When to 1-log and how to do it

TL;DR: 1-logging improves healer spreads, allows you to fix the trap faster, and gives you more time to block or relure runners when needed. The table below covers every scenario in which you can 1-log.


Why 1-log
1-logging is useful because it can improve healer spreads when healers reagro you since less time is spent at logs. Additionally, it makes it possible to fix the trap faster after killing the first 4 runners on waves 6 and 7, and the first 5 runners on wave 8, since the trap is at (1) and right-clickable instead of at (2) when killing the runners. It also leaves more time to block or relure runners in certain scenarios. This guide is intended as an overview of when it is possible to 1-log and how to do it.

Many defenders already know this and do it based on intuition, and this post is targetted towards those who want to learn how to 1-log and to those who want an overview of which scenarios it is possible


Assumptions
- No blocked runners
- You delay under the cannon until 12 seconds into the wave
- You don't waste any ticks (although in most scenarios you can afford to 'waste' a few ticks)
- You can delay by running 2 squares east of the mainstack if the 3rd healer agroes you in all these scenarios.


Some Notation
- R1(1): First runner’s 1st movement
- R1(2): First runner’s 2nd movement
- R2(1): Second runner’s 1st movement
- Hard crash: A runner crashes and the trap food is not in line of sight
- Soft crash: A runner crashes and the trap food is still in line of sight


Calculation of the probabilities
The probabilities in the table below is based on data gathered by Henke which can be found in LHC's defender guide. To summarize, the data shows that when there is no food within a runner’s line of sight, the runner has a 1/6 chance of moving west, 1/6 chance of moving east, and 4/6 chance of moving south. There are 27 different possible scenarios, with the most likely one happening about 30% of the time, and eight relatively rare scenarios that may occur with a probability of 0.46%.


When to 1-log
This guide is meant to clarify when it is possible to only grab 1 log on waves 6 and 7 in speeds/funs. On wave 8 you can 1-log using Dren's false trapping method found in LHC’s video. 

The table below shows when it is possible to 1-log and when it is not. In 20 scenarios, with a probability of roughly 79%, you can pick up 1 log, and in 7 scenarios with a probability of 21% you need to pick up 2 logs.



If you want to sort the table depending on how many logs, probability, or the runner movement, click here.


How to 1-log
Below I cover how to 1-log in a few scenarios. If there aren’t any notes written below on one of the permutations in the table it means there’s no need to relure, block, or split runners, and nothing needs to be done besides dropping food at the trap, trail and mainstack, grab the hammer, delay for the 3rd healer if agroed, grab 1 log and run back to the trap. Most of the notes are in 1-log scenarios, and if you need 2 logs then it is indicated.

NOTE: If the first runner goes west twice it is generally safer to grab 2 logs, although the permutations in the table are technically correct and you will not need more than 1 log if the first runner is a double westie. If the first runner goes west thrice you can get 1 log in some scenarios, but this overview doesn’t cover that.


SS-S
You need to block the 2nd runner for 1 tick just north of the cannon since it will sometimes go west, as seen in this video.

If the 2nd runner walks south or east, then run straight to the trap before the 3rd runner reaches it.

If you are too late to block the runner you can relure it as seen in LHC’s defender guide, but if you are too late to drop the relure food then the 3rd runner will eat at the trap, and you will reach the trap at (0).


SW-E / WS-E / EW-E / EW-W / WW-E
If the 3rd runner walks south on its first movement it needs blocked south for 1 tick if it crashes south, or alternatively relured north of the cannon.

Note that if the healer happens to block the 2nd runner (1st runner in the EW-W case) for 1 tick then you do not have to block or relure the 3rd at all.

Clip of blocking 3rd south with EW-W-S

Clip of blocking 3rd south with SW-E-S

*NEW: Clip of blocking 3rd south with WW-E-S

*NEW: Clip of blocking 3rd south with WE-E-S

SW-W / WS-W / WW-W
The 1st and 2nd runner will auto multi. If the 3rd runner walks south, you can split the runners at the trap.

If the 3rd runner walks east, you can block the 1st and 2nd runner at the corner of the cannon and let the 3rd runner eat the food at trap, then run to the trap.

For splitting runners in most scenarios, you can use DefinePro's method seen here. 

Alternatively use Thorin’s method of splitting runners seen here.

*NEW: Make sure you don't block the 1st runner when it goes to eat at main stack (thanks to flunch for pointing this out). It will either walk south, east, or west after eating, which enables you to block either of the runners such that they don't walk on the same tile. If you don't block either of the runners they will merge once they reach the corner of the cannon. Lastly, if you do block the 1st runner as it walks to mainstack they will walk on the same tile. 

If you use henke18 's mainstack, here's his solution to the puzzle:
"The way i solved it for my ms is that if you get ws/sw-w for first two runners, you have to time moving off ms.

The timing depends on what the 3rd runner does. If the 3rd runner walks west, you wait exactly 1 tick (after it starts moving) before moving off. If it walks east or south you wait 2 (or more) ticks.

This works because if you only wait 1 tick, the 1st runner will crash at ms but 2nd won't. If you wait 2 or more, both will crash at ms."


EW-S (2 logs)
The 1st and 2nd runner will auto multi. When the 3rd runner walks south it will crash and needs to be blocked for 1 tick south so that the trap food is in line of sight. Alternatively relure it by dropping a food north of the cannon.


When 2 logs are needed
It is probably easier to memorize when 2 logs are needed since there are fewer scenarios where this is the case, so here's a list of those permutations.

• SE-S
• ES-S
• EE-S
• EE-E
• EW-S
• WE-S
• WE-E

Thanks to henke18  and pi  for providing feedback and suggestions, and thank you to Faardo  for creating the google doc that allows for filtering.

If you have any further suggestions or if you find any errors feel free to post on this thread or shoot me a message ingame or on discord.

Update Feb 3rd 2019:
- Added WW-E to the list of permutations where you should block 3rd south for 1 tick
- Removed the part that mentioned you could split runners walking on the same time using Thorin's method - you cannot do this. I updated how to deal with this scenario properly.