Actual draws with a low probability of occurring

[GillesD]

The winning combination for draw #968 of the Quebec 49 (Jan. 6, 2007) was 05-15-25-35-37-45. The interesting fact is that it is the first time, to my knowledge, in either Canadian Lotto 6/49, Quebec 49 or UK 6/49, the same last digit (here 5) is repeated 5 times. This has a very low probability of happening, in this case 0.0028%.

Does anybody know of an actual winning combination in any lotery that has a very low probability of happening.

For Canadian Lotto 6/49, I know of three cases:

- for draw #1748, with numbers 38-43-44-45-46-47, a 5-1 distribution of consecutive numbers has a 0.0135% probability of happening;

- for draw #2322, with numbers 21-22-23-24-48-49, a 4-2 distribution of consecutive numbers also has a 0.0135% probability of happening;

- for draw #670, with numbers 22-27-32-37-42-47, with all numbers with the same difference between 2 numbers (here 5) has a 0.0015% probability of happening.

 

[johnph77]

I had worked on something of that nature at least a couple of years ago where all numbers drawn ended in the same digit - all odds change when the last digit is 0 (zero). I think I may have also worked something up on the same subject for Powerball and/or MegaMilions. I have no idea what I did with those files - they're around here somwhere....

 

[mrfirkin]

Hi guys,

I was thinking about the chances of the numbers 1,2,3,4,5,6 being drawn and thought that was almost guaranteed never to happen.

Then I thought they surely have the same chance as any sequence being drawn?

How do you arrive at the different probabilities you mention above, when all no's have an equal chance of being drawn?

Can't get my non mathematical pea brain around all this.

Cheers,

Paul : )

 

[GillesD]

Probability

Calculating probabilities is a little easier using the COMBIN function in Excel. This function gives the number of combinations (in any order) possible with Y numbers taken out of X numbers and the syntax is COMBIN(X,Y). I will give you 2 examples:

- The total number of combinations for a 6/49 lottery is then COMBIN(49,6) or 13,983,816 and the chance of getting 6 specific numbers (such as 1-2-3-4-5-6) is 1/13,983,816 or 0.00000715%. And this is the same for any single combination.

- If you want to calculate the probabilty of getting 2 odd numbers and 4 even numbers in a draw, you calculate the number of combinations with 2 odd numbers out of 25, then multiply this by the number of combinations with 4 even numbers out of 24 and divide this by the total number of combinations; the formula is COMBIN(25,2)*COMBIN(24,4)/COMBIN(49,6) or 300*10,626/13,983,816 or 22.796%.

I have the probabilities for quite a few possibilities (odd and even numbers, sum of numbers, low and high numbers, numbers in the previous draw, consecutive numbers, last digits, etc.). I compare these theorical values to actual values for results for Canadian Lotto 6/49. Up to now, with 2396 draws, out of 100 probabilities I calculate, 73 within ±0.5% of the theorical value, 18 within ±1.0% and only 9 over ±1.0%.

Enjoy yourself

 

[mrfirkin]

Thanks GillesD,

I'm happy to leave all that stuff to you boffin types.

Thanks for the examples though.

Cheers,

Paul.

 

[blitzed]

Hi guys,

I was thinking about the chances of the numbers 1,2,3,4,5,6 being drawn and thought that was almost guaranteed never to happen.

Paul : )

Hi mrfirkin, I've seen a draw close to that in a 5/39 game, the CA Fantasy 5, on 10DEC the draw was 1 2 3 4 39 heh!

seeya,
blitzed

 

[blitzed]

Calculating probabilities is a little easier using the COMBIN function in Excel. This function gives the number of combinations (in any order) possible with Y numbers taken out of X numbers and the syntax is COMBIN(X,Y). I will give you 2 examples:

- The total number of combinations for a 6/49 lottery is then COMBIN(49,6) or 13,983,816 and the chance of getting 6 specific numbers (such as 1-2-3-4-5-6) is 1/13,983,816 or 0.00000715%. And this is the same for any single combination.

- If you want to calculate the probabilty of getting 2 odd numbers and 4 even numbers in a draw, you calculate the number of combinations with 2 odd numbers out of 25, then multiply this by the number of combinations with 4 even numbers out of 24 and divide this by the total number of combinations; the formula is COMBIN(25,2)*COMBIN(24,4)/COMBIN(49,6) or 300*10,626/13,983,816 or 22.796%.

I have the probabilities for quite a few possibilities (odd and even numbers, sum of numbers, low and high numbers, numbers in the previous draw, consecutive numbers, last digits, etc.). I compare these theorical values to actual values for results for Canadian Lotto 6/49. Up to now, with 2396 draws, out of 100 probabilities I calculate, 73 within ±0.5% of the theorical value, 18 within ±1.0% and only 9 over ±1.0%.

Enjoy yourself

cool, I've always been a probability hound too

later,
blitzed

 

[johnph77]

Most of the lottery formulas are listed on my web page, along with payout percentages and odds.

 

[heminen]

hello

result of French loto this wednesday
on the 1er draw
31 32 36 37 38 49

total of draw from beginning 4996
it's a very anormaél draw because 5 numbers in the same decade


5 times this serie 3 consequtives +2"""""""""""""+1 > 0.6% of the total 4496 draws
0 times 6 consequtives
0 times 5 """""""""""""""" + 1
0 times 4 """""""""""""""" + 2 >> but 9 times 4 consequtives + 1 +1 >>>
1 times 3 """"""""""""""""+ """"""""""""""3
27 times 3 """""""""""""""+ 2"""""""""""""+1
3 times only on 2 """"""""""""2"""""""""" 2"""""""""""

But not only on the same decade, if you want to play few combinaisons (ex choose only 5 number in a decade) and
if you choose this strategie, you must be patient!!

20 years for this result of wednesday

cdt

 

[GillesD]

5 numbers in a decade

heminen

I am surprised that 5 numbers in a decade has not come out more often in the French lotto. My probability of this occurring is 0.317%, so it should have happened about 15-16 times with nearly 5000 draws. But you are right in saying that a 3-2-1 split in consecutive numbers has a probability of 0.57%.

By comparision, in the Canadian Lotto 6/46 with 2397 draws, 5 numbers in one decade happened 7 times (draws #191, 644, 932, 1593, 1748, 1765 and 2237) compared to 8 times in theory.

If we talk about consecutives, a 3-2-1 split happened 20 times (0.83%), a 4-1-1 split 6 times (0.25%) and a 4-2 or 5-1 split have both occurred once (0.04%).

 

[heminen]

Hello GillesD

Sorry for my calculations

i have make a new look on French draws for 5 numbers in the same decade

you have:
10/01/2007 : 31 32 36 37 38 49
25/04/2001 : 21 41 42 43 48 49
10/12/1996 : 08 10 11 14 15 16

there is also an error, the beginning of loto was in june 1976
so 30 years .... to see 3 times this event.

nb: at the beginnig, only on draw on wednesday an saturday, after september 1990 you have 2 draws on wednesday an saturday


and very interisting thing....
so you can see that this evement car appear one time on 5/6 years if you have 4 draws in a week! and it's was on thre differents decades..

may i stand 5 years before playing a combinaison with 5 numbers on 0 9 decade or 40 49 decade if and other decade must draw??
>>> how many combinaisons to play??
remenber, you have also 27 times where the numbers are draws with 3,2, 1 (Differents décades)!
>>> how many combinaisons to play ??
cdt

 

[GillesD]

5 numbers in a decade for the French loto

heminen

I am always surprised when theory and actual results differ by a wide margin, so I was curious about your comment regarding only 3 combinations with 5 numbers in a decade in nearly 5000 draws for the French Loto. It should have been more like 14. So I researched the matter and this is what I found:

Draw # ---- Date ---------- Numbers
0103 --- 1978-05-10 --- 02-04-05-08-09-29
0400 --- 1984-01-18 --- 01-03-06-07-08-30
0431 --- 1984-05-30 --- 21-40-41-45-46-49
0695 --- 1986-12-10 --- 08-10-11-14-15-16
1496 --- 1992-08-26 --- 01-03-06-08-09-18
2810 --- 1998-12-12 --- 01-02-04-06-07-28
3303 --- 2001-04-25 --- 21-41-42-43-48-49
3515 --- 2002-05-01 --- 12-14-16-17-18-38
3829 --- 2003-11-01 --- 20-23-26-27-28-38
4495 --- 2007-01-10 --- 31-32-36-37-38-49

So, I found 10 draws with 5 numbers in a decade, which is nearer the 14 expected. With 4496 draws, this amounts to 0.222% compared to a theorical value of 0.317%. And all decades are actually covered with 4 combinations in the 1-9 decade; this is also even more surprising since it is the only decade with only 9 numbers in it.

The 3 draws you mentioned in your post are also in my list (#695, 3303 and 4495) but I find rather amusing that, speaking of decades, for draw #695, the date you mention and mine are exactly one decade apart in years (typing error for one of us).

 

[heminen]

Hello GillesD

I am ok with your results, you have 10 draws with 5 numbers in the same décade.
you have also, in these results 3 draws with 3 consecutives et 2 consecutives (Always in the same decade)
in your post, the dates are exact (i have make an error, it's 1986 not 1996 for one ot the 3)

for a resume >> NUMBERS IN DECADE
0 draws for 6 numbers in a decade
10 draws for 5 numbers in a decade + 1 in other decade
61 draws for 4 numbers + 2 (two décades)
189 draws for 4 numbers in a decade and 1 in 2 decades
34 draws for 3 numbers in 2 decades
903 draws for 3 nbers in a decade + 2 in a other decade + 1 other
676 draws for 3 nbers in a decade and 3 time 1 in a other
290 draws with 2 numbers in 3 decades
1637 draws with 2 - 2 - 1 - 1 (nbr/decade)
698 draws with 2 - 1 - 1 - 1 - 1 (nbr/decade)

for a resume >> NUMBERS CONSECUTIVES
0 draw for 6, 5 - 1, 4 -2,
9 draws for 4 -1 - 1
1 draw for 3 - 3
28 draws for 3 - 2 - 1
175 draws for 3 - 1 - 1 - 1
3 draws for 2 - 2 - 2
246 draws for 2 - 2 - 1 - 1
1763 draws for 2 - 1 - 1 - 1 - 1
2273 draws for 1 - 1 - 1 - 1 - 1 - 1

After that with only one of this parameter you have too much combinaisons to play
you have to combine with several filter (odd, even, sum, with,dozen, last draw, last digit, sum of digit, horizontal, vertical,diagonal,..)

>> it's give few combinaisons to play, but risk to loose....
il's always the problem... few and the good combinaison to play !!!!!

So always the factor "luck"

for exemple:
if you want to play 5 numbers in a decade + 3 - 2 - 1 consecutives, it give 5706 combinaisons to play


good luck