Analysis - Dama

I'm finally analyzing dama hands with the help of the drastically faster shanten calculation algorithm. Let's take a look at these mysterious creatures.

My first instinct was to replicate my old Wait Win Rates by Row analysis with dama hands. However, dama hands are very complicated. Let's think about what a player with a dama hand could do.

1. Stick with their wait to the end of the game.
2. Change their wait, but remain tenpai.
3. Fold at a later point.
4. Declare riichi later.
5. Call a tile, either to widen the wait with kuinobashi or to go down a folding path.
6. Pass a win because they need to target a specific player.
7. Pass a win because they don't even have a yaku.

It's quite complex. So, what I did was gather all of those events. Because there's so many, we'll only be looking at the Second Row in this post.

Here's what we'll be doing with each outcome.

1. If they stick with their wait, it's all good.
2. If they change their wait, we'll log it as a wait change and not count it for the win rate of that wait. If it's still within the second row, we'll change their wait to that tile and go back to step 1.
3. If they lower their shanten after reaching tenpai, we'll log it as a fold and stop looking at the player and not count it for the win rate.
4. If they declare riichi on a later turn, we'll log it as a riichi and we won't count it for the win rate.
5. If they call a tile, we'll log it as a call, and won't count it for the win rate.
6. If they pass a win, we'll count it as a win and end the round, even if they didn't take it. This solves both 6 and 7. We'll also log it as a passed win.

With all that in mind, let's see how often they do each of these things.

The better the wait, the more likely it is they'll keep it. The hands that fall into the "keep" column are the ones we'll be tracking the win rates of. Also, a lot of the "Changes" in the Single Wait section could also be partial folds.

The winrates are going to be (Pass + Win) / (Total - Riichi - Change - Fold - Call).

First, let's look at the riichi win rates on Second Row for reference.

The numbers along the top are how many tiles in the wait are visible. So, the 0 column means the wait is completely live, while the 2 column would mean that two of them are either in the hand, in the discards, or the dora indicator.

Now, let's see how much the win rates go up by when the player remains dama.

"Hey, what gives? These numbers are lower!" you may be saying.

Well, you're right.

When you choose to go dama, you don't declare that you're tenpai. Since the other players don't know, they fold less often, which means they deal into you more. And this is true. The tsumo rate for a ryanmen riichi is around 60%, while for dama it's around 25%. That means much more of the dama wins are by ron.

Overall, it's about 50% for riichi and 33% for dama, as we can see in my Yaku Rates by Hand Type post.

However, if they're not folding, they're building their hands. If they don't end up cutting your tiles, they are going to also reach tenpai at some point, at which point they're competing for the win.

Let's look at the "threat" of some specific hand types.

"Calls After" is how many calls the other players made after the event in question. Higher would mean they're playing more aggressively, perhaps.

When you're the first to riichi, you win about 51% of the time, and someone else wins 32% of the time. When you're the first to dama without there being a riichi already present, you win 43% of the time, and someone else wins 41% of the time. So, it's a third more likely that someone else will win if you choose to dama.

If we look back at the first chart, we see that somewhere between 5 and 10% of dama hands either can't win or fold later, so we can increase the dama win rate a bit to compensate. Still, that leaves dama and riichi as having similar win rates, which is pretty interesting.

The spreadsheet for the dama win rates is here. You can see all the waits. The spreadsheet for the "threat" table is here.

Of course, this isn't really a case against dama. There are plenty of situations you would choose dama even without considering win rate. Wait or value upgrades, yamagoshi (passing a win to target a certain player), keeping the ability to fold, and so on.