Please add "Block Complete" randomization

[chri4354]

Expected Behavior

I would strongly recommend a feature (which I totally arbitrarily call Block Complete) in the condition randomization algorithms provided. This feature is the same as complete randomization but avoids to distribute participants in the same condition (say A) to different games and instead focuses on filling up one "A" game before assigning participants to another "A" game. This is especially important when we set Lobby time out to be Fail, as it avoids having many half full games, none of which can start.

Current Behavior

The current allowed solutions are Simple and Complete. With Simple the algorithm tosses a coin to assign a new participant to a condition A or B. This of course can, by randomness, generate unequal group sizes. Complete solves this problem, I believe, by permutation of the assignment sequence that maintain equal group sizes. So if I want three participants in each condition the algorithm takes AAA and BBB and permutes it into e.g. AABABBB.

Possible Solution

The new algorithm I suggest is Block Complete. It differs from Complete only when there are multiple instances of the same condition. So for example, say you want two games in each condition with three people each. Say the algorithm chooses to assign people according to the sequence AABBAABBAABB. Complete will assign As into "A" game 1 or "A" game 2 at random. However, say only 6 people show up. I could in principle run one game in each condition. However, because Complete does not try to fill up the game lobbies it already started, it might assign 2 people to (condition A-game 1) and one person to (condition A- game 2) (the same applies to B of course). Block Complete on the contrary takes the first 3 As of the sequence and always assign them to the same game (e.g. game 1) (same of course for B), only then starts assigning As to game 2.

Steps to Reproduce (for bugs)

Context

Often I am manipulating group size, so I cannot allow for LobbyTimeOut > Ignore. If I want to test multiple games in each condition, I run in the danger of having all my games half full and none of them actually starting, even though in principle I have enough people to run a few games in each condition.

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