How to reduce betting blokes that can guarantee max 1 incorrect

Kishan

Well-known Member
Joined
Mar 15, 2011
Messages
1,648
Office Version
  1. 2010
Platform
  1. Windows
Using Excel 2000</SPAN></SPAN>
Hi,
</SPAN></SPAN>

Here I have a question how to reduce betting blokes that can guarantee max 1 incorrect, what I mean this, for example "Euromillions" playing 8 numbers direct we are playing 56 lines it cost 140€ "Formula=COMBIN(8,5)" if out of 8 numbers 5 numbers are correct we get the 1st price guarantee 100%.
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But instead 8 numbers direct if played in reduction we play only 5 lines it cost 12.50€ but it guarantee only 4 numbers can be correct if numbers drawn any 5 out of played 8. So far 1 number less.
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My question is about to play football reduction...it is difficult how do I explain it but here is my attempt...
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Say for in example1 there are 2 teams the can have the end result in a 9 different ways as shown in the cells C6:D14...I can bet all 9 but as it is a money question I want to play less combinations but ensuring 1 must be correct out of any 9 results if I bet 3 lines as shown in the cells H6:I8 there is minimum 1 correct and 1 wrong.
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Example1...
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Book1
ABCDEFGHIJK
1
2
3
4
5Combi nTeam1Team2Combi nTeam1Team2
6111111
721X2XX
8312321
94X1
105XX
116X2
12721
1382X
14922
15
16
17
18
Sheet2


Say for in example2 there are 3 teams the can have the end result in a 27 different ways as shown in the cells C6:E32...I can bet all 27 but as it is a money question I want to play less combinations but ensuring 1 must be correct out of any 27 results if I bet 6 lines as shown in the cells H6:J11 there is minimum 2 correct and one wrong.
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Example2...

Book1
ABCDEFGHIJKL
1
2
3
4
5Combi nTeam1Team2Team3Combi nTeam1Team2Team3
611111111
7211X2XXX
831123222
941X14X11
1051XX5211
1161X261XX
127121
13812X
149122
1510X11
1611X1X
1712X12
1813XX1
1914XXX
2015XX2
2116X21
2217X2X
2318X22
2419211
252021X
2621212
27222X1
28232XX
29242X2
3025221
312622X
3227222
33
34
35
36
Sheet3
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The above result I have come up checking one by one it has took 2, 3 days to ensure.
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And I guess they are right but not sure 100%
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As the team increases lines increases...now I want to work out with 4 teams there would be 81 lines as per example3, is there any macro or VBA can extract only those lines out of 81 which has 3 correct and 1 wrong... manually I think it is not possible for me.
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Example3...

Book1
ABCDEFGHIJKLMNO
1
2
3
4
5Combi nTeam1Team2Team3Team4Combi nTeam1Team2Team3Team4
6111111
72111X?
831112?
9411X1?
10511XX?
11611X2?
1271121?
138112X?
1491122?
15101X11?
16111X1X?
17121X12?
18131XX1?
19141XXX?
20151XX2
21161X21
22171X2X
23181X22
24191211
2520121X
26211212
272212X1
282312XX
292412X2
30251221
3126122X
32271222
3328X111
3429X11X
3530X112
3631X1X1
3732X1XX
3833X1X2
3934X121
4035X12X
4136X122
4237XX11
4338XX1X
4439XX12
4540XXX1
4641XXXX
4742XXX2
4843XX21
4944XX2X
5045XX22
5146X211
5247X21X
5348X212
5449X2X1
5550X2XX
5651X2X2
5752X221
5853X22X
5954X222
60552111
6156211X
62572112
635821X1
645921XX
656021X2
66612121
6762212X
68632122
69642X11
70652X1X
71662X12
72672XX1
73682XXX
74692XX2
75702X21
76712X2X
77722X22
78732211
7974221X
80752212
817622X1
827722XX
837822X2
84792221
8580222X
86812222
87
88
89
90
Sheet4
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Thank you in advance
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Regards,
</SPAN></SPAN>
Kishan
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I can't prove this is a minimal set, but I strongly believe it is:


Book1
ABCDEFGHIJKLMN
1Values12X
2Teams4
3
4
5CombinationTeam 1Team 2Team 3Team 4ClosestCombinationTeam 1Team 2Team 3Team 4
611111111111
7211121141222
83111X1271XXX
941121133212X
1051122144322X1
116112X33472X12
12711X1162X1X2
13811X26266X21X
14911XX2776XX21
151012111
1611121214
1712121X66
1813122114
1914122214
2015122X14
211612X143
221712X214
231812XX27
24191X111
25201X1247
26211X1X27
27221X2176
28231X2214
29241X2X27
30251XX127
31261XX227
32271XXX27
332821111
3429211247
3530211X33
3631212133
3732212233
3833212X33
393421X143
403521X262
413621XX33
4237221143
4338221247
4439221X66
4540222143
4641222214
4742222X33
484322X143
494422X243
504522XX43
51462X1147
52472X1247
53482X1X47
54492X2176
55502X2247
56512X2X33
57522XX143
58532XX247
59542XXX27
6055X1111
6156X11262
6257X11X66
6358X12176
6459X12262
6560X12X33
6661X1X162
6762X1X262
6863X1XX62
6964X21166
7065X21266
7166X21X66
7267X22176
7368X22214
7469X22X66
7570X2X143
7671X2X262
7772X2XX66
7873XX1176
7974XX1247
8075XX1X66
8176XX2176
8277XX2276
8378XX2X76
8479XXX176
8580XXX262
8681XXXX27
Sheet1


I checked every combination up to 8 and did not find a match. I started running tests on combinations up to 11, but with some starting combinations included. I did not find a good set. I went back to a variation of the "Greedy" method. I went through all the combinations, and found the combination that matched the most other combinations. I flagged that one, and removed all the other combinations from consideration. I repeated the process on the remaining combinations until everything was accounted for. For 1 team and 2 teams, this algorithm came up with the same sets. For 3 teams, it came up with a set of 15! So it was with a lot of pessimism I tried on 4 teams, and with a lot of surprise when I got this list.

So I hope this helps you out! I won't be trying to lower the count, or working on 5 teams or more. (Although you can create a valid set for 5 teams by taking this list and adding 1,2,X to each combination for the Team 5 value. This gives you a set of 27.)

Good luck!
 
Upvote 0

Excel Facts

Can a formula spear through sheets?
Use =SUM(January:December!E7) to sum E7 on all of the sheets from January through December
I can't prove this is a minimal set, but I strongly believe it is:

I checked every combination up to 8 and did not find a match. I started running tests on combinations up to 11, but with some starting combinations included. I did not find a good set. I went back to a variation of the "Greedy" method. I went through all the combinations, and found the combination that matched the most other combinations. I flagged that one, and removed all the other combinations from consideration. I repeated the process on the remaining combinations until everything was accounted for. For 1 team and 2 teams, this algorithm came up with the same sets. For 3 teams, it came up with a set of 15! So it was with a lot of pessimism I tried on 4 teams, and with a lot of surprise when I got this list.

So I hope this helps you out! I won't be trying to lower the count, or working on 5 teams or more. (Although you can create a valid set for 5 teams by taking this list and adding 1,2,X to each combination for the Team 5 value. This gives you a set of 27.)

Good luck!
Hi Eric, I check all 9 you have find out of 81sets, 9 covers 4 correct and rest 72 has got 3 covered that is what I wanted thank you very much for your kind help </SPAN></SPAN>

That all you have checked one by one manually till you did find these 9 unique with 3 and 4 matches against 81 sets but is there any VBA or formula way to which could make this search easier. Because with 5 team would be 243 direct 3*3*3*3*3=243 to find as you say may could be 27 will take time to finishes may be till end of this year.
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Good Luck to you as well
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Kind Regards,
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Kishan :)
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Upvote 0
Hi,</SPAN></SPAN>

Thinking a lot working heard but do not find the way in which Eric has find in the post#11 precise only 9 sets which cover "minimum 3 within each 4 teams with possible 81 sets" may some one can make a macro to find them automatically...
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Kind Regards,
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Kishan :banghead:
</SPAN></SPAN>
 
Last edited:
Upvote 0
1) I used a variety of macros to create that set. However, there's no point in posting them. The "exhaustive" one would take far too long. I already tried the "greedy" one and it returned a set of around 36 combinations, more than the 27-member set I proposed. It was just kind of a fluke that it worked on the 4-Team problem.

2) I mentioned how to create the result for the 5-Team problem starting with the 4-Team solution. Here's a more detailed explanation. Start by writing each of the 4-Team combinations 3 times. Add a column for Team 5. For each of these new lines, put 1, 2, and X in the Team 5 position, like this:

Excel 2012
ABCDEFGHIJKL

<colgroup><col style="width: 25pxpx" https:="" www.mrexcel.com="" forum="" usertag.php?do="list&action=hash&hash=DAE7F5"" target="_blank"></colgroup><colgroup><col><col><col><col><col><col><col><col><col><col><col><col></colgroup><thead>
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[TD="align: center"]Combination[/TD]
[TD="align: center"]Team 1[/TD]
[TD="align: center"]Team 2[/TD]
[TD="align: center"]Team 3[/TD]
[TD="align: center"]Team 4[/TD]
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[TD="align: center"]Team 1[/TD]
[TD="align: center"]Team 2[/TD]
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[TD="align: center"]11[/TD]
[TD="align: center"]27[/TD]
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[TD="align: center"]14[/TD]
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[TD="align: center"]15[/TD]
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[TD="align: center"]17[/TD]
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</tbody>
Sheet9



This example shows how to do the first 4 combinations, finish with the other 5. Now think about why this set works. We know that for any possible 5-Team combination, for the first 4 teams every possible combination is covered by 3 or 4 matches. Now if you create 3 versions of each combination, with 1, 2, and X, we know that one of those will match whatever Team 5 has. This means that out of the 3-combination group, one of them will match Team 5's result, therefore, out of the 3-combination set, one of them will have a 4 or 5 team match.

I'm pretty sure that this is not a minimal set, but it's still better than the 36 combination set my macro came up with. You can easily extend this process to 6- 7- 8- teams or more, but none of them will be optimal sets.

3) I'm pretty sure there must be a way to construct optimal sets reliably, but I just don't know the method. By looking at the 4 answers we've found so far, we can see some patterns. Every set contains a combination that is full row of 1s. Every set contains a combination that starts with 1, and the rest is 2s. Almost every set has a combination that is a full row of Xs. By looking at these patterns, someone might be able to figure out a construction method. I don't have the time to devote to it, or to research if someone's already done it. And there's even a larger question. Even if you could come up with such a set, would it help you with sports betting? I suspect not, since the people making the odds have devoted much more time to calculating the odds than I have here. There are some famous examples where the oddsmakers goofed, and someone took advantage of the mathematical errors, so it is possible, but it would take a lot more analysis than what you have here.

Good luck.
 
Last edited:
Upvote 0
1) I used a variety of macros to create that set. However, there's no point in posting them. The "exhaustive" one would take far too long. I already tried the "greedy" one and it returned a set of around 36 combinations, more than the 27-member set I proposed. It was just kind of a fluke that it worked on the 4-Team problem.

2) I mentioned how to create the result for the 5-Team problem starting with the 4-Team solution. Here's a more detailed explanation. Start by writing each of the 4-Team combinations 3 times. Add a column for Team 5. For each of these new lines, put 1, 2, and X in the Team 5 position, like this:

Excel 2012
A
B
C
D
E
F
G
H
I
J
K
L

<TBODY>
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</TBODY>
Sheet9



This example shows how to do the first 4 combinations, finish with the other 5. Now think about why this set works. We know that for any possible 5-Team combination, for the first 4 teams every possible combination is covered by 3 or 4 matches. Now if you create 3 versions of each combination, with 1, 2, and X, we know that one of those will match whatever Team 5 has. This means that out of the 3-combination group, one of them will match Team 5's result, therefore, out of the 3-combination set, one of them will have a 4 or 5 team match.

I'm pretty sure that this is not a minimal set, but it's still better than the 36 combination set my macro came up with. You can easily extend this process to 6- 7- 8- teams or more, but none of them will be optimal sets.

3) I'm pretty sure there must be a way to construct optimal sets reliably, but I just don't know the method. By looking at the 4 answers we've found so far, we can see some patterns. Every set contains a combination that is full row of 1s. Every set contains a combination that starts with 1, and the rest is 2s. Almost every set has a combination that is a full row of Xs. By looking at these patterns, someone might be able to figure out a construction method. I don't have the time to devote to it, or to research if someone's already done it. And there's even a larger question. Even if you could come up with such a set, would it help you with sports betting? I suspect not, since the people making the odds have devoted much more time to calculating the odds than I have here. There are some famous examples where the oddsmakers goofed, and someone took advantage of the mathematical errors, so it is possible, but it would take a lot more analysis than what you have here.

Good luck.
Hi Eric, thank you for your time and support it has been greater help of you now it is more clearer to understand for me you have made is quite easer. </SPAN></SPAN>

Have a nice weekend and Good Luck.
</SPAN></SPAN>

Kind Regards,
</SPAN></SPAN>
Kishan :)
</SPAN></SPAN>
 
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