Board Game Arena

How is the number of ELO points gained or lost determined at the end of the game?

Elo is a horrible system for games that have a substantial luck component, like this one. No matter how great you are at this game, you aren't going to be able boost your win rate more than a couple percent.

FSKFSK wrote: ↑26 May 2025, 04:37 Elo is a horrible system for games that have a substantial luck component, like this one. No matter how great you are at this game, you aren't going to be able boost your win rate more than a couple percent.

Be careful what you say about elo, you can get banned, but Arena isn't much better. I play arena games to play better people. Tonight i had a person with the 2X stop after attaining second place. They only had 1 card higher then a 9 and could have won, but they quit. Why play if you are only playing for second.

Solarman9 wrote: ↑04 June 2025, 04:00 Be careful what you say about elo, you can get banned

Provide a justification for this statement.

In my mind ELO is ok even for luck-based games, it's just that a K factor has to account for that. Provided, that probability function p(D) stays the same for all games, K factors currently in use in both Arena and regular Elo suit long less-to-no luck based games. Luck based games should really have them much smaller to reduce unrepresentative swings. Also, as the games are shorter, smaller K factor is not an issue for settling in your rating initially, as you can just play a lot of games quickly.

It isn't enough to adjust the k factor. You also have to adjust the assumed probability distribution. Suppose that, in a 3p game, you have at most a 40% chance of winning no matter how good you are. If you play opponents whose elo is below a certain amount, you will, on average, lose elo paying against them.

The elo probability distribution assumes that someone with an elo 400 points higher has a 90% chance of winning. That's completely unattainable for any luck-based game like flip7.

FSKFSK wrote: ↑06 June 2025, 01:30 It isn't enough to adjust the k factor. You also have to adjust the assumed probability distribution. Suppose that, in a 3p game, you have at most a 40% chance of winning no matter how good you are. If you play opponents whose elo is below a certain amount, you will, on average, lose elo paying against them.

The elo probability distribution assumes that someone with an elo 400 points higher has a 90% chance of winning. That's completely unattainable for any luck-based game like flip7.

What is your suggestion for a better system?

Dynamically adjust the probability distribution based on the observed win rates of each game.

For example, in games where both players have 300+ elo, look at how often the better player wins (based on rating difference). Then use that probability distribution instead of the one elo uses.

The way elo works is that both players "ante" rating points based on their rating difference, and the winner gets the pot.

Elo uses the formula 1 / (1 + 10^(rating difference/400)) as the "better player's chance of winning", where "rating difference" is lower rated player's ranking minus high rated player's ranking.

This system works very well for chess, because a player with a 400+ better rating will almost always win, due to the lack of a luck factor.

This system fails for luck-based games, because the better player will only have a 55%-75% chance of winning, no matter how much better they are, as long as their opponent knows the basic strategy for the game.

I'm just saying that the formula 1 / (1 + 10^(rating difference/400)) needs to be replaced with something else for games with a significant luck component. Ideally, the distribution can be determined dynamically by looking at game results, maybe updating it every 3-6 months.