Things you often Wonder

[blandy]

22 minutes ago, snowychap said:

I'm not at all sure on the first and it's been a long time since I tried to work out probabilities so I'm prepared to be pulled up and told that the following is wrong:

Assuming that each played track is not allowed to be picked a second time from the playlist, I think it would be

(7/36*6/35*5/34*4/33) + (7/35*6/34*5/33*4/32) + (7/34*6/33*5/32*4/31) = 0.002

Edit: No, that's wrong, too. In the second and third possibilities, I haven't allowed for the first (in the second case) and the first and second (in the third case) having to be NOT from the album.

Edit 2:

So, (7/36*6/35*5/34*4/33) + (29/36*7/35*6/34*5/33*4/32) + (29/36*28/35*7/34*6/33*5/32*4/31) = 0.0016

Not sure that's right, is it snowy?

if 

Quote

7 of the songs are from the same album, and I had 4 of them play back to back

then given (as you correctly assume) the first one is playing and it's the odds for the next 3 being worked out, then the first calc will be 

6/35....etc. (iaw your process)

this is because the current track won't be next, and there are 6 others from that album possible, from the remaining 35 tracks on the playlist.

 

[tom_avfc]

12 minutes ago, blandy said:

then given (as you correctly assume) the first one is playing and it's the odds for the next 3 being worked out, then the first calc will be 

6/35....etc. (iaw your process)

this is because the current track won't be next, and there are 6 others from that album possible, from the remaining 35 tracks on the playlist.

 

This is only correct if the first song is from the album though as once the shuffled playlist has played through once then any song can be selected again for the second run through. Therefore the probability of the first 4 being from that album are 0.0006 (7/36 x 6/35 x 5/34 x 4/33).

The probability will then rise and fall from there depending on which songs come out in what order so if the first song has been from the album then, as you say the probability will be (6/35 x 5/34 x 4/33). 

Edited June 27, 2018 by tom_avfc

[Stevo985]

4 minutes ago, tom_avfc said:

This is only correct if the first song is from the album though as once the shuffled playlist has played through once then any song can be selected again for the second run through. Therefore the probability of the first 4 being from that album are 0.0006 (7/36 x 6/35 x 5/34 x 4/33).

The probability will then rise and fall from there depending on which songs come out in what order so if the first song has been from the album then, as you say the probability will be (6/35 x 5/34 x 4/33). 

Blandy was right.

I'm already listening to the first track. So what is the probability that the next 3 songs will be from the same album

[snowychap]

20 minutes ago, blandy said:

Not sure that's right, is it snowy?

I've just gone back and read Stevo's original post and I completely misread it.

For some reason, I had read in to it that he had played 6 tracks from that playlist and that four were from that same album playing back to back. I have absolutely no idea why I read the played 6 tracks in to it (which sent me off on the calculations above).

Thus I was looking at the run of consecutive tracks beginning either with the first, the second or the third (and I calculated it wrong again even so).

Edit: What you and Stevo have gone for, though, isn't quite what he asked, is it?

Edited June 27, 2018 by snowychap

[snowychap]

Just now, Stevo985 said:

Blandy was right.

I'm already listening to the first track. So what is the probability that the next 3 songs will be from the same album

How many tracks have you already listened to from the playlist before you are listening to that first track?

[blandy]

4 minutes ago, tom_avfc said:

This is only correct if the first song is from the album though as once the shuffled playlist has played through once then any song can be selected again for the second run through. Therefore the probability of the first 4 being from that album are 0.0006 (7/36 x 6/35 x 5/34 x 4/33).

The probability will then rise and fall from there depending on which songs come out in what order so if the first song has been from the album then, as you say the probability will be (6/35 x 5/34 x 4/33). 

@snowychap specifically said that "Assuming that each played track is not allowed to be picked a second time from the playlist," so that's why my maths is like it is and why I'm right

 

 

[snowychap]

1 minute ago, blandy said:

@snowychap specifically said that "Assuming that each played track is not allowed to be picked a second time from the playlist," so that's why my maths is like it is and why I'm right

 

 

Only if that run of four are the first four tracks from the playlist that are being listened to, surely?

 

There are going to be some very angry/bored people reading these posts.

Edited June 27, 2018 by snowychap

[blandy]

Just now, snowychap said:

How many tracks have you already listened to from the playlist before you are listening to that first track?

It doesn't matter, as long as "each played track is not allowed to be picked a second time from the playlist, until all the others have been played and the same applies for the second run through - i.e after 36 songs, it doesn't stop, but carries on. 

[Stevo985]

1 minute ago, snowychap said:

How many tracks have you already listened to from the playlist before you are listening to that first track?

no idea. A couple.

For the purposes of this I was assuming that was negligible. i.e. there were 35 other tracks to choose from (other than the one that is playing)

[blandy]

5 minutes ago, snowychap said:

There are going to be some very angry/bored people reading these posts.

And writing them

[snowychap]

1 minute ago, blandy said:

It doesn't matter, as long as "each played track is not allowed to be picked a second time from the playlist, until all the others have been played and the same applies for the second run through - i.e after 36 songs, it doesn't stop, but carries on. 

It does matter. If 4 of the 7 tracks from the album have already been played and there are at least 3 tracks remaining to be played in the playlist then the probability of the next 3 being from the same album given that you're already listening to one from that album is zero.

[blandy]

17 minutes ago, snowychap said:

It does matter. If 4 of the 7 tracks from the album have already been played and there are at least 3 tracks remaining to be played in the playlist then the probability of the next 3 being from the same album given that you're already listening to one from that album is zero.

I see. What I'm assuming (and tried to explain above) is that if the playlist carries on running endlessly, rather than coming to a stop after 36 songs, then my maths is right and it doesn't matter - if you consider the playlist running endlessly, randomly, then at the point the first song from the album is heard, then the next 35 songs will each only be played once and the odds are as per my sums.

If however the playlist stops, then you'd have to do some really complex sums to get the right answer, wouldn't you?

edit: and also need more info - e.g. are there any other albums of at least 4 songs in the list, if so how many...etc.

[snowychap]

16 minutes ago, blandy said:

I see. What I'm assuming (and tried to explain above) is that if the playlist carries on running endlessly, rather than coming to a stop after 36 songs, then my maths is right and it doesn't matter - if you consider the playlist running andlessly, randomly, then at the point the first song from the album is heard, then the next 35 songs will each only be played once and the odds are as per my sums.

If however the playlist stops, then you'd have to do some really complex sums to get the right answer, wouldn't you?

 

I'm assuming the playlist running endlessly, too, i.e. that the number of tracks remaining to play depletes by one each time until it gets to zero and then it restarts.

So, as per my post above, 4 of the tracks from the album have already been played and 28 not from the album have been played. A track from the album is now playing (33 out of 36 on the playlist) and the probability of the next three songs also being from the album is zero becuase there are only 2 possible tracks remaining from that album. If the track from the album was 34 out of 36 and there were only two remaining and they were both from that same album (and the playlist restarted randomly) then the probability would be 7/36 (2/2*1/1*7/36).

This all feeds back in what @tom_avfc posted above.

Edit: If it's just about running endlessly and not repeating the current track then it would be 6/35*6/35*6/35, wouldn't it?

Edit 2: We're moving a little bit away from what @Stevo985 originally wondered about, though.

Edited June 27, 2018 by snowychap

[Stevo985]

18 minutes ago, snowychap said:

 

Edit 2: We're moving a little bit away from what @Stevo985 originally wondered about, though.

I think you're just inventing things to do maths about now  

(I'm fully on board)

[blandy]

9 minutes ago, snowychap said:

I'm assuming the playlist running endlessly, too, i.e. that the number of tracks remaining to play depletes by one each time until it gets to zero and then it restarts.

So, as per my post above, 4 of the tracks from the album have already been played and 28 not from the album have been played. A track from the album is now playing (33 out of 36 on the playlist) and the probability of the next three songs also being from the album is zero becuase there are only 2 possible tracks remaining from that album. If the track from the album was 34 out of 36 and there were only two remaining and they were both from that same album (and the playlist restarted randomly) then the probability would be 7/36 (2/2*1/1*7/36).

This all feeds back in what @tom_avfc posted above.

Edit: If it's just about running endlessly and not repeating the current track then it would be 6/35*6/35*6/35, wouldn't it?

Edit 2: We're moving a little bit away from what @Stevo985 originally wondered about, though.

I don't think I agree, still, snowy.

If the playlist randomly plays 36 different tracks, and doesn't repeat any until the others have all been played then at any and all times, there are 35 different tracks to follow the currently playing track before we get to a possibility of a repeat. Once you hit the first track from Stevo's album, that's the only point you can then do the sums,  and you'd need to do then as per the method you initially outlined (but using the right figures  )

unless you want to do the really complex maths, which would basically be what is the chance of the first 4 tracks (of 36) being from the album (7/36 * 6/35 *  5/34 * 4/33), then factor in what is the odds of the first track not being from the album, but the next 4 all being from. so + (29/36 * 6/35 *  5/34 * 4/33 * 28/32 * 27/...etc.).. then then factor in what is the odds of the first two tracks not being from the album, but the next 4 all being from.+ (29/36 * 28/35 * 6/34 * 5/33 * 1/8 * 3/31 * 28/30 * 27/....etc.)   and so on. So that would work out the probability for 4 tracks from the album playing in succession at any point in a 36 track playlist).

We are miles away, but it's closer to going homw time and cricket watching

and also we don't have a set of defined assumptions, but that's the maths, as I understand things, at least.   

[tom_avfc]

17 minutes ago, blandy said:

I don't think I agree, still, snowy.

If the playlist randomly plays 36 different tracks, and doesn't repeat any until the others have all been played then at any and all times, there are 35 different tracks to follow the currently playing track before we get to a possibility of a repeat. Once you hit the first track from Stevo's album, that's the only point you can then do the sums,  and you'd need to do then as per the method you initially outlined (but using the right figures  )

unless you want to do the really complex maths, which would basically be what is the chance of the first 4 tracks (of 36) being from the album (7/36 * 6/35 *  5/34 * 4/33), then factor in what is the odds of the first track not being from the album, but the next 4 all being from. so + (29/36 * 6/35 *  5/34 * 4/33 * 28/32 * 27/...etc.).. then then factor in what is the odds of the first two tracks not being from the album, but the next 4 all being from.+ (29/36 * 28/35 * 6/34 * 5/33 * 1/8 * 3/31 * 28/30 * 27/....etc.)   and so on. So that would work out the probability for 4 tracks from the album playing in succession at any point in a 36 track playlist).

We are miles away, but it's closer to going homw time and cricket watching

and also we don't have a set of defined assumptions, but that's the maths, as I understand things, at least.   

The problem with this is that on shuffle a playlist will play through the 36 songs in a random order but then after the 36th will regenerate a new order for the 36 songs (otherwise you’d just get the same songs in the same order again). This means that unless the 4 tracks come out at the start then there isn’t 35 songs that could potentially be next - there’s however many are left and then potentially any song could come up once every song has been played.

It doesn’t seem to be the easiest concept to put into words so hopefully that makes sense! 

[blandy]

Just now, tom_avfc said:

The problem with this is that on shuffle a playlist will play through the 36 songs in a random order but then after the 36th will regenerate a new order for the 36 songs (otherwise you’d just get the same songs in the same order again). This means that unless the 4 tracks come out at the start then there isn’t 35 songs that could potentially be next - there’s however many are left and then potentially any song could come up once every song has been played.

It doesn’t seem to be the easiest concept to put into words so hopefully that makes sense! 

It does, yes.

I genuinely don't know whether "shuffle" feature works like that.

Admittedly we're mixing 2 different things, a stats question and a "how does a plalist shuffle work. Like I said we're missing some assumptions for the stats question, and how the shuffle works is one of them - you're right. One way would be as you describe. Another would be that the algorithm for the random feature might run once to create  "n" instances (e.g. 36 factorial) of random sequences for the 36 tracks and store that huge number in memory.

If we documented all the assumptions as to how shuffle works, when the start point is, whether tracks can play twice etc. we could work it all out, or I could get a life. One of the two.

[snowychap]

40 minutes ago, blandy said:

I don't think I agree, still, snowy.

If the playlist randomly plays 36 different tracks, and doesn't repeat any until the others have all been played then at any and all times, there are 35 different tracks to follow the currently playing track before we get to a possibility of a repeat. Once you hit the first track from Stevo's album, that's the only point you can then do the sums,  and you'd need to do then as per the method you initially outlined (but using the right figures  )

You need to restart the process after the 36 tracks have been played. If the rule is that you can't repeat a track within a rolling 36 tracks then it would cease to be random as all subsequent iterations would have to be the same as the first in order to comply with the no repeat within 36 rule.

Edited June 27, 2018 by snowychap

[mjmooney]

2 hours ago, Stevo985 said:

Yeah i don't think that math is right.

It isn't. Unless you're an American, it's maths. 

[blandy]

8 minutes ago, snowychap said:

Even with your rolling 36 track cycle, my post above still stands, I believe, i.e. that if four of the tracks from the album have already previously been out within the 32 tracks prior to the current one...

Sure - If you make one assumption, it does. If you make a different one, then it doesn't. One (your, valid)  assumption is that the question validity period is from the moment that any track is first played until 36 tracks have been played, another is (my, also valid) assumption that "if the current track being played is from the album, what is the prob. that of the other possible 35 tracks to come up (in the next 35 songs I play, with no repats), the three immediately next will all be from. the one album.

I actually took "my" assumptions from your initial post, where you said "no repeats" and where you has 3 sets of calc. I think I'd have made the same ones, anyway, but your post steered me that way. Like we've said, it's the assumptions that influence the different correct  answers we calculate