RECURRENCE ANALYSIS AND LOTTERY PREDICTION

Analysis of the EuroMillions Draw.

Of the several draws run by the UK National Lottery, the EuroMillions is one of the newer ones; at the start of June 2009 there were fewer than 280 results. This small number of results allows us a rare opportunity to analyse a lottery while still relatively young. I have broken the EuroMillions data into five column groups: {1,2} {4,5} {6,7} ('Lucky Stars') {1,2,3} and {2,3,4}. The analysis starts at draw 251 (remember, VRA prefers to work with data sets of 500 or more points).

The recurrence model is Nearest Neighbour with Euclidean measure.

Note: hyphens in the following tables indicate that VRA did not accurately predict any numbers.

Draw	Col 1	Col 2	Predicted	Dim	Del

251	8	11	9	11	3	6
252	4	8	4	20	4	6
253	2	19	-	-	-	-
254	28	29	-	-	-	-
255	1	2	2	10	3	9
256	29	30	-	-	-	-
257	7	15	3	7	3	5
258	3	17	8	17	3	5
259	32	33	-	-	-	-
260	4	29	3	4	3	5
261	10	20	-	-	-	-
262	22	33	-	-	-	-
263	9	12	3	9	4	8
264	5	9	-	-	-	-
265	13	17	9	13	3	5
266	12	24	7	12	3	7
267	12	16	12	13	3	7
268	25	33	-	-	-	-
269	2	20	6	20	3	9
270	9	14	1	9	3	6
271	4	7	7	14	3	8
272	4	14	14	15	3	7
273	5	19	-	-	-	-
274	4	23	2	23	3	6
275	8	18	7	8	3	5
276	4	13	-	-	-	-
277	2	5	-	-	-	-
278	11	19	15	19	4	6
279	6	14	-	-	-	-
280	4	16	16	19	4	8
281	6	11	11	14	4	7
282	21	29	-	-	-	-
283	6	16	-	-	-	-
284	2	8	8	11	4	7

Draw	Col 4	Col 5	Predicted	Dim	Del

251	25	41	41	49	3	5
252	35	45	-	-	-	-
253	42	49	19	49	3	6
254	46	50	-	-	-	-
255	44	50	47	50	3	6
256	37	48	37	42	3	9
257	28	48	32	48	4	6
258	49	50	17	50	4	5
259	40	49	34	49	3	5
260	35	46	37	46	3	9
261	36	40	28	36	3	9
262	40	42	40	42	3	9
263	14	48	-	-	-	-
264	44	45	37	44	4	8
265	25	35	-	-	-	-
266	36	42	33	42	3	6
267	31	35	-	-	-	-
268	38	42	35	42	4	7
269	32	46	43	46	3	7
270	37	46	30	37	3	8
271	44	47	47	49	3	6
272	24	41	-	-	-	-
273	38	47	44	47	4	6
274	29	31	31	40	3	5
275	20	42	37	42	3	6
276	33	43	41	43	3	6
277	37	47	35	37	4	9
278	35	40	26	35	4	5
279	34	50	37	50	3	6
280	20	29	29	36	3	7
281	30	39	33	39	3	6
282	46	47	47	49	4	8
283	42	46	38	42	3	5
284	32	50	48	50	3	9

Draw	Col 6	Col 7	Predicted	Dim	Del

251	2	4	1	4	3	6
252	5	8	3	8	3	5
253	2	7	4	7	3	6
254	5	7	5	6	3	5
255	1	7	1	3	3	7
256	1	5	1	5	3	7
257	1	4	4	7	3	8
258	3	6	3	6	4	8
259	2	8	2	5	3	6
260	5	8	2	8	3	7
261	3	5	-	-	-	-
262	1	2	1	7	3	5
263	1	2	1	8	3	5
264	6	9	5	6	4	5
265	5	6	5	6	3	4
266	1	4	1	5	4	5
267	4	6	6	7	4	7
268	6	7	1	6	3	5
269	1	9	1	8	3	5
270	2	4	2	6	3	4
271	1	5	3	5	3	5
272	5	8	5	8	3	5
273	3	5	3	5	4	7
274	8	9	7	8	3	6
275	5	9	5	6	3	5
276	1	6	1	6	4	6
277	3	6	1	6	3	7
278	2	5	4	5	4	5
279	4	6	3	6	3	5
280	5	7	5	6	3	6
281	2	8	3	8	3	7
282	6	8	6	7	3	5
283	1	6	1	3	3	9
284	3	7	2	3	3	6

Draw	Col 1	Col 2	Col 3	Predicted		Dim	Del

251	8	11	16	8	12	12	3	5
252	4	8	21	4	8	33	3	5
253	2	19	28	12	28	30	4	5
254	28	29	40	29	30	33	4	8
255	1	2	26	1	3	8	3	7
256	29	30	36	29	32	36	3	6
257	7	15	22	7	19	22	4	7
258	3	17	22	3	6	16	4	8
259	32	33	36	14	33	34	4	9
260	4	29	34	-	-	-	-	-
261	10	20	30	22	30	32	3	9
262	22	33	36	3	33	36	3	8
263	9	12	13	11	12	19	4	5
264	5	9	37	3	9	21	3	5
265	13	17	19	4	16	17	4	8
266	12	24	26	5	7	12	3	9
267	12	16	23	12	20	25	3	5
268	25	33	36	9	28	33	4	5
269	2	20	24	8	12	24	3	9
270	9	14	16	1	9	11	3	9
271	4	7	21	4	5	7	3	6
272	4	14	21	4	19	19	4	8
273	5	19	31	3	5	8	3	5
274	4	23	24	4	23	31	4	8
275	8	18	19	6	19	30	4	9
276	4	13	14	1	2	14	3	5
277	2	5	30	5	20	25	3	5
278	11	19	26	7	17	19	4	9
279	6	14	16	1	2	14	4	6
280	4	16	17	4	9	17	3	5
281	6	11	21	2	11	14	4	8
282	21	29	34	2	15	21	4	9
283	6	16	20	8	14	16	3	5
284	2	8	17	2	8	27	4	8

Draw	Col 2	Col 3	Col 4	Predicted		Dim	Del
	
251	11	16	25	11	19	21	4	8
252	8	21	35	16	21	25	4	9
253	19	28	42	41	42	44	4	9
254	29	40	46	28	35	40	4	9	
255	2	26	44	-	-	-	-	-
256	30	36	37	12	33	37	4	7
257	15	22	28	3	14	15	3	8
258	17	22	49	22	30	46	4	8
259	33	36	40	4	24	40	4	6
260	29	34	35	26	34	35	3	9
261	20	30	36	25	30	42	4	9
262	33	36	40	8	15	40	4	6
263	12	13	14	13	43	48	3	7
264	9	37	44	9	18	38	3	7
265	17	19	25	17	21	26	4	9
266	24	26	36	3	26	27	4	7
267	16	23	31	-	-	-	-	-
268	33	36	38	36	37	40	3	6
269	20	24	32	11	21	24	4	9
270	14	16	37	16	19	34	4	7
271	7	21	44	43	44	44	4	8   duplicate value predicted (44)
272	14	21	24	19	21	31	3	9
273	19	31	38	30	31	37	4	9
274	23	24	29	9	16	24	4	9
275	18	19	20	4	19	29	3	7
276	13	14	33	22	33	43	4	5
277	5	30	37	27	30	44	3	6
278	19	26	35	9	14	26	4	8
279	14	16	34	16	33	38	4	5
280	16	17	20	15	20	31	4	9
281	11	21	30	14	21	23	3	5
282	29	34	46	34	44	46	3	9
283	16	20	42	11	16	26	3	9
284	8	17	32	8	23	24	3	8

Note: with columns 2, 3, and 4 I am primarily attempting to predict the numbers in column 3
(columns 2 and 4 being dealt with in the other data groups). Also, using columns 3, 4 and 5
gave inconsistent results.

From these tables the commonest values of dimension and delay are:

Columns 1, 2, 3: Dimension = 3, Delay = 5

Columns 2, 3, 4: Dimension = 4, Delay = 9

Columns 1 and 2: Dimension = 3, Delay = 5

Columns 4 and 5: Dimension = 3, Delay = 6

Columns 6 and 7: Dimension = 3, Delay = 5

As more data becomes available these values should settle to certain values (an indicator of stationarity).

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