds of 8:1 against;
    • a pair will flop a full house 1 in 101 times;
    • a pair will flop 4 of a kind 1 in 407 times;
    • a pair will flop 4 to a straight 1 in 37 times;
    • if you have a pair after the flop, you’ll make at least trips on the last 2 cards 8.42% of time (odds 11:1);
    • 4-4 is only 11:10 (55%) against 6-5 (or any 2 higher cards);
    • if you have 2 pairs after the flop – you’ll make a full house or better 16.7% of time (odds 5:1)

Odds of holding an A

The odds of being dealt an A are 15% and (because the odds of being dealt a pair are 5.9%), the odds of being dealt an A or a pair are about 21%.

  • If you have an A, the probability of no one else having one is:

For 2 players = 88%, 3 = 77%, 4 = 67%, 5 = 58%, 6 = 50%, 7 = 43%, 8 = 36%, 9 = 30%. I.e. if you have an A, UTG, and there are 9 other players at the table, there’s a 70% chance that at least one other player also has an A!

Calculation of odds when you have a pair (say, 5–5) and someone puts you all in…

  • …what are your chances of winning?
    • If Villain has a higher pair, you are 4.5:1 against,
    • But (if you have 5-5), there are only 9 higher pairs and 6 ways of getting each – so 54 possible hands. Against these you’ll only win 10 (i.e. against a higher pair, you are a 4.5:1 underdog).
    • Say you feel Villain would have raised you all-in with any pair. Then you’ll win 4.5:1 times against the additional 3 pairs lower than yours – i.e. you’ll win nearly 14 out of the 18 times he’ll have these.
    • So, against ALL his possible pairs, you’ll win about 24 out of the 72 combinations of these pairs; i.e. winning 24 and losing 48 – so you are a 1-in-3 (or 2:1 against) chance.
    • But you think he would also have shoved with AK, AQ, AJs, A10s. There are 16 AK’s, 16 AQ’s, and 4 each of AJs and A10s – so 40 more combinations of cards he might have. Your 5-5 will win a little over 50% of the time against these; i.e. you’ll win around 21 of these 40 hands.
    • So, if your feeling is that he would have shoved with all of these hands, and only these, then you will win 10/54 + 14/18 + 24/72 + 21/40 times – i.e. out of the 184 combinations of cards you expect him to have, you will beat 59. As you’ll win 59 times and lose 125 times out of 184, you’ll win 32% of the time and lose 68% of the time.
    • Hence, you’ll need the pot to offer you a bit better than 2:1 in order for you to call. If it will cost you 60 to call, then the pot, after your money has gone in, needs to be more than 185 to justify your call (more on this in our Pot Odds & Implied Odds strategy guide).
  • If you have 10-10 or J-J and you think Villain would only have put you in with AA, KK, QQ or AK, then that’s 3 combinations of pairs with 6 ways of getting each (18), plus 16 ways of getting AK.
    • So, you believe he has 34 possible hands. Of these, you’ll win 20% of the 18 (3.6 times), and 55% of the 34 (18 times) – so you’ll win approximately 12 times out of 34 – and he’ll win 22.
    • Therefore, you need the pot offering you about 2:1 or more for you to call.
    • If it will cost you 60 to call, the pot, after your money has gone in, needs to be more than 185 to justify your call.

Straights

  • If you have an open-ended straight after the flop – the chance of completing it (‘filling’) on the turn or river is 31.5% (i.e. approx. 8 out of 47, twice – or 2:1 against).
  • If you have an open-ended straight flush after flop

– you have 15 outs (the 9 flush cards plus the 8 straight cards less 2 straight cards you’ve already counted as flush cards). Applying the rule of 4 and 2 tells you that there is about a 60% chance (it’s actually a 54%) that you’ll make at least a straight (odds of better than 1:1).

  • If you start with unsuited connectors;
  • the chance of flopping a straight = 1% (odds 100:1);
  • the chance of flopping an open-ended straight draw = 6% (odds 15:1);
  • 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! All other connectors from 10-9 to 5-4 will make 4 straights but only 3 will be the nuts. When cards are 1 apart – e.g. 5-3, you can only make 3 straights and only 2 will be the nuts. When cards are 2 apart e.g. 6-4, only 2 straights are possible and only 1 is the nuts.

Trips

  • If you have trips on the flop – the chance of ending up with a full house or better is 33% (odds of 2:1).

Flushes

  • If you start with any 2 suited cards:
    • you’ll flop a flush 1 in 119 times – i.e. less than 1%;
    • you’ll flop at least a four-flush 11.8% of the time – (odds 7.5:1);
    • when four-flushed on the flop – you have a 35% chance to get a flush on the turn or river.

Therefore, any 2 suited cards are approximately 4% to fill to a flush if you stay to the river (and ~2% to fill to a straight if connected).

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 = even money.

Other odds

  • Any 2 cards vs any 2 lower cards (e.g. AK vs 7-2) – are about a 9:5 chance (63%), i.e. less than 2:1
  • Two higher cards vs a pair (e.g. KQ vs 9-9) = 9:11, or 45%
  • Two suited higher cards vs a pair (e.g. KQs vs 9-9) = 47:52, i.e. nearly 50%
  • One card higher and one lower than a pair (e.g. K-10 vs QQ) is only 2:5 underdog
  • One card higher and one in between Villain’s 2 cards (e.g. AJ vs K9) = 3:2
  • One card higher and one lower than Villain’s 2 cards (e.g. A-2 vs J-4) = 6:5 (56%)
  • One card the same as Villain’s, the other higher (e.g. A-10 vs A-9) = 71%
  • No pair improving to at least a pair = 27%

Some nice insights

  • Most flops miss 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 = allow at least 10% (Harrington[1]).
  • 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.

  • Drawing odds from 47 unseen cards:

Number of Outs Probability of Hitting on the Turn Probability of Hitting on the Turn or River
15 32%         or      2.1 : 1 54%         or      1 : 1.2    (that’s 1.2 : 1 in favour)
14 30%         or      2.3 : 1 51%         or      1 : 1
13 27.5%     or      2.6 : 1 48%         or      1.1 : 1
12 25.5%     or      2.9 : 1   45%         or      1.2 :1
11 23.5%     or      3.3 : 1 42%         or      1.4 : 1
10 21%         or      3.8 : 1 38%         or      1.6 : 1
9 19%         or      4.3 : 1 35%         or      1.9 : 1
8 17%         or      4.9 : 1 31.5%     or      2.2 : 1
7 15%         or      5.7 : 1 27.5%     or      2.6 : 1
6 13%         or      6.8 : 1 24%         or      3.2 : 1
5 10.5%     or      8.5 : 1 20%         or      4 : 1
4 8.5%        or      10.8 : 1 16.5%     or      5.1 : 1
3 6.5%        or      14.4 : 1 12.5%     or      7 : 1
2 4%            or      24 : 1 8.5%        or      10.8 : 1
1 2%            or      49 : 1 4.5%        or      22.8 : 1

 

In Summary

Odds are fun – but they can also help you a lot.

Odds tell you what your chances are.

Pot Odds tell you whether there is enough money in the pot to for you take that chance.

Implied Odds look at how much more money might go into the pot and so make your decision easier.

We now invite you to take your understanding of odds one step further with our Pot Odds & Implied Odds strategy guide.

ENJOY!

[1] Harrington, D. and Robertie, B., 2010. Harrington On Hold ‘Em. Two Plus Two Publishing.