Even and Odd

[Stone]

I had been looking at the appearance of even and odd numbers in draws, initially I was just looking at the number of even and odd numbers:

out of 1667 draws:
0 odd 6 even = 15 draws
1 odd 5 even = 125 draws
2 odd 4 even = 411 draws
3 odd 3 even = 515 draws
4 odd 2 even = 403 draws
5 odd 1 even = 179 draws
6 odd 0 even = 19 draws

I realise there's more possible sequences that the evens and odds can be drawn in in 3+3 (20) than in all odd(1) or all even(1) but even still, the average for 3+3 is 25 so it got me wondering why.

Initially there are 25 odd and 24 even so there's a slightly higher chance of the first ball drawn being odd, if the first ball is odd then that leaves an equal number of even and odd in the machine so it's 50/50 what the second ball will be, but if the first ball is even then there are 2 more odd than even in the machine and the odds of the second ball being odd increase a little. And so on

I'm not sure if I'm making much sense but I'm just wondering why some odd/even sequences occur more than others and if something like that can explain it.

Stone

 

[PAB]

Hi Stone,

I assume you are referring to the UK 649 Lotto?
The distribution of ODD & EVEN numbers and the total combinations for each in a 649 Lotto are :-

ALL Possible Odd & Even Numbers
Distribution Combinations Percent Expected 1 in Every
0 Odd + 6 Even 134,596 0.96% 103.89 Draws
1 Odd + 5 Even 1,062,600 7.60% 13.16 Draws
2 Odd + 4 Even 3,187,800 22.80% 4.39 Draws
3 Odd + 3 Even 4,655,200 33.29% 3.00 Draws
4 Odd + 2 Even 3,491,400 24.97% 4.01 Draws
5 Odd + 1 Even 1,275,120 9.12% 10.97 Draws
6 Odd + 0 Even 177,100 1.27% 78.96 Draws
Totals > 13,983,816 100.00%

Regards,
PAB

 

[blitzed]

hiya PAB, you are sure on the ball

take it easy,
blitzed

 

[Stone]

Thanks PAB, I know that but what I'm wondering about is the sequence that the odd and even come out the machine, there's 64 possible sequences.

the balls have come out as EOEOEO on 17 occasions

but EOOOEE on 35 occasions

While the numbers would have to come out the machine in a different order, both these sequences have the same number of possible combinations.

As you showed above, the numbers of even/odd coming out are pretty close to what's expected so I'm curious as to why some sequences appear more.

 

[PAB]

Thanks blitzed .

Hi Stone,

I will have a look later and see if there is anything I can derive.

For others watching this thread, here are ALL 64 possible sequences of ODD & EVEN numbers and the total combinations for each with respect to ALL 13,983,816 combinations of a 649 Lotto.

Distribution Combinations Percent Expected 1 in Every
OOOOOO 177,100 1.27 78.96 Draws
OOOOOE 177,100 1.27 78.96 Draws
OOOOEO 230,230 1.65 60.74 Draws
OOOEOO 230,230 1.65 60.74 Draws
OOOOEE 177,100 1.27 78.96 Draws
OOOEOE 230,230 1.65 60.74 Draws
OOOEEO 230,230 1.65 60.74 Draws
OOOEEE 177,100 1.27 78.96 Draws
OOEOOO 230,230 1.65 60.74 Draws
OOEOOE 230,230 1.65 60.74 Draws
OOEOEO 296,010 2.12 47.24 Draws
OOEEOO 230,230 1.65 60.74 Draws
OOEOEE 230,230 1.65 60.74 Draws
OOEEOE 230,230 1.65 60.74 Draws
OOEEEO 230,230 1.65 60.74 Draws
OOEEEE 177,100 1.27 78.96 Draws
OEOOOO 230,230 1.65 60.74 Draws
OEOOOE 230,230 1.65 60.74 Draws
OEOOEO 296,010 2.12 47.24 Draws
OEOEOO 296,010 2.12 47.24 Draws
OEOOEE 230,230 1.65 60.74 Draws
OEOEOE 296,010 2.12 47.24 Draws
OEOEEO 296,010 2.12 47.24 Draws
OEOEEE 230,230 1.65 60.74 Draws
OEEOOO 230,230 1.65 60.74 Draws
OEEOOE 230,230 1.65 60.74 Draws
OEEOEO 296,010 2.12 47.24 Draws
OEEEOO 230,230 1.65 60.74 Draws
OEEOEE 230,230 1.65 60.74 Draws
OEEEOE 230,230 1.65 60.74 Draws
OEEEEO 230,230 1.65 60.74 Draws
OEEEEE 177,100 1.27 78.96 Draws
EOOOOO 177,100 1.27 78.96 Draws
EOOOOE 177,100 1.27 78.96 Draws
EOOOEO 230,230 1.65 60.74 Draws
EOOEOO 230,230 1.65 60.74 Draws
EOOOEE 177,100 1.27 78.96 Draws
EOOEOE 230,230 1.65 60.74 Draws
EOOEEO 230,230 1.65 60.74 Draws
EOOEEE 177,100 1.27 78.96 Draws
EOEOOE 230,230 1.65 60.74 Draws
EOEOEO 296,010 2.12 47.24 Draws
EOEEOO 230,230 1.65 60.74 Draws
EOEOOO 230,230 1.65 60.74 Draws
EOEOEE 230,230 1.65 60.74 Draws
EOEEOE 230,230 1.65 60.74 Draws
EOEEEO 230,230 1.65 60.74 Draws
EOEEEE 177,100 1.27 78.96 Draws
EEOOOO 177,100 1.27 78.96 Draws
EEOOOE 177,100 1.27 78.96 Draws
EEOOEO 230,230 1.65 60.74 Draws
EEOEOO 230,230 1.65 60.74 Draws
EEOOEE 177,100 1.27 78.96 Draws
EEOEOE 230,230 1.65 60.74 Draws
EEOEEO 230,230 1.65 60.74 Draws
EEOEEE 177,100 1.27 78.96 Draws
EEEOOO 177,100 1.27 78.96 Draws
EEEOOE 177,100 1.27 78.96 Draws
EEEOEO 230,230 1.65 60.74 Draws
EEEEOO 177,100 1.27 78.96 Draws
EEEOEE 177,100 1.27 78.96 Draws
EEEEOE 177,100 1.27 78.96 Draws
EEEEEO 177,100 1.27 78.96 Draws
EEEEEE 134,596 0.96 103.89 Draws
Totals 13,983,816 100.00

Best regards,
PAB

 

[Stone]

Thanks PAB, I take it that's with the numbers ordered numerically? I'm looking at the drawn order, that's still interesting though, if someone wanted to filter using odd/even it could be taken further than just the 2+4 or 3+3 sort of thing.

 

[PAB]

Hi Stone,

I think I might have confused the issue.
The previous post listed ALL of the 64 sequences of ODD & EVEN numbers and the total combinations from a 649 Lotto equating to the 13,983,816 combinations.
The order they are drawn is interesting solely per ball but not as the entirety of the 6 number combination on completion of draw.

Kind regards,
PAB

 

[blitzed]

hi guys, cool seein some action on the forum

Stone, I just flipped a silver dollar 6times, 4heads in a row...sometimes order has stretches of chaosand nothing will balance out as you'd like.

later
blitzed

 

[Stone]

hi guys, cool seein some action on the forum

Stone, I just flipped a silver dollar 6times, 4heads in a row...sometimes order has stretches of chaosand nothing will balance out as you'd like.

later
blitzed

What I was kind of getting at was something like this, say in a 6/49 lottery the first 5 balls drawn are even, in the machine are left 25 odds and 19 evens. Since each ball still in there has an equal chance of coming out there's a larger chance of the 6th ball being an odd than even. Maybe I'm wrong but I don't see that quite the same as the coin tosses which are always 50/50 each flip.

Stone

 

[blitzed]

What I was kind of getting at was something like this, say in a 6/49 lottery the first 5 balls drawn are even, in the machine are left 25 odds and 19 evens. Since each ball still in there has an equal chance of coming out there's a larger chance of the 6th ball being an odd than even. Maybe I'm wrong but I don't see that quite the same as the coin tosses which are always 50/50 each flip.

Stone

right, only if first ball is odd, then second ball draw is equal to a coin flip or red/black bet on roulette.

later,
blitzed

 

[Stone]

right, only if first ball is odd, then second ball draw is equal to a coin flip or red/black bet on roulette.

later,
blitzed

Yes, but unlike the coin or roulette, after the second ball is drawn it becomes unbalanced again with the direction depending on what the second ball was.

Stone

 

[PAB]

I was just thinking using coins as the example suggested by blitzed.

If you were to get 49 coins, turn 25 of them up HEADS representing the ODD numbers, and turn 24 of them up TAILS representing the EVEN numbers, then mix them up and stack them in a single pile and then start by taking off the top one and continue working your way down I think this would give you far more structured results than using the actual sequence of balls drawn from a Lotto machine.
I say this because once the coins have been sorted and stacked in a pile nothing can change the sequence of any of the coins from that point on because there is no outside influence, whereas with the Lotto balls because they are spinning in the drum in total chaos being knocked around by each other this leaves the next ball to be drawn totally random.

Anyway, following on from what Stone initially said about ODD’s and EVEN’s, listed below are the actual results from the UK Lotto up to and including draw 1,668.
The first figure is the ODD/EVEN distribution.
The second figure is the TOTAL combinations possible for each distribution from ALL 13,983,816 combinations.
The third figure is the EXPECTED times drawn to date.
The forth figure is the ACTUAL times drawn to date.
The fifth figure is the +/- difference drawn to date.

Distribution Combinations Expected Actual Diff
OOOOOO 177,100 21.12 19 -2.12
OOOOOE 177,100 21.12 26 +4.88
OOOOEO 230,230 27.46 39 +11.54
OOOEOO 230,230 27.46 31 +3.54
OOOOEE 177,100 21.12 25 +3.88
OOOEOE 230,230 27.46 32 +4.54
OOOEEO 230,230 27.46 28 +0.54
OOOEEE 177,100 21.12 21 -0.12
OOEOOO 230,230 27.46 35 +7.54
OOEOOE 230,230 27.46 23 -4.46
OOEOEO 296,010 35.31 30 -5.31
OOEEOO 230,230 27.46 24 -3.46
OOEOEE 230,230 27.46 30 +2.54
OOEEOE 230,230 27.46 23 -4.46
OOEEEO 230,230 27.46 23 -4.46
OOEEEE 177,100 21.12 20 -1.12
OEOOOO 230,230 27.46 32 +4.54
OEOOOE 230,230 27.46 28 +0.54
OEOOEO 296,010 35.31 39 +3.69
OEOEOO 296,010 35.31 34 -1.31
OEOOEE 230,230 27.46 22 -5.46
OEOEOE 296,010 35.31 28 -7.31
OEOEEO 296,010 35.31 30 -5.31
OEOEEE 230,230 27.46 29 +1.54
OEEOOO 230,230 27.46 23 -4.46
OEEOOE 230,230 27.46 20 -7.46
OEEOEO 296,010 35.31 32 -3.31
OEEEOO 230,230 27.46 18 -9.46
OEEOEE 230,230 27.46 32 +4.54
OEEEOE 230,230 27.46 28 +0.54
OEEEEO 230,230 27.46 25 -2.46
OEEEEE 177,100 21.12 20 -1.12
EOOOOO 177,100 21.12 16 -5.12
EOOOOE 177,100 21.12 15 -6.12
EOOOEO 230,230 27.46 26 -1.46
EOOEOO 230,230 27.46 27 -0.46
EOOOEE 177,100 21.12 23 +1.88
EOOEOE 230,230 27.46 31 +3.54
EOOEEO 230,230 27.46 25 -2.46
EOOEEE 177,100 21.12 31 +9.88
EOEOOE 230,230 27.46 26 -1.46
EOEOEO 296,010 35.31 36 +0.69
EOEEOO 230,230 27.46 25 -2.46
EOEOOO 230,230 27.46 24 -3.46
EOEOEE 230,230 27.46 29 +1.54
EOEEOE 230,230 27.46 29 +1.54
EOEEEO 230,230 27.46 23 -4.46
EOEEEE 177,100 21.12 16 -5.12
EEOOOO 177,100 21.12 25 +3.88
EEOOOE 177,100 21.12 21 -0.12
EEOOEO 230,230 27.46 27 -0.46
EEOEOO 230,230 27.46 27 -0.46
EEOOEE 177,100 21.12 24 +2.88
EEOEOE 230,230 27.46 29 +1.54
EEOEEO 230,230 27.46 27 -0.46
EEOEEE 177,100 21.12 25 +3.88
EEEOOO 177,100 21.12 28 +6.88
EEEOOE 177,100 21.12 32 +10.88
EEEOEO 230,230 27.46 30 +2.54
EEEEOO 177,100 21.12 23 +1.88
EEEOEE 177,100 21.12 24 +2.88
EEEEOE 177,100 21.12 19 -2.12
EEEEEO 177,100 21.12 21 -0.12
EEEEEE 134,596 16.05 15 -1.05
Totals 13,983,816 1,668.00 1,668.00 0.00

Regards,
PAB

 

[Stone]

I was just thinking using coins as the example suggested by blitzed.

If you were to get 49 coins, turn 25 of them up HEADS representing the ODD numbers, and turn 24 of them up TAILS representing the EVEN numbers, then mix them up and stack them in a single pile and then start by taking off the top one and continue working your way down I think this would give you far more structured results than using the actual sequence of balls drawn from a Lotto machine.
I say this because once the coins have been sorted and stacked in a pile nothing can change the sequence of any of the coins from that point on because there is no outside influence, whereas with the Lotto balls because they are spinning in the drum in total chaos being knocked around by each other this leaves the next ball to be drawn totally random.

That sounds closer but the randomness in the stack of coins comes from the process of picking each coin to put on the stack, so as you stack each coin, the odds of whether the next one put on the stack is head or tail vary according to what's already on the stack and what's left in the pool even though they've not yet been observed, it would be like only looking at the lottery balls in sequence after the draw is complete.

The list you posted above, is that from the draw order? For draw order, the number of combinations for each sequence is much higher than for numerical order with the total being nearly 1.5 billion.

Stone

 

[Stone]

PAB, your coin example is quite useful, I was just thinking of stacking the randomly selected coins one on top of the other as they were selected, if instead they were randomly selected and then inserted into the stack at random positions that would be quite different.

Stone

 

[PAB]

Stone, I am not sure of where you got ...

For draw order, the number of combinations for each sequence is much higher than for numerical order with the total being nearly 1.5 billion.

... from as the 64 sequences of ODD & EVEN numbers are ALL the sequences possible of drawing 6 numbers from 49 numbers.

The list previously posted was in NUMERICAL ORDER.
The list below is in DRAWN ORDER and is the actual results from the UK Lotto up to and including draw 1,668.

The first figure is the ODD/EVEN distribution.
The second figure is the TOTAL combinations possible for each distribution from ALL 13,983,816 combinations.
The third figure is the EXPECTED times drawn to date.
The forth figure is the ACTUAL times drawn to date.
The fifth figure is the +/- difference drawn to date.

Distribution Combinations Expected Actual Difference
OOOOOO 177,100 21.12 19 -2.12
OOOOOE 177,100 21.12 28 6.88
OOOOEO 230,230 27.46 35 7.54
OOOEOO 230,230 27.46 31 3.54
OOOOEE 177,100 21.12 28 6.88
OOOEOE 230,230 27.46 35 7.54
OOOEEO 230,230 27.46 16 -11.46
OOOEEE 177,100 21.12 23 1.88
OOEOOO 230,230 27.46 29 1.54
OOEOOE 230,230 27.46 30 2.54
OOEOEO 296,010 35.31 24 -11.31
OOEEOO 230,230 27.46 17 -10.46
OOEOEE 230,230 27.46 25 -2.46
OOEEOE 230,230 27.46 28 0.54
OOEEEO 230,230 27.46 31 3.54
OOEEEE 177,100 21.12 24 2.88
OEOOOO 230,230 27.46 24 -3.46
OEOOOE 230,230 27.46 20 -7.46
OEOOEO 296,010 35.31 30 -5.31
OEOEOO 296,010 35.31 36 0.69
OEOOEE 230,230 27.46 31 3.54
OEOEOE 296,010 35.31 23 -12.31
OEOEEO 296,010 35.31 26 -9.31
OEOEEE 230,230 27.46 23 -4.46
OEEOOO 230,230 27.46 30 2.54
OEEOOE 230,230 27.46 28 0.54
OEEOEO 296,010 35.31 21 -14.31
OEEEOO 230,230 27.46 28 0.54
OEEOEE 230,230 27.46 32 4.54
OEEEOE 230,230 27.46 22 -5.46
OEEEEO 230,230 27.46 29 1.54
OEEEEE 177,100 21.12 25 3.88
EOOOOO 177,100 21.12 32 10.88
EOOOOE 177,100 21.12 28 6.88
EOOOEO 230,230 27.46 24 -3.46
EOOEOO 230,230 27.46 35 7.54
EOOOEE 177,100 21.12 35 13.88
EOOEOE 230,230 27.46 23 -4.46
EOOEEO 230,230 27.46 23 -4.46
EOOEEE 177,100 21.12 33 11.88
EOEOOE 230,230 27.46 26 -1.46
EOEOEO 296,010 35.31 17 -18.31
EOEEOO 230,230 27.46 26 -1.46
EOEOOO 230,230 27.46 25 -2.46
EOEOEE 230,230 27.46 31 3.54
EOEEOE 230,230 27.46 25 -2.46
EOEEEO 230,230 27.46 27 -0.46
EOEEEE 177,100 21.12 23 1.88
EEOOOO 177,100 21.12 25 3.88
EEOOOE 177,100 21.12 31 9.88
EEOOEO 230,230 27.46 17 -10.46
EEOEOO 230,230 27.46 30 2.54
EEOOEE 177,100 21.12 32 10.88
EEOEOE 230,230 27.46 21 -6.46
EEOEEO 230,230 27.46 28 0.54
EEOEEE 177,100 21.12 18 -3.12
EEEOOO 177,100 21.12 24 2.88
EEEOOE 177,100 21.12 31 9.88
EEEOEO 230,230 27.46 32 4.54
EEEEOO 177,100 21.12 21 -0.12
EEEOEE 177,100 21.12 18 -3.12
EEEEOE 177,100 21.12 14 -7.12
EEEEEO 177,100 21.12 27 5.88
EEEEEE 134,596 16.05 15 -1.05
Totals > 13,983,816 1,668.00 1,668 0.00

All the best,
PAB

 

[Stone]

Hi PAB, there are 13,983,816 combinations of numbers in numerical order.

1 of those combinations is 1,2,3,4,5,6

but that could come out the machine in many different orders

6,5,4,3,2,1 for example which isn't included in the 13,983,816 combinations.

In total there are almost 1.5 billion different ways that 6 numbers could come out the machine.

Stone

 

[PAB]

Hi Stone, I can see where you are coming from now.

There are 13,983,816 COMBINATIONS.
There are 10,068,347,520 PERMUTATIONS.

Regardless though, EVERY permutation will be accommodated for in the 64 sequences previously described and posted, or am I missing something?

All the best,
PAB

 

[Stone]

Hi PAB, sorry, yes 10 billion, my program was trying to do the calc with 32 bits. Anyway, since it's the sequence of odd and even as they come out of the machine I'm looking at, the number of combinations for each odd/even sequence should really be the number of permutations if it's to be compared with the frequency of the unsorted even/odd sequences.

Stone

 

[Stone]

For example:

6,5,4,3,2,1 = EOEOEO

1,3,5,2,4,6 = OOOEEE

1,6,4,3,5,2 = OEEOOE

etc.

But when sorted,all become

1,2,3,4,5,6 = OEOEOE

But I'm looking at how the random numbers come out the machine.

Stone

 

[PAB]

Hi Stone,

I am still unsure of what you are actually trying to calculate from the ODD/EVEN unsorted drawn results.
If you are talking about the ACTUAL ball number ( 6 or 12 or 34 etc ) being ODD/EVEN instead of whether the ball itself is actually ODD or EVEN as they are drawn ( PERMUTATIONS ) then yes, but the results you get from this would be so negligible because of minuscule of data available in comparison to the huge total of the PERMUTATIONS sequences, this would only be one for each of the draws so far, as it possibly would for several years to come.
If you are talking about ODD & EVEN numbers regardless of the ball number then my previous post stands true.
For example, if we use your combinations in the above post ...

6,5,4,3,2,1 = EOEOEO ( Sequence number 42 in the list below )
1,3,5,2,4,6 = OOOEEE ( Sequence number 08 in the list below )
1,6,4,3,5,2 = OEEOOE ( Sequence number 26 in the list below )

... and regardless of ANY combination drawn whether it be a COMBINATION or a PERMUTATION will be found in the list below.
I am sorry but I am not seeing what you are actually trying to calculate.

Sequence Distribution
1 OOOOOO
2 OOOOOE
3 OOOOEO
4 OOOEOO
5 OOOOEE
6 OOOEOE
7 OOOEEO
8 OOOEEE
9 OOEOOO
10 OOEOOE
11 OOEOEO
12 OOEEOO
13 OOEOEE
14 OOEEOE
15 OOEEEO
16 OOEEEE
17 OEOOOO
18 OEOOOE
19 OEOOEO
20 OEOEOO
21 OEOOEE
22 OEOEOE
23 OEOEEO
24 OEOEEE
25 OEEOOO
26 OEEOOE
27 OEEOEO
28 OEEEOO
29 OEEOEE
30 OEEEOE
31 OEEEEO
32 OEEEEE
33 EOOOOO
34 EOOOOE
35 EOOOEO
36 EOOEOO
37 EOOOEE
38 EOOEOE
39 EOOEEO
40 EOOEEE
41 EOEOOE
42 EOEOEO
43 EOEEOO
44 EOEOOO
45 EOEOEE
46 EOEEOE
47 EOEEEO
48 EOEEEE
49 EEOOOO
50 EEOOOE
51 EEOOEO
52 EEOEOO
53 EEOOEE
54 EEOEOE
55 EEOEEO
56 EEOEEE
57 EEEOOO
58 EEEOOE
59 EEEOEO
60 EEEEOO
61 EEEOEE
62 EEEEOE
63 EEEEEO
64 EEEEEE

All the best,
PAB