Analysis - Four Winds Draw

While watching a ないおトン stream, he verbally acknowledged cutting the third wind to aim for the draw, as his hand was bad. And, it worked. Let's run an analysis on this case.

1.5 million Houou games. Around 2 million four wind draws. Here's the details of the data collection:

1. If the first player does not discard a wind, the round is ignored.
2. If the next player does not discard or have one copy of the wind, the round ends there.
• If they have multiple copies, there's no chance of the draw
3. The shanten of the player is checked.
4. If they discard the same wind, that's logged as a "Discarded" for that turn and shanten.
1. There is then a check to see if the round ends in an abortive draw, and if so, that's logged as a "Draw."
5. If they discard a different tile, but had one copy of the wind, that's logged as an "Avoided."
6. Return to step 2.

Here's the results:

Some things to keep in mind.

• The data is quite thin, as this does not happen often. Many of the cells for the third or fourth player have less than a thousand cases.
• As evidenced by the 100% fourth tile discarded at tenpai, Houou players do not always pay attention. Not all of these are going to be conscious choices.
• Winds that have been cut once or twice are quite safe tiles, so for the worse shantens at discard 2 and 3, there's a choice between aiming for the draw or keeping a safe tile around.
• I'd guess the Draw rate is higher after a double riichi for the obvious reason.

Perhaps we can say based on the fourth tile 1-shanten and 5/6-shanten numbers that Houou players aren't consciously aware of the four wind draws 15-25% of the time. Not sure what that says about your chances of making this sort of play work in lower rooms, but in Houou at least, discarding the third wind gives you an ~8% chance of getting a new hand.

Replays where the player discarded the fourth wind while in tenpai:

1. https://tenhou.net/5/?log=2014042022gm-00a9-0000-c4786e46&tw=2&ts=4
2. https://tenhou.net/5/?log=2016030315gm-00a9-0000-8bfd19f9&tw=3&ts=5
3. https://tenhou.net/5/?log=2017120218gm-00a9-0000-450c8e05&tw=3&ts=6
4. https://tenhou.net/5/?log=2018081120gm-00a9-0000-cceefd20&tw=1&ts=13 
• This player didn't lose their riichi stick at least
5. https://tenhou.net/5/?log=2018081610gm-00a9-0000-b1bb1262&tw=2&ts=4

Definitely one of the most minor analyses I've run. Here's the raw data: