SPECIAL LOTTERY DRAWINGS - ANALYSIS OF AN UNCONVENTIONAL INVESTMENT
               OPPORTUNITY

Castello, Jaques Deivinson da Silva; Milioni, Armando Zeferino

doi:10.1590/0101-7438.2015.035.01.0091

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Articles • Pesq. Oper. 35 (1) • Jan-Apr 2015 • https://doi.org/10.1590/0101-7438.2015.035.01.0091 copy

SPECIAL LOTTERY DRAWINGS - ANALYSIS OF AN UNCONVENTIONAL INVESTMENT OPPORTUNITY

Authorship SCIMAGO INSTITUTIONS RANKINGS

Quina Loto is one of the most popular lottery games in Brazil. Prizes are paid as a percentage of each drawing's revenues. After deductions and taxes, 34% of the revenues are destined for the payments of prizes on each drawing, 29% divided among winners and 5% saved in order to contribute for the major prize of the special drawing held annually, in June 24^th. Due to the low expected return on investment, lotteries are widely regarded as a bad investment decision. Experience, however, shows that the special drawing might be an exception. In this paper we provide a thorough analysis of a theoretical investment in the special drawing of 2013, considering players' behavior, lesser prizes earnings, effects of the own investment in the jackpot, probabilities of sharing the prizes and outcomes covering methods. Finally, we compare our conclusions against the result of the lottery on June 24^th, 2013.

Lotto; Wallenius random variable; investment decision; applied probability; applied statistics

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Numbers selected	Outputs covered	Price	Outputs/ price ratio
5	1	R$ 0.75	1.33
6	6	R$ 3.00	2.00
7	21	R$ 7.50	2.80

70	61	50	66	60	76	38	71	31	58
40	51	68	69	30	46	57	52	41	63
73	80	39	59	64	36	74	77	67	65
75	20	42	78	72	22	49	62	32	79
29	47	28	45	44	56	21	23	54	53
43	48	2	1	16	34	15	37	33	19
55	8	35	27	26	24	18	12	17	11
25	6	14	3	10	4	9	7	5	13

Ticket type	Number of tickets	Total cost	Outputs covered	Multiple coverage (variation)
				2×	3× or above
7	1,113,809	R$ 8,353,567.50	20,282,735	2,602,488	244,371
6	407,798	R$ 1,223,394.00	1,890,917	406,092	71,626
5	1,866,364	R$ 1,399,773.00	1,866,364	0	0
Total	3,387,971	R$ 10,976,734.50	24,040,016	3,008,580	315,997

Field	Description	Value (R$)
1	Total jackpot = (2)+(6)+(8)	115,249,195.12
2	1 ^st tier - 5 correctmatches (quina) = (3)+(4)+(5)	96,992,153.65
3	50% of revenue share destined to prizes	18,257,041.47
4	Amount saved from regular drawings	77,749,655.41
5	Rolled-over prize from previous drawing	985,456.76
6	2 ^nd tier - 4 correctmatches (quadra) = (7)	9,128,520.74
7	25% of revenue share destined to prizes	9,128,520.74
8	3 ^rd tier - 3 correctmatches (terno) = (9)	9,128,520.74
9	25% of revenue share destined to prizes	9,128,520.74

k-correct matches	n-bet type	N_n-number of players			t_b - 'birthday numbers' drawn (probability of occurrence)
			0 (8%)	1 (27%)	2 (36%)	3 (22%)	4 (6%)	5 (1%)
	5	79,589,643	2.5	2.7	3.1	3.9	5.6	9.0
5	6	6,529,069	1.2	1.3	1.5	1.9	2.7	4.4
	7	3,765,934	2.5	2.7	3.1	3.9	5.5	8.8
	Total	89,884,645	6.2	6.7	7.7	9.7	13.9	22.3
	5	79,589,643	960	1,044	1,191	1,445	1,870	2,549
4	6	6,529,069	234	254	290	351	452	612
	7	3,765,934	311	338	385	465	597	805
	Total	89,884,645	1,504	1,635	1,866	2,261	2,918	3,966
	5	79,589,643	74,298	80,732	90,289	103,923	122,497	146,792
3	6	6,529,069	11,893	12,920	14,432	16,570	19,453	23,179
	7	3,765,934	11,709	12,716	14,187	16,248	18,996	22,507
	Total	89,884,645	97,900	106,367	118,909	136,741	160,946	192,478

70	61	50	66	60	76	38	71	31	58
40	51	68	69	30	46	57	52	41	63
73	80	39	59	64	36	74	77	67	65
75	20	42	78	72	22	49	62	32	79
29	47	28	45	44	56	21	23	54	53
43	48	2	1	16	34	15	37	33	19
55	8	35	27	26	24	18	12	17	11
25	6	14	3	10	4	9	7	5	13

70	61	50	66	60	76	38	71	31	58
40	51	68	69	30	46	57	52	41	63
73	80	39	59	64	36	74	77	67	65
75	20	42	78	72	22	49	62	32	79
29	47	28	45	44	56	21	23	54	53
43	48	2	1	16	34	15	37	33	19
55	8	35	27	26	24	18	12	17	11
25	6	14	3	10	4	9	7	5	13

70	61	50	66	60	76	38	71	31	58
40	51	68	69	30	46	57	52	41	63
73	80	39	59	64	36	74	77	67	65
75	20	42	78	72	22	49	62	32	79
29	47	28	45	44	56	21	23	54	53
43	48	2	1	16	34	15	37	33	19
55	8	35	27	26	24	18	12	17	11
25	6	14	3	10	4	9	7	5	13