Hi Everyone,
I have Done Some Work and Analysis on Palindromic Numbers for the Canadian 649 Lotto.
Palindromic Numbers are Numbers that are the Same when Written Forwards OR Backwards, they are in Effect what I Call Mirrored Numbers.
In a 649 Lotto there are 13 Palindromic Numbers, they are :-
01,02,03,04,05,06,07,08,09,11,22,33 & 44.
These 13 Numbers Produce 1,716 Combinations.
The Following Table Lists the Number of Palindromic Numbers, the Total Combinations Available from ALL 13,983,816 Combinations, the Percentage Available from ALL 13,983,816 Combinations & the Expected to be Drawn 1 in Every Draws Based on the 13,983,816 Combinations.
0 Palindromic 1,947,792 Combs 13.93% Expected 1 in Every 7.18 Draws
1 Palindromic 4,900,896 Combs 35.05% Expected 1 in Every 2.85 Draws
2 Palindromic 4,594,590 Combs 32.86% Expected 1 in Every 3.04 Draws
3 Palindromic 2,042,040 Combs 14.60% Expected 1 in Every 6.85 Draws
4 Palindromic 450,450 Combs 3.22% Expected 1 in Every 31.04 Draws
5 Palindromic 45,045 Combs 0.32% Expected 1 in Every 310.44 Draws
5 + Palindromic 1,287 Combs 0.01% Expected 1 in Every 10,865.44 Draws
6 Palindromic 1,716 Combs 0.01% Expected 1 in Every 8,149.08 Draws
Totals = 13,983,816 Combinations 100.00% Percent
I Ran ALL 1,716 Palindromic Combinations Against the Canadian 649 Lotto as at Draw 2,219 ( Wednesday the 27th of April 2005 ) and came up with the Following Results Table.
Matched 0 Palindromic Numbers = 1,703,997
Matched 1 Palindromic Number = 1,553,018
Matched 2 Palindromic Numbers = 481,259
Matched 3 Palindromic Numbers = 65,324
Matched 4 Palindromic Numbers = 4,099
Matched 5 Palindromic Numbers = 104
Matched 5 + the Bonus Palindromic Numbers = 2
Matched 6 Palindromic Numbers = 1
Total Combinations Checked = 3,807,804
As you can See, it ACTUALLY Hit 104 Matched 5 Numbers, 2 Matched 5 + the Bonus Number ( Draws 73 & 1,176 ) & 1 JACKPOT ( Draw 575 ).
The Table Below Lists the Palindromic Numbers Actually Drawn as at Draw 2,219 ( Wednesday the 27th of April 2005 ) in the Canadian 649 Lotto.
Matched 0 Palindromic Numbers = 330
Matched 1 Palindromic Number = 803
Matched 2 Palindromic Numbers = 709
Matched 3 Palindromic Numbers = 294
Matched 4 Palindromic Numbers = 74
Matched 5 Palindromic Numbers = 6
Matched 5 + the Bonus Palindromic Numbers = 2
Matched 6 Palindromic Numbers = 1
Total Draws Checked = 2,219
The Following Table Lists the Number of Palindromic Numbers Drawn as at Draw 2,219 ( Wednesday the 27th of April 2005 ) in the Canadian 649 Lotto, the Expected Times Drawn, the Actual Times Drawn & the Difference.
0 Palindromic Expected = 309.08 Actual = 330 Difference = 20.92
1 Palindromic Expected = 777.69 Actual = 803 Difference = 25.31
2 Palindromic Expected = 729.09 Actual = 709 Difference = -20.09
3 Palindromic Expected = 324.04 Actual = 294 Difference = -30.04
4 Palindromic Expected = 71.48 Actual = 74 Difference = 2.52
5 Palindromic Expected = 7.15 Actual = 6 Difference = -1.15
5 + the Bonus Palindromic Expected = 0.20 Actual = 2 Difference = 1.80
6 Palindromic Expected = 0.27 Actual = 1 Difference = 0.73
Here are Two Links to MathWorld if Anyone is Interested Any Further :-
http://mathworld.wolfram.com/PalindromicNumber.html
http://www.research.att.com/cgi-bin/access.cgi/as/njas/sequences/eisA.cgi?Anum=A002113
Just thought it was an Interesting Exercise to do.
All the Best.
PAB
I have Done Some Work and Analysis on Palindromic Numbers for the Canadian 649 Lotto.
Palindromic Numbers are Numbers that are the Same when Written Forwards OR Backwards, they are in Effect what I Call Mirrored Numbers.
In a 649 Lotto there are 13 Palindromic Numbers, they are :-
01,02,03,04,05,06,07,08,09,11,22,33 & 44.
These 13 Numbers Produce 1,716 Combinations.
The Following Table Lists the Number of Palindromic Numbers, the Total Combinations Available from ALL 13,983,816 Combinations, the Percentage Available from ALL 13,983,816 Combinations & the Expected to be Drawn 1 in Every Draws Based on the 13,983,816 Combinations.
0 Palindromic 1,947,792 Combs 13.93% Expected 1 in Every 7.18 Draws
1 Palindromic 4,900,896 Combs 35.05% Expected 1 in Every 2.85 Draws
2 Palindromic 4,594,590 Combs 32.86% Expected 1 in Every 3.04 Draws
3 Palindromic 2,042,040 Combs 14.60% Expected 1 in Every 6.85 Draws
4 Palindromic 450,450 Combs 3.22% Expected 1 in Every 31.04 Draws
5 Palindromic 45,045 Combs 0.32% Expected 1 in Every 310.44 Draws
5 + Palindromic 1,287 Combs 0.01% Expected 1 in Every 10,865.44 Draws
6 Palindromic 1,716 Combs 0.01% Expected 1 in Every 8,149.08 Draws
Totals = 13,983,816 Combinations 100.00% Percent
I Ran ALL 1,716 Palindromic Combinations Against the Canadian 649 Lotto as at Draw 2,219 ( Wednesday the 27th of April 2005 ) and came up with the Following Results Table.
Matched 0 Palindromic Numbers = 1,703,997
Matched 1 Palindromic Number = 1,553,018
Matched 2 Palindromic Numbers = 481,259
Matched 3 Palindromic Numbers = 65,324
Matched 4 Palindromic Numbers = 4,099
Matched 5 Palindromic Numbers = 104
Matched 5 + the Bonus Palindromic Numbers = 2
Matched 6 Palindromic Numbers = 1
Total Combinations Checked = 3,807,804
As you can See, it ACTUALLY Hit 104 Matched 5 Numbers, 2 Matched 5 + the Bonus Number ( Draws 73 & 1,176 ) & 1 JACKPOT ( Draw 575 ).
The Table Below Lists the Palindromic Numbers Actually Drawn as at Draw 2,219 ( Wednesday the 27th of April 2005 ) in the Canadian 649 Lotto.
Matched 0 Palindromic Numbers = 330
Matched 1 Palindromic Number = 803
Matched 2 Palindromic Numbers = 709
Matched 3 Palindromic Numbers = 294
Matched 4 Palindromic Numbers = 74
Matched 5 Palindromic Numbers = 6
Matched 5 + the Bonus Palindromic Numbers = 2
Matched 6 Palindromic Numbers = 1
Total Draws Checked = 2,219
The Following Table Lists the Number of Palindromic Numbers Drawn as at Draw 2,219 ( Wednesday the 27th of April 2005 ) in the Canadian 649 Lotto, the Expected Times Drawn, the Actual Times Drawn & the Difference.
0 Palindromic Expected = 309.08 Actual = 330 Difference = 20.92
1 Palindromic Expected = 777.69 Actual = 803 Difference = 25.31
2 Palindromic Expected = 729.09 Actual = 709 Difference = -20.09
3 Palindromic Expected = 324.04 Actual = 294 Difference = -30.04
4 Palindromic Expected = 71.48 Actual = 74 Difference = 2.52
5 Palindromic Expected = 7.15 Actual = 6 Difference = -1.15
5 + the Bonus Palindromic Expected = 0.20 Actual = 2 Difference = 1.80
6 Palindromic Expected = 0.27 Actual = 1 Difference = 0.73
Here are Two Links to MathWorld if Anyone is Interested Any Further :-
http://mathworld.wolfram.com/PalindromicNumber.html
http://www.research.att.com/cgi-bin/access.cgi/as/njas/sequences/eisA.cgi?Anum=A002113
Just thought it was an Interesting Exercise to do.
All the Best.
PAB
