Analysis - Lone Dora Dragons

In this post, we'll analyze the Houou replays to see when players discard a lone dora dragon from their hand, as well as what happens when they do.

Sorry about the delay with this post. Hurricane Dorian knocked out my power so I couldn't run the analysis. But, now it's here, so let's get into it.

Our sample size this time is 969,823 rounds that had a dragon tile as the dora, which is fairly substantial. Let's start by looking at what turn the player discarded the tile, as well as whether it was called, dealt in, or passed safely.

You'll probably want to click that to make it bigger. The bulk of the discards happen in the first 6-7 turns. Logically, you don't want to cut it immediately in case it pairs, but you don't want to cut it too late, since that gives people more time to build hands that can call or ron it.

The call rate peaks at turn 9, then starts to drop. Of course, this is because the deal-in rate is going up at the same time. The total percent of bad things that happen after discarding the tile only grows. We can put this into a chart to make it easier to see.

Of course, the tile being called isn't nearly as bad as if it deals in. The person who calls it might never win the hand, after all. So, let's look at how often the person calling the tile actually wins the hand after calling it.

As one might expect, the win rate slowly declines the later the call happens. Combining these percentages with the previous ones, we could say things like, "If you discard the lone dora dragon from your hand on turn 6, you'll regret it about nine percent of the time." The call rate is close to 20%, and the winrate after calling is close to 40%, so that combines into around 8%, then add the 0.72% deal-in chance.

We can do this for all the turns. I'll call it "Regret Chance" because that's amusing, but really it's the chance the opponent wins with the dragon you give them.

Moving on, let's look at some other factors that could influence the decision about whether to cut the dragon. Do you think people are more or less likely to discard it the later into the game it is? Let's see what the data says.

South 2 is around average. Before that, people are less likely to cut it, and after that, they're more likely to cut it. My theory is that, in the earlier rounds, people feel like they have more time to chase value, but in the later rounds, they have to go more for speed, and maybe wish to take less risks by holding onto it.

Other than the round, the player's shanten is also probably a big factor. With a good hand, you're more justified in your risk-taking, so perhaps the majority of the discards are from low shanten hands. That would line up with what Houou players have told me their strategy is with the tile -- "Hold it until my hand's shape becomes clear."

Yes, most of the discards come from hands that are 2-shanten or better. The massive increase for tenpai hands is likely players tsumogiri-ing the tile. The discards with a completed hand are from when the player couldn't win due to being in atozuke.

The "Kept Upon Reaching" column is "The player advanced in shanten to this number, and did not discard the lone dora dragon from their hand." The "Discarded" column is simply "The player was at this shanten when they discarded the lone dora dragon."

One other thing we can look at is seat and placement, though it comes with the same issues as it did in the previous post. Perhaps later I'll change it to be the player's lead (+5k over second, -5k below third, etc), but even that's difficult. Is it more important that the player is 10k above fourth, or that they're 10k below first? Hmmm... Well, here's the table, in any case.

That's all I have for this analysis. You could take it further by looking at why the dragon dora was never discarded. Did two players have a pair? Did one player have a pair and the rest in parts of the wall that were never reached? Maybe a closed kan? It could be interesting.

You can find the tables shown in this post in this spreadsheet. You can find the script used to parse the data on Github. Next week, we'll look at the call, deal-in, and yaku rates for each round individually, in both hanchan and tonpu separately. Will the tonpu rounds line up with the South rounds of a hanchan? Do players like tanyao more the later the game goes on? We'll find out next week.