Saturday, December 01, 2007

No two poker hands are the same (non-grumpy content)

For some odd reason, I have lately been wondering whether any two poker hands will ever be exactly the same (assuming a random shuffle; i.e., barring the use of a deck set up deliberately in some way). Once you do the math, it turns out that it isn't even a close question.

Let's just focus on Texas hold'em poker, and assume a ten-handed game. Because we don't care about the order in which the two down cards are dealt, the number of possible starting hands for the first player is given by C(52,2), which is 1326. (For an explanation of this notation, see Then there are 50 cards left, so for each of those 1326 possibilities we have C(50,2) starting hands for the second player, which is 1225. Continuing in that fashion, we find that there are 2.99 x 10^29 ways of dealing two cards to each of ten players.

Then we have a flop of three cards out of the remaining 32, and C(32,3)=4960. Finally we multiply by 29 for the number of different turn cards and by another 28 for the number of different river cards, for a grand total of 1.21 x 10^36. (For you math geeks, that's 1.21 undecillion.)

Suppose that we set all six billion people on earth to doing nothing but playing poker. That would be 600,000,000 games going. (We'll let the players deal their own cards, so nobody is left out having to be the full-time dealer.) Suppose we can knock out one hand a minute, because we're all extremely quick. We could get through 3.15 x 10^14 hands per year. In 200 years (approximately the amount of time that poker has existed), we could play 6.31 x 10^16 hands. In 20,000 years (about the amount of time since the last Ice Age), we could have done 6.31 x 10^18 hands. That's a pretty good approximation of the number of grains of sand on the world's beaches (see But it's only a miniscule fraction of the number of possible hold'em hands. In fact, it would amount to way less than one one-millionth of one one-billionth of the number of possible hands.

And we haven't even considered all of the other forms of poker (Omaha, in which every player is given four cards to begin with, obviously has vastly more potential), or all the extra variations that come by playing with fewer than ten players at a time. And, of course, no two players use identical strategies, so if you combine all of the possible choices that each player has at each point in the hand with the number of hands, I think we might get up to a number comparable to the number of atoms in the universe (which is on the order of 10^80).

In short, it is virtually certain that there have never been two identical hands of poker played in the entire history of the game.

The chess nerds will boast that their game is vastly more complex, because the estimated number of possible chess games is something like 10^120 or maybe 10^123 (see But if they're so smart, why aren't any of them getting rich from their game, huh?

Friday, November 30, 2007

The winds of Las Vegas (non-grumpy, non-poker content)

I was amused by the afternoon television news here, in which the news team was all in a lather about the fact that it had rained today. It wasn't a flash-flood kind of rain, just a slow drizzle, totalling--brace yourself for this--about one-third of an inch. Wow! But they had their full crew out on alert, doing live updates from various places about this incredible breaking weather story. (Yawn.) They even featured a segment reminding people how to drive on wet roads. Coming from Minnesota, I just had to laugh. It would be great fun (a destructive, sadistic sort of fun, that is) to dump about a foot of snow on this city and watch the mayhem that resulted.

Anyway, this reminded me of a little blurb I wrote roughly a year ago for a newspaper back home, about a weather phenomenon that is moderately common here but almost never seen there. Enjoy.

Las Vegas is a dirty city—in a literal sense. To start with, it’s in a desert, and there’s just dust everywhere. The day after you wash your car, it’s covered in a thin but easily visible layer of dirt again. But additionally, there’s more trash left around than anyplace else I’ve lived. I suppose part of that is the dependence on drunk tourists. But there’s also the fact that vendors shove all sorts of handouts and other crap at passersby on the Strip, much of which just gets dropped and left. Finally, the city appears to spend precious little on such niceties as street sweeping, and nobody seems to care much about open dumping of stuff in vacant lots.

Last week we had a windstorm. I had not previously seen the Strip in this condition, and it was eerily spectacular. There were straight-line winds blowing a constant cloud of dust from the west, and it was like the shiny mega-resorts had been submerged in murky, sandy water. The wind was strong enough to loosen a large sign on the Venetian hotel, causing authorities to shut down the Strip for a while, lest the thing come off completely and do serious damage.

But there were also wonderful dust devils everywhere, filled with more man-made debris than any I’ve seen before. I was immediately and strongly reminded of that strangely beautiful scene in “American Beauty,” in which a young photographer marvels at the elegant randomness of a plastic bag being tossed about by the winds.

Watching plastic bags and papers and other trash being lifted, swirled, buffeted back and forth, then dropped again in a new location, seemed perfectly emblematic of the city. People come here to dance drunkenly, to let themselves be tossed to and fro by the whims of chance, only to collapse in a heap when the winds of fortune and fun inevitably die down. The city has a shockingly high rate of suicide.

If you come here for a visit—and I hope you do—be sure that you remain tethered financially and by friends and family. The winds can be both delightful and destructive.

Poker vs. church

I'm not trying to get a whole trend of church-bashing posts going here, but I was trying to think of a snappy punchline for the previous entry, and the following sort of evolved in my brain:

The top ten reasons why putting money into the pot at a poker table is better than putting it into the collection plate at church:

10. You don't have to waste an hour listening to a sermon before getting your money in the pot.
9. You don't have to wait a week before doing it again.
8. No risk of the checks in the pot bouncing.
7. In a good poker room, food service is more than a sip of wine and a tasteless little wafer.
6. Even if you lose the pot, you can be pretty sure the money won't be going to pay the salary of an authority-abusing pedophile.
5. Noisily shuffling your change before dropping it in the collection plate is frowned upon.
4. You don't earn comp dollars for every hour you're sitting in a pew.
3. No valet parking at your average church.
2. After they collect all the money, ain't no preacher gonna be pushing you that collection plate back to keep.

And the number one reason that putting money into the pot at a poker table is better than putting it into the collection plate at church:

1. Nobody suggests that you're going to hell if you decide not to put money in this time around.

"We've got to go 'all-in' on Jesus"

In case the previous post didn't sufficiently leave you shaking your head, here's a little more gagitude I just found, accompanying the photo above (from

Last year when I preached on doubt, I used the illustration of poker players going “all in” in order to win the game. That’s what we have to do with our faith. At some point we’ve got to go “all in” on Jesus. A few months later Pastor Greg Kuehn decided to use that phrase as a call for commitment after a sermon on Romans 12:1-2. A man in the church who does embossing offered to make these “All In for Jesus” poker chips. At the end of the service, hundreds of people came forward to receive their chip. Church members carry the chips around to remind themselves of their commitment.

Right. And I carry around a little Jesus figurine to remind me to play poker.

Addendum, November 30, 2007

See the comment below from "Short-Stacked Shamus" (and read his always insightful and well-written blog at The last minute that he refers to is somebody (I can't tell who) singing a stupid song about "I'm all-in with Jesus." I was curious whether this was a real song that I could locate, so did a Google search. I didn't find anything about the song, but in the process, I came across this bit of drivel, eerily similar to the paragraph quoted above, from

Chaplain’s Message

Perhaps you have seen recently on television the World
Series of Poker. I was at my brother’s house watching it one night and I noticed that whenever a player felt that he had a particularly strong hand, he would attempt to weaken the other players or player, or even get them out of the game outright, by, and this is the phrase they used, “going all in.” It was a risk, because if the other player had a better hand then the one going all in would be severely weakened himself or even out of the game.

Reflecting on this in light of the Gospel, I am reminded that we are asked to “go all in” with Jesus. He does not ask for half of our heart or part of our life. He wants it all! He even goes so far as to say that if we do not put him ahead of our own families, then we cannot enter the kingdom of God. Either we “go all in” with Jesus or nothing. After all, God has “gone all in” for us in Jesus; if we do not respond in kind, then God cannot respond in us....

Now if you'll excuse me, I need to go throw up.

Thursday, November 29, 2007

Anything for a buck

Last night I was reading an article about how atheists have a dearth of stuff they can buy with their stamp of non-faith on it ( The author, Greg Beato, points out that you can't buy a Madalyn Murray O’Hair action figure, or atheist yo-yos or perfume.

This sentence caught my attention in particular: "In fact, the Lord has called so many believers to spread the Good News via faith-based salt scrubs and godly poker chips during the last few decades that the annual U.S. market for Christian-themed products, often dismissed as “Jesus junk,” is now $4.6 billion." (Emphasis added.)

"Godly poker chips"? Surely that was just a cute rhetorical flourish, right? But the more I thought about it, the more likely it seemed to me that, yeah, somebody, somewhere probably really did make such a thing. And, as you can see above, somebody actually did. You can order them at, though I'm not sure why you would want to.

I also quickly came across the other half of what you'd need for a full-blown, full-gospel home poker game: the scripture cards (, which, conveniently, you can get in either King James Version or New International Version.

Some things just don't go together. Like ketchup-filled doughnuts. Like "Remember: No Premarital Sex" brand beer for sale at spring break destinations. Like "Never Squeak" grease to put on your car's brakes. A friend back in Minnesota liked to collect bizarre patents, and his favorite was a combination sunscreen and lock de-icer. (You may have to think about that one for a second.)

There's just something fundamentally incongruous about mixing poker with a proselytizing message. It's as strange as, say, seeing an ad for First Church of the Brethren in the back of an issue of Hustler magazine, or "Praise the Lord" vodka in the corner liquor store, or a Christians-only brothel in Pahrump.

I don't ask to play poker in the back row of your church, so please don't inject your attempts to save my soul into a poker game.

Monday, November 26, 2007

Should one speak up when not involved?

Reading through my old emails today reminded me of one I wrote a year ago about a quandary I faced when, on two consecutive days, I witnessed with a situation in which a rule violation by one player put another at a disadvantage. The dilemma for me was whether to speak up about it or not, when the dealers didn't correct the situations. There is something of a tradition in poker that players not involved in a hand should keep their noses out of it. That's certainly correct insofar as giving advice to those involved, but I don't believe it should also extend to sitting by silently when a rule violation hurts a player.

I'll describe the situations, briefly explain my rationale for non-involved players taking the initiative to speak up, then open the question to readers for comments.

Story #1.

A $1-$2 no-limit hold'em game at the Las Vegas Hilton. After the turn card is dealt, Player A bets $15. Player B moves all-in for $25. Player C calls. The dealer turns back to A, who immediately pushes all-in for around $90. As the dealer turns to C for his action, I speak up and point out that A does not have the option to re-raise there. Before anybody can react to my comment, though, C calls (for a little less than what A had put in). It turns out that C--a fairly weak and inexperienced player--was on a flush draw and missed. He then left the table.

After the hand, Player A acknowledged that he was wrong. He had had a very strong hand, and was eager to get all his chips in. I believe that his mistake was inadvertent. The dealer also acknowledged that he missed the fact that B's all-in was not a full raise, and therefore A could only fold or call. OK--everybody makes mistakes, and the actions happened so quickly that it would be easy to miss.

But what bothered me most was that Player A and two others at the table chastised me for attempting to intervene when I wasn't involved in the hand.

Story #2.

The next day I'm in the same type of game at Bally's. Player A raises. Player B pushes all-in for a substantial re-raise. Player C reluctantly calls. Player A appears equally unhappy about the re-raise, but eventually calls, and as he does so asks C, "You want to just check it down?" C agrees. The dealer does nothing. This time I didn't speak up, largely because the damage was already done: clearly, even if the dealer tells them that such an agreement is in violation of the rules, they'll both officially rescind the deal, but check anyway.

But I think that part of why I didn't protest was having just been criticized the previous day for intervening when I wasn't in the hand, and I didn't feel like being the bad guy twice in a row. I did get up and talk to the floorperson privately about the situation. He came to the table and asked the dealer about it. The dealer said he heard the collusion, but it had happened so fast that he couldn't stop it.

My general thoughts.

To my way of thinking, no player can help another make a decision, but every player has a duty to the integrity of the game, and the integrity of the game includes giving every player the full protection of the rules.

In my first scenario, if the illegal re-raise had been halted in time, I suspect that Player C would have been happy to be able to see the last card for the cheaper price, and save his last money if his draw didn't hit. In the second scenario, Player B would presumably not be pleased with the agreement between A and C, since he would prefer to have one of them push the other out of the pot, and thus only have to beat one other hand at the showdown, rather than two.

I don't know whether the disadvantaged players in these games didn't know the rules, weren't paying enough attention, or were too shy or intimidated to speak up. But even players who don't know all of the intricacies of the rules are entitled to their protection--and if the dealer doesn't act to enforce the rules protecting one player from the illegal action of another, it seems to me that other players should do so. It's just the old golden rule: I would want somebody else to speak up if I were being disadvantaged by an action I didn't know was illegal (because of being inexperienced, distracted, or whatever), so I should do the same in return.

I would also argue that it's better for the game in the long run if weaker players are protected by the more knowledgeable ones; if they know that their inexperience isn't going to be taken unfair advantage of, they'll be more likely to keep coming back.

These two stories occurred shortly after I had bought and read Cooke's Rules of Real Poker. One of the points that had caught my attention in that new book was rule 16.17: "A player should speak up immediately when he sees an error such as an incorrect amount going into the pot; a pot that is about to be awarded to the wrong person; a card going to the wrong person; or a flashed or marred card."


If you are so inclined, dear readers, I would appreciate any comment you might have on whether I was right to speak up in the first situation (although I wasn't quite quick enough to prevent the damage from being done), whether I should have said something immediately at the table in the second situation (versus just keeping quiet, or going to the floor person after the hand was over, which is what I settled on). Also, if you like, comment on how there developed in some circles an unwritten rule that players not involved in the hand should keep quiet about any perceived irregularities, and how we can change that part of poker culture (assuming that you agree it should be changed), or why we should keep such a practice (if you think that players not in the hand should keep mum).

"I am SO drunk!" (Non-grumpy content)

I'm just not feeling the inspiration to come up with an original rant, so I'm again going to the well of the stories I wrote to a friend back home last year, when I was just getting started in Vegas poker. This was written at 7:05 a.m., September 26, 2006, after an all-night session at the Hilton.


The easiest read of an opponent ever: I have 9-9 on the button. I raise. One caller. Flop is a 10 and two small cards. He bets, so I think he has a 10 and I'm behind. But he's a pretty unskilled player, and extremely drunk, so I think maybe I can steal the pot from him. I put in a sizable raise. He calls. Damn.

Turn card is a blank. He checks, so now I think maybe he was just on a draw and won't pay to see another card, or maybe he does have a 10 but with a bad kicker that he won't want to spend more money on, or maybe I can convince him I have a pocket pair bigger than 10s. So I bet. He calls again. DAMN!

River is another 10--just awful. Now I think he has trip 10s to my measly pair of 9s, and I'm ready to throw the hand away and take my lumps. The guy leans forward to look closely at the board (he's drunk enough that he's having a hard time focusing), then picks up his hole cards, looks hard at them, gets a horrible scowl, and says, "Oh, damn! I am SO drunk! I thought I had a 10, and I don't! God, I'm so stupid! I can't bet at this. I check."

He is NOT acting. He really is way too drunk to be making this up as an act. I put out $40, and he instantly folds.

Sometimes, one doesn't have to be Doyle Brunson to figure out how to win.