ESO_player123 wrote: »I do not know if that 50/50 "coin" is fair, but your chance of going first did not change:
1004/2106 = 0.4767331434 (~47 .67 %)
1404/2933 = 0.47869076031 (~47.87 %)
In fact, it even got a tiny bit better (or should I say closer to 50/50) by 0.00195761691 (~0.2 %).
Personofsecrets wrote: »ESO_player123 wrote: »I do not know if that 50/50 "coin" is fair, but your chance of going first did not change:
1004/2106 = 0.4767331434 (~47 .67 %)
1404/2933 = 0.47869076031 (~47.87 %)
In fact, it even got a tiny bit better (or should I say closer to 50/50) by 0.00195761691 (~0.2 %).
Thank you for sharing.
Regarding the fairness aspect, there are some specific players who I go first against more often, but some other players who are pests as they seem to go first against me all of the time.
ESO_player123 wrote: »Personofsecrets wrote: »ESO_player123 wrote: »I do not know if that 50/50 "coin" is fair, but your chance of going first did not change:
1004/2106 = 0.4767331434 (~47 .67 %)
1404/2933 = 0.47869076031 (~47.87 %)
In fact, it even got a tiny bit better (or should I say closer to 50/50) by 0.00195761691 (~0.2 %).
Thank you for sharing.
Regarding the fairness aspect, there are some specific players who I go first against more often, but some other players who are pests as they seem to go first against me all of the time.
I do agree that It feels that I go second against some players more often. Do you have the statistics per player (without naming them of course)? It also feels that going first/second goes in clusters (kind of like in this playing session you get to go first most of the time and in this one second most of the time).
LootAllTheStuff wrote: »The problem with a 50:50 chance is that, if you get a big run (or series of runs) against you in the initial stages, it can take a long time to bring the observed rate up to that 50% line. In other games where I've tracked similar statistics, it's very much been an exponential curve. In effect, you need to keep doubling the number of observations in order to see the observed rate change much at all.
I'd also point out that it's not the absolute deficit you should be looking at, since the total number of observations is obviously changing - you want to look at the relative deficit.
So, as ESO_player123 points out, for your first 2106 runs you 'won' 1004/2106 times (47.677%) giving you a relative deficit of 49/2106 = 0.0233 (2.33%)
For your next (2933-2106) = 827 runs, you won (1404-1004) = 400 times (48.37%) giving you a relative deficit of 13.5/827 = 0.0163 (1.63%). IOW you were still winning the toss fewer times than an exact 50:50, but not by as wide a margin.
To meaningfully compare, though, you'd want the next ~2000 instead of 827 runs. Alternatively, if you have all the individual stats, you could break it down into 3 equal blocks and do the same calculations.
I have a love-hate relationship with statistics - I love playing around with it, but I hate experiencing the results!

Personofsecrets wrote: »ESO_player123 wrote: »Personofsecrets wrote: »ESO_player123 wrote: »I do not know if that 50/50 "coin" is fair, but your chance of going first did not change:
1004/2106 = 0.4767331434 (~47 .67 %)
1404/2933 = 0.47869076031 (~47.87 %)
In fact, it even got a tiny bit better (or should I say closer to 50/50) by 0.00195761691 (~0.2 %).
Thank you for sharing.
Regarding the fairness aspect, there are some specific players who I go first against more often, but some other players who are pests as they seem to go first against me all of the time.
I do agree that It feels that I go second against some players more often. Do you have the statistics per player (without naming them of course)? It also feels that going first/second goes in clusters (kind of like in this playing session you get to go first most of the time and in this one second most of the time).
Yes, I have these statistics on a per player basis. I can try to extract that info from how ever impressive stats stores it. The only issue in the per player analysis is that there are many players who I haven't played that many games against. For example, I think that one of these players had gone 1st against me like the first 6 games we played, but then things leveled out after initial burst.
And yea, 1st / 2nd player seems to cluster. IDK how I would prove that with the data. There are other strange RNG things too which just seem wacky.
LootAllTheStuff wrote: »Personofsecrets wrote: »ESO_player123 wrote: »Personofsecrets wrote: »ESO_player123 wrote: »I do not know if that 50/50 "coin" is fair, but your chance of going first did not change:
1004/2106 = 0.4767331434 (~47 .67 %)
1404/2933 = 0.47869076031 (~47.87 %)
In fact, it even got a tiny bit better (or should I say closer to 50/50) by 0.00195761691 (~0.2 %).
Thank you for sharing.
Regarding the fairness aspect, there are some specific players who I go first against more often, but some other players who are pests as they seem to go first against me all of the time.
I do agree that It feels that I go second against some players more often. Do you have the statistics per player (without naming them of course)? It also feels that going first/second goes in clusters (kind of like in this playing session you get to go first most of the time and in this one second most of the time).
Yes, I have these statistics on a per player basis. I can try to extract that info from how ever impressive stats stores it. The only issue in the per player analysis is that there are many players who I haven't played that many games against. For example, I think that one of these players had gone 1st against me like the first 6 games we played, but then things leveled out after initial burst.
And yea, 1st / 2nd player seems to cluster. IDK how I would prove that with the data. There are other strange RNG things too which just seem wacky.
Clustering is expected behaviour for binary outcomes from true RNGs. However, run lengths would also be expected to follow a certain distribution (allowing for sample size). That's getting pretty deep into statistical theory, but the short version is that it's one of the things statisticians look for in identifying truly random versus non-random outcomes. If you have access to an actual stats package of some kind, it's something you could look into. That's getting pretty deep in the weeds, though.
LootAllTheStuff wrote: »Personofsecrets wrote: »ESO_player123 wrote: »Personofsecrets wrote: »ESO_player123 wrote: »I do not know if that 50/50 "coin" is fair, but your chance of going first did not change:
1004/2106 = 0.4767331434 (~47 .67 %)
1404/2933 = 0.47869076031 (~47.87 %)
In fact, it even got a tiny bit better (or should I say closer to 50/50) by 0.00195761691 (~0.2 %).
Thank you for sharing.
Regarding the fairness aspect, there are some specific players who I go first against more often, but some other players who are pests as they seem to go first against me all of the time.
I do agree that It feels that I go second against some players more often. Do you have the statistics per player (without naming them of course)? It also feels that going first/second goes in clusters (kind of like in this playing session you get to go first most of the time and in this one second most of the time).
Yes, I have these statistics on a per player basis. I can try to extract that info from how ever impressive stats stores it. The only issue in the per player analysis is that there are many players who I haven't played that many games against. For example, I think that one of these players had gone 1st against me like the first 6 games we played, but then things leveled out after initial burst.
And yea, 1st / 2nd player seems to cluster. IDK how I would prove that with the data. There are other strange RNG things too which just seem wacky.
Clustering is expected behaviour for binary outcomes from true RNGs. However, run lengths would also be expected to follow a certain distribution (allowing for sample size). That's getting pretty deep into statistical theory, but the short version is that it's one of the things statisticians look for in identifying truly random versus non-random outcomes. If you have access to an actual stats package of some kind, it's something you could look into. That's getting pretty deep in the weeds, though.
ESO_player123 wrote: »LootAllTheStuff wrote: »Personofsecrets wrote: »ESO_player123 wrote: »Personofsecrets wrote: »ESO_player123 wrote: »I do not know if that 50/50 "coin" is fair, but your chance of going first did not change:
1004/2106 = 0.4767331434 (~47 .67 %)
1404/2933 = 0.47869076031 (~47.87 %)
In fact, it even got a tiny bit better (or should I say closer to 50/50) by 0.00195761691 (~0.2 %).
Thank you for sharing.
Regarding the fairness aspect, there are some specific players who I go first against more often, but some other players who are pests as they seem to go first against me all of the time.
I do agree that It feels that I go second against some players more often. Do you have the statistics per player (without naming them of course)? It also feels that going first/second goes in clusters (kind of like in this playing session you get to go first most of the time and in this one second most of the time).
Yes, I have these statistics on a per player basis. I can try to extract that info from how ever impressive stats stores it. The only issue in the per player analysis is that there are many players who I haven't played that many games against. For example, I think that one of these players had gone 1st against me like the first 6 games we played, but then things leveled out after initial burst.
And yea, 1st / 2nd player seems to cluster. IDK how I would prove that with the data. There are other strange RNG things too which just seem wacky.
Clustering is expected behaviour for binary outcomes from true RNGs. However, run lengths would also be expected to follow a certain distribution (allowing for sample size). That's getting pretty deep into statistical theory, but the short version is that it's one of the things statisticians look for in identifying truly random versus non-random outcomes. If you have access to an actual stats package of some kind, it's something you could look into. That's getting pretty deep in the weeds, though.
Is clustering related to a playing session expected though? It feels like a player gets assigned some kind of number(s) on login that defines how "lucky" they are going to be during that session. I understand that it is in humans' nature to seek patterns even where there is only random noise, but this is not related only to ToT. There are accounts of getting more leads from treasure maps if you already got one during that playing session. Same for infamous trophies (that is how I finished my collection).

It would be sort of pointless to play if the game went: "I see your win rate is going too far above 50%. Better start making you go second now until you're back down to 50".
ESO_player123 wrote: »On a related note, today the tavern dealt me 3 kwama egg mine/ebony mine cards on the same turn.Two back to back and then another one card apart.
Personofsecrets wrote: »It would be sort of pointless to play if the game went: "I see your win rate is going too far above 50%. Better start making you go second now until you're back down to 50".Personofsecrets wrote: »It would be pointless unless you are a game developer.
Personofsecrets wrote: »It would be pointless unless you are a game developer.
I hate how they got rid of the edit on web browser. Didn't mean to hit reply.
LootAllTheStuff wrote: »
Just so you know, the edit function isn't actually gone, it's just that the icon is no longer being loaded. If you move your cursor around in the area just left of the post number (#4 or whatever) you should see the tooltip pop up and you can click on it.