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Mines

Last updated: Oct 16, 2023

Mines

Introduction

Mines is an entertaining game based on luck, where players click on squares in a 5x5 grid, attempting to avoid hidden mines. The objective is to reveal the maximum number of safe squares while dodging the mines to increase winnings. To the best of my knowledge, this game can only be experienced at BetFury.

Rules

The game is played on a 5x5 grid.
At the beginning of the game, players make a wager and decide how many mines will be concealed in the grid, with a choice ranging from 1 to 24.
Each square in the grid that doesn't conceal a mine will reveal a diamond.
Players then select squares in the grid, aiming to uncover diamonds while steering clear of the mines.
Each time a player successfully unveils a diamond, their potential winnings tend to grow.
After each selection, players have the option to either cash out their winnings or select another square, provided there are still diamonds left to find.

The subsequent table illustrates the payouts based on the number of diamonds discovered when there are 1 to 6 mines in total. The payouts are calculated 'for one' diamond found.

One to Six Mines

Diamonds Found	One Mine	Two Mines	Three Mines	Four Mines	Five Mines	Six Mines
1	1.03	1.03	1.07	1.13	1.18	1.25
2	1.04	1.12	1.23	1.35	1.5	1.66
3	1.05	1.23	1.41	1.64	1.91	2.25
4	1.05	1.35	1.64	2	2.48	3.1
5	1.06	1.5	1.91	2.48	3.25	4.34
6	1.07	1.66	2.25	3.1	4.34	6.2
7	1.07	1.86	2.67	3.92	5.89	9.06
8	1.08	2.09	3.21	5.04	8.15	13.59
9	1.09	2.37	3.9	6.6	11.55	21
10	1.1	2.71	4.8	8.8	16.8	33.61
11	1.12	3.13	6	12	25.21	56.02
12	1.14	3.65	7.63	16.8	39.21	98.04
13	1.16	4.31	9.93	24.27	63.72	182
14	1.19	5.18	13.24	36.41	109.25	364.16
15	1.23	6.33	18.2	57.22	200.29	801.16
16	1.28	7.91	26.01	95.37	400.58	2000
17	1.34	10.17	39.01	171.67	901.31	6001
18	1.44	13.57	62.42	343.55	2400	24004
19	1.59	19	109.25	801.16	8410	168000
20	1.82	28.5	218.5	2400	50470
21	2.24	47.5	546.25	12020
22	3.06	95	2190
23	5.12	285
24	23.74

Another table outlines the payouts for finding diamonds when the total number of mines ranges from 7 to 12, with winnings calculated on a 'for one' basis.

7 to 12 Mines

Diamonds Found	7 Mines	8 Mines	9 Mines	10 Mines	11 Mines	12 Mines
1	1.31	1.39	1.48	1.58	1.69	1.82
2	1.86	2.09	2.37	2.71	3.13	3.65
3	2.67	3.21	3.9	4.8	6	7.63
4	3.92	5.04	6.6	8.8	12	16.8
5	5.89	8.15	11.5	16.8	25.21	39.21
6	9.06	13.59	21	33.61	56.02	98.04
7	14.34	23.48	39.91	70.96	133.06	266.12
8	23.48	42.26	79.83	159.67	342.15	798.36
9	39.91	79.83	169.65	387.77	969.44	2710
10	70.96	159.67	387.77	1030	3100	10860
11	133.06	342.15	969.44	3100	11630	54290
12	266.12	798.36	2710	10860	54290	380000
13	576.59	2080	8820	47050	353000	4940000
14	1380	6230	35290	282000	4230000
15	3810	22830	194000	3110000
16	12690	114000	1940000
17	57080	1030000
18	457000

Yet another table details the payouts for discovering diamonds when the total number of mines is between 13 and 18, also calculated 'for one' diamond found.

13 to 18 Mines

Diamonds Found	13 Mines	14 Mines	15 Mines	16 Mines	17 Mines	18 Mines
1	1.97	2.15	2.51	2.63	2.96	3.39
2	4.31	5.18	6.33	7.91	10.17	13.57
3	9.93	13.24	18.2	26.01	39.01	62.42
4	24.27	36.41	57.22	95.37	171.67	343.35
5	63.72	109.25	200.29	458	901.31	2400
6	182.08	364.16	801.16	2000	6010	24030
7	576.59	1380	3810	12690	57080	457000
8	2080	6230	22830	114000	1030000
9	8820	35290	193000	1940000
10	47050	282000	3100000
11	353000	4230000
12	4940000

The next table presents the payouts for the number of diamonds found when there are 19 to 24 mines, calculated similarly on a 'for one' basis.

19 to 24 Mines

Diamonds Found	19 Mines	20 Mines	21 Mines	22 Mines	23 Mines	24 Mines
1	3.95	4.75	5.93	7.91	11.87	23.75
2	19	28.5	47.5	95	285
3	109.25	218.5	546.25	2190
4	801.16	2400	12020
5	8410	50470
6	168000

Analysis

This table reveals the winning probabilities and the expected returns for various combinations of mine distributions and selections.

Mines Analysis

Mines	Picks	Pays	Prob. Win	Return
1	1	1.03	0.960000	0.988800
1	2	1.04	0.920000	0.956800
1	3	1.05	0.880000	0.924000
1	4	1.05	0.840000	0.882000
1	5	1.06	0.800000	0.848000
1	6	1.07	0.760000	0.813200
1	7	1.07	0.720000	0.770400
1	8	1.08	0.680000	0.734400
1	9	1.09	0.640000	0.697600
1	10	1.1	0.600000	0.660000
1	11	1.12	0.560000	0.627200
1	12	1.14	0.520000	0.592800
1	13	1.16	0.480000	0.556800
1	14	1.19	0.440000	0.523600
1	15	1.23	0.400000	0.492000
1	16	1.28	0.360000	0.460800
1	17	1.34	0.320000	0.428800
1	18	1.44	0.280000	0.403200
1	19	1.59	0.240000	0.381600
1	20	1.82	0.200000	0.364000
1	21	2.24	0.160000	0.358400
1	22	3.06	0.120000	0.367200
1	23	5.12	0.080000	0.409600
1	24	23.74	0.040000	0.949600
2	1	1.03	0.920000	0.947600
2	2	1.12	0.843333	0.944533
2	3	1.23	0.770000	0.947100
2	4	1.35	0.700000	0.945000
2	5	1.5	0.633333	0.950000
2	6	1.66	0.570000	0.946200
2	7	1.86	0.510000	0.948600
2	8	2.09	0.453333	0.947467
2	9	2.37	0.400000	0.948000
2	10	2.71	0.350000	0.948500
2	11	3.13	0.303333	0.949433
2	12	3.65	0.260000	0.949000
2	13	4.31	0.220000	0.948200
2	14	5.18	0.183333	0.949667
2	15	6.33	0.150000	0.949500
2	16	7.91	0.120000	0.949200
2	17	10.17	0.093333	0.949200
2	18	13.57	0.070000	0.949900
2	19	19	0.050000	0.950000
2	20	28.5	0.033333	0.950000
2	21	47.5	0.020000	0.950000
2	22	95	0.010000	0.950000
2	23	285	0.003333	0.950000
3	1	1.07	0.880000	0.941600
3	2	1.23	0.770000	0.947100
3	3	1.41	0.669565	0.944087
3	4	1.64	0.578261	0.948348
3	5	1.91	0.495652	0.946696
3	6	2.25	0.421304	0.947935
3	7	2.67	0.354783	0.947270
3	8	3.21	0.295652	0.949043
3	9	3.9	0.243478	0.949565
3	10	4.8	0.197826	0.949565
3	11	6	0.158261	0.949565
3	12	7.63	0.124348	0.948774
3	13	9.93	0.095652	0.949826
3	14	13.24	0.071739	0.949826
3	15	18.2	0.052174	0.949565
3	16	26.01	0.036522	0.949930
3	17	39.01	0.024348	0.949809
3	18	62.42	0.015217	0.949870
3	19	109.25	0.008696	0.950000
3	20	218.5	0.004348	0.950000
3	21	546.25	0.001739	0.950000
3	22	2190	0.000435	0.952174
4	1	1.13	0.840000	0.949200
4	2	1.35	0.700000	0.945000
4	3	1.64	0.578261	0.948348
4	4	2	0.473123	0.946245
4	5	2.48	0.383004	0.949850
4	6	3.1	0.306403	0.949850
4	7	3.92	0.241897	0.948237
4	8	5.04	0.188142	0.948237
4	9	6.6	0.143874	0.949565
4	10	8.8	0.107905	0.949565
4	11	12	0.079130	0.949565
4	12	16.8	0.056522	0.949565
4	13	24.27	0.039130	0.949696
4	14	36.41	0.026087	0.949826
4	15	57.22	0.016601	0.949897
4	16	95.37	0.009960	0.949930
4	17	171.67	0.005534	0.949953
4	18	343.55	0.002767	0.950534
4	19	801.16	0.001186	0.949992
4	20	2400	0.000395	0.948617
4	21	12020	0.000079	0.950198
5	1	1.18	0.800000	0.944000
5	2	1.5	0.633333	0.950000
5	3	1.91	0.495652	0.946696
5	4	2.48	0.383004	0.949850
5	5	3.25	0.291813	0.948391
5	6	4.34	0.218859	0.949850
5	7	5.89	0.161265	0.949850
5	8	8.15	0.116469	0.949223
5	9	11.55	0.082213	0.949565
5	10	16.8	0.056522	0.949565
5	11	25.21	0.037681	0.949942
5	12	39.21	0.024224	0.949807
5	13	63.72	0.014907	0.949863
5	14	109.25	0.008696	0.950000
5	15	200.29	0.004743	0.949992
5	16	400.58	0.002372	0.949992
5	17	901.31	0.001054	0.949997
5	18	2400	0.000395	0.948617
5	19	8410	0.000113	0.949746
5	20	50470	0.000019	0.949934
6	1	1.25	0.760000	0.950000
6	2	1.66	0.570000	0.946200
6	3	2.25	0.421304	0.947935
6	4	3.1	0.306403	0.949850
6	5	4.34	0.218859	0.949850
6	6	6.2	0.153202	0.949850
6	7	9.06	0.104822	0.949689
6	8	13.59	0.069881	0.949689
6	9	21	0.045217	0.949565
6	10	33.61	0.028261	0.949848
6	11	56.02	0.016957	0.949904
6	12	98.04	0.009689	0.949953
6	13	182	0.005217	0.949565
6	14	364.16	0.002609	0.949983
6	15	801.16	0.001186	0.949992
6	16	2000	0.000474	0.948617
6	17	6001	0.000158	0.948775
6	18	24004	0.000040	0.948775
6	19	168000	0.000006	0.948617
7	1	1.31	0.720000	0.943200
7	2	1.86	0.510000	0.948600
7	3	2.67	0.354783	0.947270
7	4	3.92	0.241897	0.948237
7	5	5.89	0.161265	0.949850
7	6	9.06	0.104822	0.949689
7	7	14.34	0.066203	0.949358
7	8	23.48	0.040458	0.949946
7	9	39.91	0.023799	0.949803
7	10	70.96	0.013387	0.949922
7	11	133.06	0.007140	0.949994
7	12	266.12	0.003570	0.949994
7	13	576.59	0.001648	0.949988
7	14	1380	0.000686	0.947368
7	15	3810	0.000250	0.951113
7	16	12690	0.000075	0.950364
7	17	57080	0.000017	0.949948
7	18	457000	0.000002	0.950697
8	1	1.39	0.680000	0.945200
8	2	2.09	0.453333	0.947467
8	3	3.21	0.295652	0.949043
8	4	5.04	0.188142	0.948237
8	5	8.15	0.116469	0.949223
8	6	13.59	0.069881	0.949689
8	7	23.48	0.040458	0.949946
8	8	42.26	0.022476	0.949856
8	9	79.83	0.011899	0.949922
8	10	159.67	0.005950	0.949982
8	11	342.15	0.002777	0.949982
8	12	798.36	0.001190	0.949994
8	13	2080	0.000458	0.951945
8	14	6230	0.000153	0.950420
8	15	22830	0.000042	0.949865
8	16	114000	0.000008	0.948617
8	17	1030000	0.000001	0.952315
9	1	1.48	0.640000	0.947200
9	2	2.37	0.400000	0.948000
9	3	3.9	0.243478	0.949565
9	4	6.6	0.143874	0.949565
9	5	11.5	0.082213	0.945455
9	6	21	0.045217	0.949565
9	7	39.91	0.023799	0.949803
9	8	79.83	0.011899	0.949922
9	9	169.65	0.005600	0.949985
9	10	387.77	0.002450	0.949982
9	11	969.44	0.000980	0.949996
9	12	2710	0.000350	0.948445
9	13	8820	0.000108	0.949791
9	14	35290	0.000027	0.950061
9	15	194000	0.000005	0.949596
9	16	1940000	0.000000	0.949596
10	1	1.58	0.600000	0.948000
10	2	2.71	0.350000	0.948500
10	3	4.8	0.197826	0.949565
10	4	8.8	0.107905	0.949565
10	5	16.8	0.056522	0.949565
10	6	33.61	0.028261	0.949848
10	7	70.96	0.013387	0.949922
10	8	159.67	0.005950	0.949982
10	9	387.77	0.002450	0.949982
10	10	1030	0.000919	0.946258
10	11	3100	0.000306	0.949320
10	12	10860	0.000087	0.950195
10	13	47050	0.000020	0.949993
10	14	282000	0.000003	0.948984
10	15	3110000	0.000000	0.951431
11	1	1.69	0.560000	0.946400
11	2	3.13	0.303333	0.949433
11	3	6	0.158261	0.949565
11	4	12	0.079130	0.949565
11	5	25.21	0.037681	0.949942
11	6	56.02	0.016957	0.949904
11	7	133.06	0.007140	0.949994
11	8	342.15	0.002777	0.949982
11	9	969.44	0.000980	0.949996
11	10	3100	0.000306	0.949320
11	11	11630	0.000082	0.949729
11	12	54290	0.000017	0.950020
11	13	353000	0.000003	0.950330
11	14	4230000	0.000000	0.948984
12	1	1.82	0.520000	0.946400
12	2	3.65	0.260000	0.949000
12	3	7.63	0.124348	0.948774
12	4	16.8	0.056522	0.949565
12	5	39.21	0.024224	0.949807
12	6	98.04	0.009689	0.949953
12	7	266.12	0.003570	0.949994
12	8	798.36	0.001190	0.949994
12	9	2710	0.000350	0.948445
12	10	10860	0.000087	0.950195
12	11	54290	0.000017	0.950020
12	12	380000	0.000002	0.949945
12	13	4940000	0.000000	0.949945
13	1	1.97	0.480000	0.945600
13	2	4.31	0.220000	0.948200
13	3	9.93	0.095652	0.949826
13	4	24.27	0.039130	0.949696
13	5	63.72	0.014907	0.949863
13	6	182.08	0.005217	0.949983
13	7	576.59	0.001648	0.949988
13	8	2080	0.000458	0.951945
13	9	8820	0.000108	0.949791
13	10	47050	0.000020	0.949993
13	11	353000	0.000003	0.950330
13	12	4940000	0.000000	0.949945
14	1	2.15	0.440000	0.946000
14	2	5.18	0.183333	0.949667
14	3	13.24	0.071739	0.949826
14	4	36.41	0.026087	0.949826
14	5	109.25	0.008696	0.950000
14	6	364.16	0.002609	0.949983
14	7	1380	0.000686	0.947368
14	8	6230	0.000153	0.950420
14	9	35290	0.000027	0.950061
14	10	282000	0.000003	0.948984
14	11	4230000	0.000000	0.948984
15	1	2.51	0.400000	1.004000
15	2	6.33	0.150000	0.949500
15	3	18.2	0.052174	0.949565
15	4	57.22	0.016601	0.949897
15	5	200.29	0.004743	0.949992
15	6	801.16	0.001186	0.949992
15	7	3810	0.000250	0.951113
15	8	22830	0.000042	0.949865
15	9	193000	0.000005	0.944701
15	10	3100000	0.000000	0.948372
16	1	2.63	0.360000	0.946800
16	2	7.91	0.120000	0.949200
16	3	26.01	0.036522	0.949930
16	4	95.37	0.009960	0.949930
16	5	458	0.002372	1.086166
16	6	2000	0.000474	0.948617
16	7	12690	0.000075	0.950364
16	8	114000	0.000008	0.948617
16	9	1940000	0.000000	0.949596
17	1	2.96	0.320000	0.947200
17	2	10.17	0.093333	0.949200
17	3	39.01	0.024348	0.949809
17	4	171.67	0.005534	0.949953
17	5	901.31	0.001054	0.949997
17	6	6010	0.000158	0.950198
17	7	57080	0.000017	0.949948
17	8	1030000	0.000001	0.952315
18	1	3.39	0.280000	0.949200
18	2	13.57	0.070000	0.949900
18	3	62.42	0.015217	0.949870
18	4	343.35	0.002767	0.949980
18	5	2400	0.000395	0.948617
18	6	24030	0.000040	0.949802
18	7	457000	0.000002	0.950697
19	1	3.95	0.240000	0.948000
19	2	19	0.050000	0.950000
19	3	109.25	0.008696	0.950000
19	4	801.16	0.001186	0.949992
19	5	8410	0.000113	0.949746
19	6	168000	0.000006	0.948617
20	1	4.75	0.200000	0.950000
20	2	28.5	0.033333	0.950000
20	3	218.5	0.004348	0.950000
20	4	2400	0.000395	0.948617
20	5	50470	0.000019	0.949934
21	1	5.93	0.160000	0.948800
21	2	47.5	0.020000	0.950000
21	3	546.25	0.001739	0.950000
21	4	12020	0.000079	0.950198
22	1	7.91	0.120000	0.949200
22	2	95	0.010000	0.950000
22	3	2190	0.000435	0.952174
23	1	11.87	0.080000	0.949600
23	2	285	0.003333	0.950000
24	1	23.75	0.040000	0.950000

The earlier table indicates that with 2 to 24 mines, the anticipated return is consistently around 95%. Generally, the expected return for the first selection is around 95%, while it approaches 100% for all selections thereafter.

One exception occurs with just a single mine, where the expected return for one selection is 96%. This drops to close to 95% with 24 selections and significantly lowers, hitting as low as 41% for anywhere between 2 to 23 selections.

My recommendation for players is to either bet on a minimum of two mines and continue playing for as long as they desire, or to choose one mine and either cash out after finding one diamond or continue all the way to uncover all 24.

Written by: Michael Shackleford