| | 
"THREE callers at the River? What were you all THINKING?!"
All sorts of interesting hand odds and probabilities for the wonderful game that is Texas Hold'em. Yes, I really really need to get out more...
As anyone will tell you I generally only play The Beer Hand or American Airlines (although in a pinch I'll reluctantly call the Big Blind with Big Slick, but only if it's suited, only in position, and only in an unraised pot) and this means that during the average tourney I play about one in a hundred hands, or perhaps two at best, before being blinded out on the bubble with some crap like 8-4 offsuit. Below for your delectation please find some interesting statistics regarding the probabilities of your receiving these or any other 2 particular hole cards pre-flop. Enjoy!
| Hole cards | % Chance | Probability | Odds Against | | The Beer Hand, 7-2 offsuit | 0.9% | 1 in 111 | 110 : 1 | | AK suited | 0.3% | 1 in 338 | 331 : 1 | | AA | 0.45% | 1 in 221 | 220 : 1 | | AQ or AJ suited | 0.60% | 1 in 166 | 165 : 1 | | AK offsuit | 0.9% | 1 in 111 | 110 : 1 | | AA or KK | 0.9% | 1 in 111 | 110 : 1 | | Any premium pr - KK, QQ or JJ | 1.36% | 1 in 74 | 73 : 1 | | Any premium pr - AA, KK, QQ, JJ | 1.80% | 1 in 56 | 55 : 1 | | AQ or AJ offsuit | 1.81% | 1 in 55 | 54 : 1 | | Any 2 cards Jacks or better | 9.00% | 1 in 11 | 10 : 1 | | Any 2 suited connectors | 2.11% | 1 in 48 | 47 : 1 | | Ax (T or less) suited | 2.71% | 1 in 37 | 36 : 1 | | Any pair | 6.00% | 1 in 17 | 16 : 1 | | Any 2 offsuit connectors | 6.33% | 1 in 16 | 15 : 1 | | Ax (T or less) offsuit | 8.14% | 1 in 12 | 11 : 1 | | Any Ace | 16.00% | 1 in 6 | 5 : 1 | | Any 2 suited cards | 23.53% | 1 in 4 | 3 : 1 | | Any hand containing a pair or Ace | 20.36% | 1 in 5 | 4 : 1 |
So the hand you've waited for all night has come - Big, Slick, Walking Back to Houston, call it what you will - and you're about to see the flop. What is the likelihood of some dumbass whos has called your pre-flop raise with 9-3 offsuit sending you home early? This and other questions are not answered in the frankly rather educational table shown below.
| The Probability of the flop being | % Chance | Probability | Odds Against | | QJT of your suit (a Royal Flush) | 0.01% | 1 in 19,600 | 19,599 : 1 | | AAA or KKK (to give you quads) | 0.01% | 1 in 9,800 | 9,799 : 1 | | AAK or KKA (to give you a boat) | 0.09% | 1 in 1089 | 1,088 : 1 | | 3 of a kind (anything from trip 2-Q) | 0.22% | 1 in 445 | 444 : 1 | | QJT of any suit (flopped straight) | 0.32% | 1 in 311 | 310 : 1 | | AAx or KKx (to give you trips) | 1.35% | 1 in 74 | 73 : 1 | | Any 2 of your suit with an A or K | 1.68% | 1 in 59 | 58 : 1 | | Any 3 cards of your suit (nut flush) | 1.84% | 1 in 55 | 54 : 1 | | AQ or AJ offsuit | 1.81% | 1 in 55 | 54 : 1 | | AK + any other card (top two pair) | 2.02% | 1 in 50 | 49 : 1 | | 3 card of another suit (not yours!) | 4.38% | 1 in 23 | 22 : 1 | | Any 2 of your suit (4 to the flush) | 10.94% | 1 in 9 | 8.5 : 1 | | Any pair less than an Ace or King | 11.79% | 1 in 8 | 7.5 : 1 | | Any pair + an Ace | 20.36% | 1 in 5 | 4 : 1 | | Any 2 cards + a K or an A (top pr) | 32.43% | 1 in 3 | 2 : 1 |
I have seen AA run into KK headsup just once in my lifetime (Christmas 2004), and was so startled to stumble across the odds of such an event happening that it spurred me on to provide the info below for anyone with sufficient time on their hands and insufficient work to do to bore themselves silly with. Feel free to bore yourself silly.
| What in Alan's name of are the odds of this? | Probability | Odds against | | AA running into KK preflop (heads up) | 1 in 22,560 | 22,599 : 1 | | Hitting a backdoor straight (runner, runner) | 1 in 68 | 67 : 1 | | Hitting a Backdoor Flush (suited runner, runner) | 1 in 24 | 23 : 1 | | Pocket pair improving to 3 of a kind after flop | 1 in 11 | 10 : 1 | | If you have suited cards, flopping a four flush | 1 in 9 | 8 : 1 | | Pocket pair improving to 3 of a kind on the flop | 1 in 8 | 7 : 1 | | Catching Ace on the Turn or River (missed flop) | 1 in 8 | 7 : 1 | | Completing a Gutshot Straight by the River | 1 in 6 | 5 : 1 | | 2 pair improving to a boat by the River | 1 in 5.8 | 5 : 1 | | Flop pair improving to 2 pair or 3 of a kind by River | 1 in 4.7 | 4 : 1 | | No pair improving to a pair on the flop (either card) | 1 in 3 | 2 : 1 | | Completing an Open Ended Straight by the River | 1 in 2.9 | 2 : 1 | | 3 of a kind improving to a boat/quads by the River | 1 in 2.7 | 3 : 2 | | 4 to a flush hitting the 5th card by the River | 1 in 2.6 | 3 : 2 | | Gutshot and pair improving to two pair or better | 1 in 2.6 | 3 : 2 | | Two overcards improving to a pair by the River | 1 in 2.3 | 3 : 2 | | A-K preflop (Odds of hitting A or K by the River) | 1 in 2 | 1 : 1 | | Open Ended Straight-Flush (eg 8c, 9c, 10c, Jc) completing to a flush or a straight by the River | 1 in 1.85 | 1 : 1 | | Q-Q versus A-K heads up until the River | 1 in 1.78 | 14 : 11 |
Shovelled it all in there pre-flop and been looked up? Are you a dog? In a minute it won't really matter, but here's how it looks for you so you can bitch about how far ahead you were before your opponent caught runner runner for his straight...
| You hold these | You win | Your opponent holds these | They win | | 7c2h [offsuit] | 12.5% | AdAs | 87.5% | | 7c2h [offsuit] | 30.5% | AdKd [suited] | 69.5% | | 7c2h [offsuit] | 32.5% | AdKc [offsuit] | 67.5% | | 7c2h [offsuit] | 29.1% | Jh, Th [suited] | 70.9% | | 7c2h [offsuit] | 30.4% | Jh, Td [offsuit] | 69.6% | | 7c2h [offsuit] | 48.8% | 5h6h [suited] | 51.2% | | 7c2h [offsuit] | 51.5% | 5h6s [offsuit] | 48.5% | | 7c2h [offsuit] | 30.9% | 3c3s | 69.1% | | AcAh | 81.4% | KsKd | 18.6% | | AcAh | 87.8% | AdKd [suited] | 12.2% | | AcAh | 93.5% | AdKc [offsuit] | 6.5% | | AdKd [suited] | 75.7% | AsQh [offsuit] | 24.3% | | AdKc [offsuit] | 74.4% | AsQh [offsuit] | 25.6% | | AdKd [suited] | 71.6% | AhQh [suited] | 28.4% | | AdKc [offsuit] | 69.8% | AhQh [suited] | 30.2% | | AdKd [suited] | 64.2% | 5h6s [offsuit] | 35.8% | | AdKc [offsuit] | 61.5% | 5h6s [offsuit] | 38.5% | | AdKd [suited] | 60.6% | 5h6h [suited] | 39.4% | | AdKc [offsuit] | 57.7% | 5h6h [suited] | 42.3% | | Kc, Ks | 79.7% | Jh, Th [suited] | 20.3% | | Kc, Ks | 83.3% | Jh, Td [offsuit] | 16.7% | | 5c, 5s | 50.3% | JhTd [offsuit] | 49.7% | | 5c, 5s | 47.7% | JhTh [suited] | 52.3% | | TsTh | 57.3% | AdJc [offsuit] | 42.7% | | TsTh | 54.2% | AdJd [suited] | 45.8% | | AdKd [suited] | 49.5% | 3c3s | 50.5% | | AdKc [offsuit] | 46.5% | 3c3s | 53.5% | | KcJc [suited] | 41.4% | AsQh [offsuit] | 58.6% | | KcJc [suited] | 38.8% | AsQs [suited] | 61.2% | | KcJd [offsuit] | 37.9% | AsQh [offsuit] | 62.1% | | KcJd [offsuit] | 35.0% | AsQs [suited] | 65.0% |
All the above figures were produced during a quiet afternoon at the office using the marvellous Texas Hold'em calculator kindly provided by the lads at Cardplayer.com - have a butcher's at it here. Sometimes I rounded the figures up and sometimes I rounded 'em down just to keep you all on your toes, so if you see anything you disagree with just keep it to yourselves...
- "Behold the power of the Beer Hand!" -
| |
