Hi. Come on in. I've heated up some chili, hot dogs, buns, and cheese. Help yourself.
"Where are my big pairs? And I haven't seen A-K since forever. Shouldn't I be getting better cards, according to probability? Or, has probability deserted my part of the poker table?"
We talked a few weeks back about probability and the odds against being dealt certain starting hands in a game of seven-card stud, and I promised we'd do the same for hold'em. Being a man of my word, I have returned with the relevant numbers.
Let us enumerate. We'll begin at the top again – with a pair of aces. According to probability, you should be dealt this very best hold'em starting hand once out of 221 deals (odds against of 220-to-1). We'll again assume that your game is being dealt an average of 30 hands per hour and that you play poker six hours a day. Adjust those figures to your actual game and playing time.
Those beautiful aces should appear in your preflop hand an average of once every seven hours and 20 minutes of playing time, which would be once every 1.2 playing days (that's 221 hands divided by 30 hands per hour, which is then divided by the six hours of your playing day). These numbers will hold true for any specific pair (K-K, Q-Q, and so on).
The probability of being dealt any pair is once out of every 17 deals (odds against of 16-to-1). That is once every half-hour (34 minutes), on average.
You'll be dealt a big pair – tens through aces – an average of once every 44 hands of dealing. That means you'll probably start with a big pair every hour and 28 minutes, on average.
"Hmm, I'm beginning to think I'm not being treated as badly as I thought by probability."
A medium pair – sixes through nines – should appear an average of once out of 55 hands, so watch for them every hour and 50 minutes.
A small pair – deuces through fives – appears on the same schedule.
The probability of starting with one of any two specific pair, such as kings or queens, is once in every 111 deals. That translates to one time every three hours and 41 minutes.
Probability tells us that you should be dealt A-K suited an average of once every 332 times the dealer tosses the cards your way. When we figure that out, we learn that hand should appear every 11 hours, which would be every 1.8 playing days.
A-K offsuit shows up once every 111 deals, on average, which translates to once every three hours and 41 minutes. The probability of any A-K – suited or not – is once out of 83 deals. So, "Big Slick" will come around every two hours and 46 minutes, on average, according to probability.
You'll be dealt an ace with a facecard one out of 28 times. That's about once every 55 minutes. Probability says an ace with any card of the same suit will arrive with the same frequency.
The chances of getting any two specific suited cards are one out of 332. That's 11 hours of playing time. Any two specific unsuited cards can be figured at 110-to-1, which is once every three hours and 41 minutes.
Make up your own combinations of cards using the previous information.
Now you know the probabilities of receiving various starting hands, but probability has a way of deviating, sometimes for long periods of time.
A friend of mine who deals in statistical probability tells me that it isn't at all unusual for cards to run at far less than probability for six months. "Ouch! Just the thought of that hurts all the way down to my toes."
After all of this, I want you to keep in mind that your task is not to gripe about your lousy cards, but to play them as best you can.
You're right, the chili-cheese dogs could use some chopped onions. Next time. Now I require repose. Kill the light on your way out.
Editor's note: Roy West, author of the bestseller 7 Card Stud, the Complete Course in Winning (available from Card Player), continues to give his successful poker lessons in Las Vegas to both tourists and locals. Ladies are welcome. Get his toll-free 800 number from his ad on Page 106.