Analysis - Second Dora Dragon

This is a quick followup to one of my previous analyses, Lone Dora Dragons. In that, we looked at the danger of discarding a lone dora dragon from your hand. In this, we'll look at the danger of discarding the second.

In the last analysis, we looked at 969,823 rounds that had a dragon as the dora. Since then, I realized how to check the dora for rounds that ended in a draw, so this time, we have 1,175,549 rounds to look at. I might re-run the old analysis and update that post later, if I have time.

First, let's bring back the chart present in the Lone Dora Dragons analysis. We'll be looking at more and comparing to it, so it's good to have handy.

Cool. Now let's look at the same type of data, but for the second dora dragon. What are the chance the second gets called, or deals in, on any given turn?

As always, I'll remind you that you can click on the image to make it larger. Regret chance is basically the chance that the opponent wins with the dragon you gave them. Let's also pull this data into a graph, so we can compare it to the previous.

Now, note that this graph goes from 0% to 5%, while the old graph went from 0% to 60%. For better comparison, I'll set the scales to be the same:

Yeah. Not looking very dangerous like that, is it? But, wait, this isn't really the whole story. Shouldn't the number of turns that have passed since the first was discarded matter more? Let's look at that instead. First, the table.

That's a lot less flat. Still, it's hard to read a table, so it's graph time.

When we looked at the danger on each turn, the average was around 2-3% total chance. This exceeds that pretty fast, after around 4-5 turns. If we look at the counts, we can see that around 75% of the second dora dragon discards happen within 3 turns of the first being discarded. In the first six turns, 90% of the second discards happen. So, everything after 6 turns on this graph represents 10% of the total sample size, which explains the discrepancy.

Like before, let's also set the scale to the same as the old graph.

So, the second dora dragon is, as you would expect, much safer than the first. Even at its most dangerous, it's still less dangerous than the first is on the first turns. If you check the table, the regret chance rarely exceeds 6%, which is the chance the first has starting on turn 3.

We're starting to get to the point where we need a control for these numbers. Perhaps next time, I'll look at the chance of each tile dealing in or being called at each turn in the game, so we have a reference. Sounds complicated to get right, but we'll see.

The spreadsheet for this analysis can be found here. The code can be found on GitHub here. Until next time!