Re: So many repeats
Posted: 06 November 2022, 14:15
Tip for the designer: if you want the probability to drop below 10%, you need 1617 words, and 16828 words to drop below 1% (always selecting 13 words).
But that's misleading because in most games the players don't see all 13 words. According to the statistics for "all players", the average is 11 rounds played per game (which is higher than I expected, to be honest).
It is in fact coded as 110 cards with 5 words each. And yes, game randomly selects a card on the game start. After that it randomly chooses a number from 0 to 4 as $wordID. Then it picks this shuffled cards list and uses this one $wordId 110 or 13 times with random $cardId. If 110 words is not enough (Infinite words option), it does $wordID+1 (or $wordID = 0 if previous $wordID was 4) and takes 110 words 4 more times. Then it puts everything in a database. So what you will see in a database after game setup is 13 (or 550) combinations of $cardId-$wordId with the first 110 $wordId being the same. But cards are shuffled which means it's still random distribution after all.fruktansvärt wrote: ↑06 November 2022, 12:49 IS the game here on BGA coded with "110 cards with 5 words each"?
Wow, thanks a lot for the maths, that makes this mostly discussed problem of words randomness to another level!Jellby wrote: ↑06 November 2022, 10:12 ...
So the probability of at least 1 repeated word in two independent games is actually much higher than 16%, and higher than one in four. Maybe an appropriate suggestion would be to allow players to choose a word from each card, instead of having them randomly selected.
Wait... what? Are you saying that it chooses 13 random cards, and then, for instance, the 2nd word of every one of these cards (not necessarily in this order, but effectively)? If that's the case that's totally wrong, that would mean that once you know it's the 2nd word of a card, you can rule out all words which are not 2nd in their card. I think it would also increase the probability of multiple repetitions.KuWizard wrote: ↑15 November 2022, 14:48It is in fact coded as 110 cards with 5 words each. And yes, game randomly selects a card on the game start. After that it randomly chooses a number from 0 to 4 as $wordID. Then it picks this shuffled cards list and uses this one $wordId 110 or 13 times with random $cardId.
I can't see how exactly it would increase the probability. However during game was in alpha and in beta the algorithm was different (before Infinite games were introduced). Even then the amount of complaints about repetitions was not lower than it is now. So I can fix that, no problem, but this won't solve the problem.Jellby wrote: ↑15 November 2022, 15:42Wait... what? Are you saying that it chooses 13 random cards, and then, for instance, the 2nd word of every one of these cards (not necessarily in this order, but effectively)? If that's the case that's totally wrong, that would mean that once you know it's the 2nd word of a card, you can rule out all words which are not 2nd in their card. I think it would also increase the probability of multiple repetitions.KuWizard wrote: ↑15 November 2022, 14:48It is in fact coded as 110 cards with 5 words each. And yes, game randomly selects a card on the game start. After that it randomly chooses a number from 0 to 4 as $wordID. Then it picks this shuffled cards list and uses this one $wordId 110 or 13 times with random $cardId.
This point is key. If the implementation were altered so that the "judge" each turn could select the word (from among five on a card), then complaints about repeated words would be reduced, presuming that groups usually play a few games per session with only small changes in the composition of the group of players. Because the judge, presumably, would avoid any word recently seen in a game with the same players.
I ran two simulations of a million trials each, each trial consisting of three games. Algorithm 1: 13 distinct cards out of 110 are chosen randomly and for each chosen card 1 word out of 5 is chosen randomly. Result for algorithm 1: in my simulation of a million three-game sets, 613,151 three-game sets (61.3%) contained at least one repeat. Algorithm 2: 13 distinct words out of 550 are chosen randomly. Result for algorithm 2: in my simulation of a million three-game sets, 614,219 three-game sets (61.4%) contained at least one repeat.Proclivitas wrote: ↑05 November 2022, 09:49 I should not be seeing the same word every 2-3 games, sometimes back to back. That's just extremely unlikely.