Probability of tapping success

The probability of hit with the Lotto can be determined over the hypergeometric distribution:

H 49,6,6H 45,6,6nAmount of (n)Probability (n) in %nAmount of (n) Probability (n) in %06.096.454 43,59603.262.623 40,05615.775.588 41,30213.454.542 42,41321.851.150 13,23821.233.765 15,1473246.820  1,7653182.780  2,244413.545  0,097411.115  0,1365258  0,0025234  0,00361" " 0,000007161" " 0,00001213.983.8161008.145.060100Expectancy value0,735Expectancy value0,800Dispersion0,578Dispersion0,615Who sums the numbers, it sees from the table that the chance for one is "rivets "(0, 1 or 2 correct of 6 numbers) with the Austrian Lotto with 97,6 %, with the German Lotto with 98,1 %.

The expectancy value gives by the way the average number of numbers turned out correctly with a 6er touches lightly.

Who e.g. with 6 from 49 the same tap a hundred times along, can count on approximately 73 numbers turned out correctly altogether. (600 would be maximally possible, with a hundred times 6 correct.)

With the Austrian Lotto one receives more frequently 1 correct one than 0 correct ones, like above table shows (6 from 45, H 45.6.6). This applies also to the Litaui Lotto (6 from 30), with that even 2 correct ones still more frequently appears than 0 correct ones.

The profit possibilities "with auxiliary number "with the Lotto in Germany represent in each case special cases with 5, 4 and/or 3 correct ones: from the 43 numbers remained an auxiliary number is drawn.

The following probabilities result:

nAmount of (n)Probability (n) in %Explanation5 + Z6" 0,0000429from the 258 cases with 5 correct ones also the auxiliary number in 1/43 of all cases is correct4 + Z630" 0,00451from the 13,545 cases with 4 correct ones also the auxiliary number in 2/43 of all cases is correct3 + Z17.220 0,123from the 246,820 cases with 3 also the auxiliary number in 3/43 of all cases tunes correct ones == number of tapping combinations ==

With the help of the combinatorial mathematics the number of possible number combinations can be calculated with the Lotto. With the play one can select 6 from 49 (combination without putting back) from 49 objects 6 without putting back and without attention of the sequence. There are 13.983.816 possibilities in the sum exactly. In the new system with "supernumber "this number grows 6 from 45 again on tenfold, thus gives it to 8.145.060 possibilities.

Lotto systems

With a Lotto system more than the usual 5 or 6 numbers are marked. Thus the chance is accordingly higher on a profit. There are in principle two kinds of Lotto systems: Full systems and subsystems. Systems can be played also in the form of portions (from a full system). One pays the increased chance of winning however with increased employment and thus the reduced multiplication possibility of the employment.

Profits

Germany

The first millionaire in the German Lotto 6 from 49 was on 2 September 1956. It won accurately 1.043.364, 50 DM. That would correspond to 533,463, 80 euro, the value at that time after the official exchange rate lay however inflation conditioned around a repeated over it.

The single gain largest with 23.919.517, 10 euro (for 6 correct ones + supernumber) won to 25. May 2005 a person from Baden-Wuerttemberg. Two divided the largest profit sum 6 of 49 at a value of 26.704.972, 20 euro tip by from North Rhine-Westphalia after the drawing from 15 December 2004. The lowest profit for 6 correct ones with supernumber became to 26. May 1999 of 9 winners attains. It amounted to 406,987, 80 DM (208,089, 56 euro). Simultaneous most winners were to be registered here.

The highest profit for 6 correct ones without supernumber was reached by a winner on 4 December 1999. It amounted to 8.034.874, 50 DM (4.108.166, 10 euro). The lowest profit for 6 correct ones was won on 25 April 1984, the 69 winners received ever 16,907, 00 DM (8,644, 41 euro).

The lottery from 23 January 1988 had most winners for 6 correct ones. 222 winners the two triplets 24, 25, 26 and 30, 31, 32 had typed. Everyone won 84,803, 90 DM (43,359, 55 euro). On 10 April 1999 the numbers 2, 3, 4, 5, 6 and 26 were drawn. In the consequence 38,008 players with 5 correct numbers won in each case 379.90 DM. 6 numbers in the arrangement of a U crossed 1997 124 fellow players on 4 October. They won 9, 13, 23, 27, 38 and 40 53,982 DM with the numbers each. The profit numbers of the Dutch Lotto of the previous week took over on 18 June 1977 205 playing express takers. For the 6 correct numbers there were 30,737, 80 DM.

Austria

With the Austrian Lotto on 19 February 2003 the largest single gain at a value of 7.164.511, 40 euro was won.

See also

• Klassenlotterie
• Weihnachtslotterie in Spain
• Tombola
• Schlesi Lotterie also Kartenlotterie, a map gambling
• Lotterieaufstand in Albania

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