Rare hand

At first glance, this appears to be two pretty ordinary fouled hands in a game of open-face Chinese poker.

But look again. There's something peculiar about the hand on the right. Go ahead--take a closer look. I'll wait.




Do you see it? She got 13 cards with no pair--a 13-card straight!

If you dealt out 13 cards from a well-shuffled deck, what is the probability that you'd get that result? I don't know, but let's figure it out.

The first card can obviously be anything. To state the trivially obvious, the probability of getting a non-pairing first card is 1.00, or 100%. The second card can be anything except a pair to the first. So with 51 cards left in the deck, 3 kill our hopes for the Big Straight, and 48 keep it going. The probability of a card that doesn't pair the first one, then, is 48/51, or 0.941, or 94.1%.

The third card must not pair either of the first two. There are 50 cards left in the deck, of which 6 will create a pair and 44 will not. So the probability of getting a non-pairing card is 44/50, or 0.880, or 88.0%.

We continue this pattern. When we're ready to deal the 13th card, there are 40 cards left in the deck, of which just 4 will complete our lovely 13-card straight, while 36 will pair one of the first 12 cards now on the board. The probability of hitting one of our "outs" is therefore 4/40, or 0.100, or 10.0%.

Because every one of the 13 events we've described must occur in order to end up with the 13-card-no-pair hand, we multiply all of the individual probabilities together: 1.00 x 0.941 x 0.880 ... x 0.100. The final product, if I didn't screw up the calculation, is 0.000106, or 0.0106%. To put it in the conceptually easiest terms, this will occur about 1 in 9460 hands. If I've ever seen this happen before in an OFC game, I didn't notice it.

You may be tempted to think that knowing 13 other cards along the way (i.e., the ones dealt to me in the picture above) changes this probability, but it doesn't. It would change our ongoing estimate, card by card, as to whether this hand will play out as a 13-card straight. But the question I've really asked is how often the deck will have been arranged by a random shuffle so the 13 cards destined to go to player X will contain no pairs. When asked that way, it makes no difference what happens to the other 39 cards, whether they are seen or unseen. The answer does change if instead we ask the probability of a shuffled deck yielding a 13-card straight to somebody when two (or three, or four) players are dealt in, but it makes my head hurt to think about how to calculate that, so I'll leave it to somebody else.

Three open-face Chinese poker hands

I installed a Chinese Poker app on my Android phone recently and have been playing quite a bit this weekend. Here are three hands of some interest that have come up.

1. This is the first time I managed to make a flush both in back and in the middle. Nice bonuses ensue.

2. This was a sticky dilemma. At first glance, that ace of diamonds looks beautiful. But in reality, it's probably the worst card in the deck that could have come. As David Sklansky would say, DUCY?

The only possible play that does not trigger a fouled hand is to put it on top (which, incidentally, makes the strongest possible hand there--three aces), then hope for exactly the ace of clubs plus another diamond. But a tiny chance to survive is better than none at all.

The game was suspended after I made that move, so I don't yet know whether I will get extremely lucky and pull off an amazing hand with an ace-high flush, a king-high flush, and trip aces.

3. Against one friend, we're playing with a variant called "Fantasyland." If you make a valid hand with QQ or better on the top, you get the Fantasyland bonus--which means that on the next hand you get to set your cards all at once, as in traditional Chinese poker. But your opponent has to do his in the usual OFC manner--five, then one at a time--without first seeing your hand. It's an overwhelming advantage, virtually impossible to beat. But getting it is not easy; queens or better up top without fouling is tricky. I tried a few times and failed. But then the heavens did open and choirs of angels did sing:

Whee! My first trip to Fantasyland!

Sadly, I was so excited that I failed to screenshot it, but I made a full house in back and a straight in the middle. I scooped and won some ungodly bonus, giving me the lead by something like 38 points.

I might be up at 5:30 a.m. playing a little, but I'm not addicted. I could quit anytime I wanted to. No, really! Just one more game.

Open-face Chinese poker problem (quasi-poker content!)

Cardgrrl's house is now finished and she has moved in. Last night I was over there for dinner and recreation. I taught her how to play OFC poker. I've only played once before for money, though a few days ago I bought an app for my Android phone and have been playing some no-money games with friends around the country. So my experience with the game is not quite zero, but pretty close to it. Which means that situations I haven't seen or thought of are going to come up from time to time.

Last night, for example, I ended up making this hand:

Cardgrrl had fouled her hand, so I potentially had a big score here--a scoop plus a royalty for the full house. But neither of us knew whether this hand was valid or fouled because both the top and middle had J-10-7. And it's not like Cardgrrl has a few Chinese Poker rule books sitting around the house that we could consult.

So I posted the picture on Twitter and asked for opinions from those with more experience playing. I was surprised but pleased that the answers I got were unanimous: It's a valid hand.

But then that just made me wonder why it's valid. Is it because:

(A) Jack of spades is a higher card than jack of hearts?

(B) The two hands are considered equal, and being equal is valid?

(C) The middle hand is J-10-7-5-4, which is better than just J-10-7 on top?

Here Twitter delivered some variability in the explanation, with all three possible rationales getting at least one nod. But the answers from the most experienced players were consistently (B). Apparently two hands tying is as valid as the stronger one being below the weaker one. So, for instance, if you happen to make a seven-high straight on both the back and the middle, that's a legitimate hand, not fouled. To put it another way, I had been under the impression that each hand must be stronger than the one above it, but the actual rule is that no hand can be stronger than the one below it--which is not quite the same thing.

So now you know. (Or maybe, unlike me, you already did.)



BONUS SUBJECT AND PHOTO:

Both Cardgrrl and I had long been wanting a cat but were in living situations where it could not happen. As you know by now, I remedied that very soon after moving in to my apartment. (If you want to watch a couple of stupid videos of me playing "cat hockey" with my darling Lucy, see here and here. Do not expect cinematic epicness.)

Well, on Saturday Cardgrrl also cured her catlessness. She went to one of the local animal shelters and brought home a tiny bundle of feline furriness named Loki. He is, as she accurately puts it, ALL OF THE CUTENESS ALL OF THE TIME. My guess is that if you did a chemical analysis of him, he would turn out to be 99% cuteness and 1% carbon/nitrogen/oxygen. See more of Loki's sweetness here.

Here's the three of us last night posing for a selfie:

Survey question: How adorable are we?

1. Very.
2. Extremely.
3. Super-duper.
4. OMG!

Unusual day

Sunday was a highly atypical day for me.


Family

First I had a late lunch with my sister, her husband, one of their daughters, and her husband, all in town for the annual rodeo. Then we went bowling at Sam's Town. I won both games, scoring 139 and 150, which is pretty good for me--especially since I haven't bowled in about 18 months.

Unfortunately, in the process I somehow managed to wrench my back, so now I'm in pain and walking funny, dreading when I have to change positions. Getting old sucks.


Chinese

Came home, did some work. In the evening I sort of invited myself to a home game some friends were having--@spencer_chen, @gamble24x7, @veggiepoof, and one other whose Twitter I don't know. It was my first chance to play open-faced Chinese poker, which seems to be all the rage these days. I had never even played regular Chinese before, though I had watched it a few times and understood the basic idea.

My entire knowledge of OFCP comes from an article in Card Player magazine by Jennifer Shahade , a blog post a few days ago by Shamus, and an article by Dave Behr in the December issue of Bluff magazine, which by coincidence I had just read yesterday. So I was green as green could be, and knew I was likely to lose money. Which I did--$89, to be exact, at $1/point. But that's OK. Learning new forms of poker always costs money as one makes mistakes and, hopefully, learns from them to play better.

But ya know what? I'm gonna go out on a limb here and say that OFCP is not, in fact, a form of poker. For that matter, neither is traditional Chinese poker.

This is a point that I haven't seen raised in any of the three sources I mentioned, but which occurred to me as I watched the others play during the one hand out of five I had to sit out. (A maximum of four people can play at once, since each player needs 13 cards.) There are several ways to express the basic element that is missing, but they all amount to the same thing:

• There are no hole cards, no secrets that you hold which are unknown to the other players. 
• There is no betting on the strength of your hand. 
• It is a game of perfect rather than imperfect information. 
• You cannot bluff. 

Mike Matusow is generally not a font of wisdom that I turn to, but Michael Craig quotes him as saying, "If you can't steal, it ain't poker." He's absolutely right. 

Mike Caro has argued that the ability to bluff is more a defining element of poker than are cards. He describes an imaginary game of "cow chip poker," in which the players scout a nearby field for cow chips, conceal what they find in paper bags, then reassemble to bet on who has the biggest one. You can win with an empty bag by betting in such a way as to convince your opponents that you found the biggest cow chip. That's poker, even with no cards. In another hypothetical situation, he describes how two people can play poker with a deck of just three cards, because you still have the crucial elements of being able to have a secret card and bluff with the worst hand. 

Video poker is not poker, in part because it's played against the house rather than against other players, but also because it lacks secret information and bluffing. OFCP fails by that same criterion. They are both games that superficially resemble poker because they use the standard 52-card deck and poker's traditional five-card hand rankings. But resembling is not being. They are not poker. 

It was, nevertheless, highly enjoyable. I didn't find it nearly as addictive as others breathlessly describe it after first exposure, but it's definitely an intriguing game. 

Oh, and the other important thing I learned about OFCP is that people say "fuck" a lot. Really a lot. 

Television

After I got home, I watched the premier of "Sin City Rules" on TLC, which I had taped earlier. The only reason I was interested in it is because one of the stars is Jennifer Harman, whom I like. But I thought the whole thing was awful, painful, unwatchable. Jennifer is fine, but the other women are completely unbearable. They're self-absorbed attention whores. Judging by the first episode and the teaser on TLC's web site, the show exists mainly to capture and televise the catfights among them. Ick. I can't understand why anybody would watch such trash. The preview for next week's show seemed to focus more on Harman's life as a mother and poker player, so I'll probably give it one more try, but I can't see myself tuning in much beyond that. I'm kind of perplexed how she got associated with the show; she seems not at all like the others. 

And that was my completely out-of-the-ordinary day.