### Possible die problem StreetSoccer

25 replies. Last post: 2003-10-24

Possible die problem
• agoui (limited edition) at 2003-09-11

Ever since Richard modified his die throw routine I have noticed that some extraordinary die throws happened.
I will mention three exambles from games where I was involved. I will also try to calculate the possibilities of the event happening, even though I am not an expert on these (so be kind if I make a mistake):

Examble 1: one player had five 1s in a row. The chances of this event happening are 1 in 7776! Btw the next two throws of the same player were 3 and again 1!

Examble 2: one player had a sequence of 6, 5, 5, 4, 6, 5 and the other had at the same time 2, 1, 3, 1, 3, 3. The chances for six in a row throws of 4+ or 3- are 1 in 64. For both events to happen at the same time it is 1 in 4096!

Examble 3: one player had four 6s in a row then a 3 and then two 5s. The chances of four 6s are 1 in 1296! Btw the total pips for the two players were 106 to 80.

If only one of the above happened I wouldn’t consider it strange. It seems though that there are too many extraordinary throw combinations and in my opinion there should be a problem somewhere. And as I said these are not the only exambles!

• FC Cwali at 2003-09-11

(The first turn the chance on a 1 is 5/15, so 33%.)

• Taral at 2003-09-11

I just did some quick calculations, regarding your example 1. (Of course, I may have made some wrong calculations.)

The probability that during 25 throws the same number shows up on five consecutive throws is 1.36%. Thus, the probability that at least one of the players in a game has five consecutive throws with the same number is 2.70%.

There are currently 3360 Street Soccer games on Little Golem (including both finished games and games in progress), and with the assumption that all of these last exactly 52 turns, we would expect that in about 46 of these games one player throws the same number five times in a row.

Though, I believe that the average number of turns is somewhat higher than 52.

• Tore S at 2003-09-11

The dice works better now than before. May be Richard could do a stats on the spread of the difference of total pips between the two players in a match: Most games shouĂ¸d come up with a low difference in the total pips between the two players.

If the difference is normal there should not be too much to worry about.

On the other hand: Even if the spread is normal there should not be too many extraordinary occurences like those agoui describes.

• michael at 2003-09-14

corne:
“(The first turn the chance on a 1 is 5/15, so 33%.)”

I thought the first die throw could be anything but a 6 ... so to me the chance on throwing a 1 in first throw is 1/5 or 20%. could u please explain your 5/15 more thoroughly?

• FC Cwali at 2003-09-14

"I thought the first die throw could be anything but a 6 ... so to me the chance on throwing a 1 in first throw is 1/5 or 20%. could u please explain your 5/15 more thoroughly?"

In the first turn of StreetSoccer both coaches throw the die after placing their players (alternating).
In this online version both coaches did ‘throw’ the die before placing their players. The coach who threw the highest, is the coach who start and must place his players first. He starts with the difference between his die-roll and the die-roll of the other coach. (If both coaches throw the same number, then you throw again.)
This means:
Chance on a 1 before the kick-off: 5/15.
Chance on a 2 before the kick-off: 4/15.
Chance on a 3 before the kick-off: 3/15.
Chance on a 4 before the kick-off: 2/15.
Chance on a 5 before the kick-off: 1/15.
(Only in case of a 6 and a 1 the difference is 5.)

• agoui (limited edition) at 2003-09-15

Here is a more analytical examble of one of my games that appears to be “normal”. The game ended 1-0 in extra time so someone could say that the die was more or less balanced. If we look at the sequence of the throws however I think that we will see unusual events. The total pips were 90-83.

This is the list of all the die throws (hopefully the tabs will work):
P1: 2,3,4,3,2, 1,2,1,5,3, 4,1,1,1,5, 4,3,6,3,6, 3,3,5,4,5, 2,2,6.

P2: 2,2,4,5,1, 6,6,4,1,2, 2,6,2,2,1, 4,3,5,3,3, 3,1,4,3,2, 1,2,3.

The main events that I see are:
Event 1: Player 1 had three 1s in a row.
Event 2: Player 1 had seven throws 3 or less in his first eight moves.
Event 3: In moves 16 to 19 the two players had almost identical throws.
Event 4: Player 2 had seven throws less than 2 in eight moves from his 9th-15th move.
Event 5: Player 2 had 3 or less in nine of his last ten moves.
Event 6: Player 2 had eight 2s in his 28 moves.

These events could all happen. In my opinion the really extraordinary event is the frequencey that they happen. It does appear to me that the chances for each a number in die are not 16.7%.
The die that my kids use to play snakes and ladders certainly does not behave like this one!

• Mac S at 2003-09-15

If the die-rolls would be 1,2,3,4,5,6,1,2,3,4,5,6,1,2 etc. then I would be more concerned.
I’d like to see averages over many games, and not only the average die-roll but also some patterns like difference between current and previous roll, difference between players etc.
Maybe Richard can do some calculations with data taken from the system, I’m not going to type in the die-rolls of a few hundred games!

• michael at 2003-09-15

the chances of getting 5 4 2 or 1 1 1 are exactly the same 1/216. what is interesting though, is that in this example 66% of the die rolls were {1, 2, 3} even on a move sequence of only 56 moves this looks strange indeed.

• michael at 2003-09-15

And ty Corne for the insight into a rule i obviously did not know about. I don’t see those moves when i watch streetsoccer games played on this server.

• LZJ at 2003-09-15

Another example – game 76711 I won 5:0:
Overall dice 87:74
Average 3.5:3.0 (seems not big difference)

Details
Ones 4:3 (OK)
Twos 4:9 (nine times two – terrible)
Threes 4:5 (OK)
Fours 2:3 (little less both)
Fives 7:4 (big advantage for first)
Sixs 3:0 (no six – very bad)

Fives+Sixs 10:4 (die generator error or really bad luck)

• michael at 2003-09-15

Libor Janda’s game {1,2,3}:{4,5,6}-29:18
61.7% of the moves are in groupe {1,2,3}

• michael at 2003-09-15

I wish i could somehow edit my posts.
Anyway here is correction of previous post 29:19 instead, which is 60.4% (still too much).

• michael at 2003-09-15

Can anyone show a game where the frequency of {4,5,6}is bigger than {1,2,3}?

• FC Cwali at 2003-09-15

"Can anyone show a game where the frequency of {4,5,6}is bigger than {1,2,3}?"

Yes, many. ca. 50% of the matches, I suppose. I looked at some games to see that. Didn’t do much chance-calculation but the averages look normal.

• agoui (limited edition) at 2003-09-15

in examble 3 of my original thread the 4,5,6 were more than 1,2,3. If there is a bug I do not think that it has to do with a specific number or numbers.

• Robin at 2003-09-15

I think you all have gone paranoid.

• Phlegm at 2003-09-26

The dice gods will get you guys for doubting them.

Just accept what happens.

• Telestes at 2003-09-26

The last 10 dice of my game #75333:

2-1-2-1-2-2-1-2-3-1

I think that’s enough argument for
a new Anti-Kill-Joy die generator!

• FC Cwali at 2003-09-26

I don’t hear anyone complaining about the die when getting 10 times 4, 5 or 6 in a row. :-)

• agoui (limited edition) at 2003-09-27

In a recently completed game I did not score a goal, even though I could, because the die was so much in my favour (I had 4, 6, 6, 5, 6). I do not think anyone feels comfortable with either repeated throws of 6s and 5s or 1s and 2s. But I quess we all notice it more when we are on the low throw site. In another recent game my opponent had 2, 2, 2, 1, 2... If someone picks up a die and throws it 25 times will he have this combinations (and so much frequency)? It does appear to me that the number selection is not as random as it should be.

• Marius Halsor at 2003-09-27

If there really is any doubt wether the dice are fair or not, I suggest someone (those most in doubt?) make a thourough examination of all the games played after the change in random generation. I have not done this, and can therefor not tell wether it’s fair or not. But you all should remember that every sequence is equally probable (negating the first die). Thus, the sequence 1-1-1-1 is just as probable as 2-6-3-4.

Every sequence of 25 consecutive throws has an extremely low probability of occuring, but nevertheless, one sequence WILL happen. If someone really is going to search the numbers, I suggest examining:

1) The number of times each of the possible outcomes 1-6 occurs (negating the first die)
2) After each outcome 1-6, what number of times each of the possible outcomes 1-6 occurs, for the next player and for the same player

If the numbers occur about the same number of times, I say the die is probably random enough. Richards first algorithm would pass the first test, but not the second (the opponents die was not independent of your die). I hope, and believe, that the current algorithm will pass both tests.

Marius

• Tore S at 2003-10-05

So it is my turn to complain. In my ongoing game against agoui I start with 10 times 4,5,6 and among them only one 4.

My poor opponent has still to get a 6. No wonder I lead that game:)

Total pips is 36 vs 55.

I am aware that such sequences will occu from time to time, but since this issue is under investigation I thougt I would let u all know.

• Hjallti at 2003-10-24

I think many people are making to much fuzz out of rare occasions.
If we are gather with more then 23 people the chance 2 of us share the same birthday is more then the chance none of us share the same birthday. Never the less most people think that you need 183 people to say that...

I just mean, here, it is quite normal that you have once in a while a sequence of 5 the same numbers, or that one player gets 90:60 in acummulated throws.
We always tend to focus on that strange occurance! Example the chance on a sequence of 5 equals in 5 throws is 1/1296 indeed, but in a series of 10 throws it is (almost) 1/216 (since the first 6 numbers could open a series). So in a game of 50 throws it will be around 1/40 (I didn’t actually calculated but I know it is a good guess), if you play 40 games it probably will occur.

totally independently another strange occurance could as well be on the way. (almost all throws even numbers, or all throws less or equal to 3 (both should happen with same frequency))....

• agoui (limited edition) at 2003-10-24

It appears that some have not understood the possible problem that the die might have. It is NOT the fact that rare incidences happen. It is the fact that rare incidences happen TOO OFTEN.

And to try to get the message across, for the last time, I will write 3 such events from my SS championship games. These events are all rolls of one player:
Event 1: 5,6,4,5,6,5,5,5,6,5
Event 2: 6,6,3,5,6,6,6,5,5,5
Event 3: 5,6,6,4,6,5,6

These 3 separate events were happening in my first 9 completed games. That means 1 in 3 games!
In one of the other 7 completed championship games one of the players had rolls of 1,1,3,2,2,2,2,1. If we count this game too then it is 4 out of 16 completed games.

And in my opinion that shows that there is a problem with the die. Even if you do not agree, is it at least clear as to what the possible problem might be?