Blackjack Martingale

mikemartingale,

Here are the numbers I generated from a 400-million-round sim using CVData for a 6D, S17 game with 75% pen for a heads-up player using your Martingale system. The output below shows how the player fared as a function of the number of units bet on that round. Note that all bets of 50 or more units are lumped together at the bottom of the table: this is a limitation of the CVData output. Note also that I made the second bet $30 rather than $35, so that I could use $15 units: otherwise, I'd have had to use $5 units, and then everything from $300 up would have been lumped together. Note also that the maximum bet I used was only 160 units, or $2,400: CVData does not permit a max bet of more than 200 units.

As for playing, as per your instructions the player uses Basic Strategy except that he never splits, doubles down, or surrenders. This strategy provides the player an Initial Bet Advantage of -2.313% overall. Overall, the player wins 43.35% of the rounds, loses 47.96% of the rounds, and pushes the remaining 8.69% of the rounds. If we exclude pushes, the player wins 47.47% of the decisive rounds, and loses the remaining 52.53% of the decisive rounds.

As you can see by the data below, regardless of the number of units he bets, the player loses more bets than he wins.

Bet	Bet	Hands	Hands	Hands	Hands	Units	Units	Advantage	Advantage
Units	$	Total	Won	Lost	Tied	Bet	Won/Lost	Percent	Std. Dev.
1	$15	208,742,688	90,474,304	-100,128,896	18,139,484	208,742,800	-4,932,977	-2.36%	0.008
2	$30	100,128,824	43,405,056	-48,018,892	8,704,875	200,257,600	-4,697,970	-2.35%	0.011
5	$75	48,018,828	20,819,292	-23,022,082	4,177,454	240,094,100	-5,569,235	-2.32%	0.016
10	$150	23,022,068	9,977,179	-11,042,017	2,002,872	230,220,600	-5,425,931	-2.36%	0.023
20	$300	11,042,004	4,790,012	-5,291,976	960,016	220,840,000	-5,024,870	-2.28%	0.03
40	$600	5,291,970	2,294,236	-2,536,822	460,912	211,678,800	-4,899,960	-2.32%	0.05
>50	$1200+	3,753,581	1,627,588	-1,799,161	326,832	397,627,600	-8,982,600	-2.26%	0.06

This next table shows your streaks by hour of play. Each row shows the number of times you've won "Win (Number)" or lost "Lose (Number)" the indicated number of units per hour. For example, if you look at the row labeled "5", you'll see that you had 12,273 hours where you won 5 units, and 7,260 hours where you lost 5 units. CVData assumes the game was played at 100 rounds per hour, so the 400-million-round sim comprised 4,000,000 hours of playing time. Thus, the "Win (Percent)" column shows that you won 5 units 0.31% of the hours (12,273/4,000,000 = 0.00306825 = 0.31%), while the "Lose (Percent)" column shows that you lost 5 units 0.18% of the hours you played. The "Cum%" columns show that you had an hour of winning 5 units OR MORE 74.40% of the time, while you had an hour of losing 5 units OR FEWER (that is, any result of -5 units or better: -4, -3, -2, etc., including wins) 76.80% of the time. The last column shows the difference between the number of winning hours and the number of losing hours for each result.

Thus, if you look at the top row, you'll see that more than three-fourths of the hours you play will be break-even or better. Therefore, less than one-fourth of the hours will actually be losers. This is why Martingale systems are so seductive: they APPEAR to work over the short term. If you look further down the table, to the row labeled "41", you'll see that just over half the hours played will result in wins of 41 units or more. Still farther down, we see that 10% of the time you'll win 68 or more units in an hour. Even farther down, we see that 1% of the time you'll win 122 units or more in an hour.

In fact, if you look down the "Win-Loss" column, you'll see that for every result of 102 units or less, you have a better chance of Winning that number than of Losing that number. This is also true for results of 126 to 145.

Let's look for the BIG hours! At the bottom of the table, you'll see that 0.07% of the time, you'll win more than 207 units in an hour: Easy Street, here I come!

Of course, if you look a bit further to the right, you'll see that you LOST 207 or more units in an hour 534,214 times: that means 13.36% of the hours you play will cost you more than 207 units, or in other words, more than $3,105.

All this supposes, by the way, that you NEVER run out of money. If you do have to stop because you run out, your actual results will be even worse than what is shown here.

	Units per Hour	Units per Hour	Units per Hour	Units per Hour	Units per Hour	Units per Hour	Win-Loss
Units	Win (Number)	Win (Percent)	Cum%	Lose (Number)	Lose (Percent)	Cum%
0	4,559	0.11%	75.70%		0.00%	75.70%	4559
<1	4,795	0.12%	75.60%	4,521	0.11%	75.80%	274
1	9,918	0.25%	75.40%	8,645	0.22%	76.00%	1273
2	10,409	0.26%	75.20%	8,294	0.21%	76.20%	2115
3	10,868	0.27%	74.90%	8,015	0.20%	76.40%	2853
4	11,561	0.29%	74.70%	7,742	0.19%	76.60%	3819
5	12,273	0.31%	74.40%	7,260	0.18%	76.80%	5013
6	12,954	0.32%	74.10%	7,011	0.18%	77.00%	5943
7	13,633	0.34%	73.70%	6,550	0.16%	77.10%	7083
8	14,302	0.36%	73.40%	6,590	0.17%	77.30%	7712
9	14,952	0.37%	73.00%	6,183	0.16%	77.40%	8769
10	15,609	0.39%	72.70%	5,936	0.15%	77.60%	9673
11	16,242	0.41%	72.30%	5,783	0.15%	77.70%	10459
12	17,188	0.43%	71.90%	5,638	0.14%	77.90%	11550
13	17,556	0.44%	71.40%	5,809	0.15%	78.00%	11747
14	18,324	0.46%	71.00%	5,586	0.14%	78.20%	12738
15	18,911	0.47%	70.50%	5,567	0.14%	78.30%	13344
16	19,584	0.49%	70.10%	5,686	0.14%	78.40%	13898
17	19,723	0.49%	69.60%	5,797	0.15%	78.60%	13926
18	20,783	0.52%	69.10%	5,939	0.15%	78.70%	14844
19	21,194	0.53%	68.60%	5,948	0.15%	78.90%	15246
20	21,701	0.54%	68.00%	6,168	0.15%	79.00%	15533
21	22,470	0.56%	67.50%	6,324	0.16%	79.20%	16146
22	23,338	0.58%	66.90%	6,564	0.16%	79.40%	16774
23	23,771	0.59%	66.30%	6,383	0.16%	79.50%	17388
24	24,645	0.62%	65.80%	6,583	0.17%	79.70%	18062
25	25,758	0.64%	65.10%	6,581	0.17%	79.80%	19177
26	26,793	0.67%	64.50%	6,445	0.16%	80.00%	20348
27	28,183	0.71%	63.80%	6,338	0.16%	80.20%	21845
28	29,660	0.74%	63.10%	6,283	0.16%	80.30%	23377
29	31,303	0.78%	62.40%	6,101	0.15%	80.50%	25202
30	32,380	0.81%	61.60%	5,937	0.15%	80.60%	26443
31	34,312	0.86%	60.80%	5,896	0.15%	80.80%	28416
32	35,817	0.90%	59.90%	5,689	0.14%	80.90%	30128
33	37,661	0.94%	59.00%	5,459	0.14%	81.10%	32202
34	39,398	0.99%	58.10%	5,280	0.13%	81.20%	34118
35	41,466	1.04%	57.10%	4,940	0.12%	81.30%	36526
36	43,401	1.09%	56.10%	4,704	0.12%	81.40%	38697
37	45,289	1.13%	55.00%	4,589	0.12%	81.50%	40700
38	47,231	1.18%	53.90%	4,325	0.11%	81.60%	42906
39	49,345	1.23%	52.70%	4,166	0.10%	81.80%	45179
40	51,431	1.29%	51.40%	4,029	0.10%	81.90%	47402
41	53,110	1.33%	50.20%	3,752	0.09%	81.90%	49358
42	55,398	1.39%	48.80%	3,588	0.09%	82.00%	51810
43	57,915	1.45%	47.40%	3,367	0.08%	82.10%	54548
44	59,203	1.48%	46.00%	3,270	0.08%	82.20%	55933
45	60,964	1.52%	44.50%	3,100	0.08%	82.30%	57864
46	63,070	1.58%	43.00%	2,965	0.07%	82.40%	60105
47	64,923	1.62%	41.40%	2,883	0.07%	82.40%	62040
48	66,397	1.66%	39.80%	2,766	0.07%	82.50%	63631
49	68,303	1.71%	38.10%	2,477	0.06%	82.60%	65826
50	69,279	1.73%	36.40%	2,302	0.06%	82.60%	66977
51	70,971	1.77%	34.70%	2,243	0.06%	82.70%	68728
52	70,960	1.77%	32.90%	2,069	0.05%	82.70%	68891
53	71,180	1.78%	31.10%	1,985	0.05%	82.80%	69195
54	71,231	1.78%	29.40%	1,911	0.05%	82.80%	69320
55	70,531	1.76%	27.60%	1,805	0.05%	82.90%	68726
56	68,992	1.73%	25.80%	1,849	0.05%	82.90%	67143
57	67,606	1.69%	24.10%	1,639	0.04%	83.00%	65967
58	65,017	1.63%	22.40%	1,571	0.04%	83.00%	63446
59	61,988	1.55%	20.80%	1,532	0.04%	83.00%	60456
60	59,170	1.48%	19.20%	1,470	0.04%	83.10%	57700
61	55,885	1.40%	17.70%	1,584	0.04%	83.10%	54301
62	52,178	1.30%	16.40%	1,391	0.04%	83.10%	50787
63	48,138	1.20%	15.00%	1,454	0.04%	83.20%	46684
64	44,420	1.11%	13.80%	1,415	0.04%	83.20%	43005
65	40,657	1.02%	12.70%	1,378	0.03%	83.20%	39279
66	37,032	0.93%	11.70%	1,341	0.03%	83.30%	35691
67	33,031	0.83%	10.80%	1,257	0.03%	83.30%	31774
68	29,868	0.75%	10.00%	1,270	0.03%	83.30%	28598
69	27,105	0.68%	9.20%	1,187	0.03%	83.40%	25918
70	24,351	0.61%	8.50%	1,157	0.03%	83.40%	23194
71	21,572	0.54%	7.90%	1,089	0.03%	83.40%	20483
72	19,537	0.49%	7.40%	1,048	0.03%	83.50%	18489
73	17,354	0.43%	6.90%	1,013	0.03%	83.50%	16341
74	15,917	0.40%	6.50%	989	0.03%	83.50%	14928
75	14,473	0.36%	6.10%	921	0.02%	83.50%	13552
76	12,923	0.32%	5.70%	928	0.02%	83.60%	11995
77	11,625	0.29%	5.40%	877	0.02%	83.60%	10748
78	10,609	0.27%	5.10%	844	0.02%	83.60%	9765
79	9,827	0.25%	4.80%	823	0.02%	83.60%	9004
80	9,101	0.23%	4.60%	832	0.02%	83.60%	8269
81	8,166	0.20%	4.40%	782	0.02%	83.70%	7384
82	7,613	0.19%	4.20%	817	0.02%	83.70%	6796
83	6,989	0.18%	4.00%	740	0.02%	83.70%	6249
84	6,520	0.16%	3.80%	810	0.02%	83.70%	5710
85	6,035	0.15%	3.60%	830	0.02%	83.70%	5205
86	5,861	0.15%	3.50%	813	0.02%	83.80%	5048
87	5,359	0.13%	3.30%	873	0.02%	83.80%	4486
88	5,198	0.13%	3.20%	893	0.02%	83.80%	4305
89	4,984	0.13%	3.10%	909	0.02%	83.80%	4075
90	4,645	0.12%	2.90%	975	0.02%	83.80%	3670
91	4,481	0.11%	2.80%	977	0.02%	83.90%	3504
92	4,310	0.11%	2.70%	1,161	0.03%	83.90%	3149
93	4,179	0.10%	2.60%	1,219	0.03%	83.90%	2960
94	4,086	0.10%	2.50%	1,271	0.03%	84.00%	2815
95	3,722	0.09%	2.40%	1,356	0.03%	84.00%	2366
96	3,665	0.09%	2.30%	1,503	0.04%	84.00%	2162
97	3,503	0.09%	2.20%	1,601	0.04%	84.10%	1902
98	3,192	0.08%	2.10%	1,780	0.05%	84.10%	1412
99	3,063	0.08%	2.00%	1,879	0.05%	84.20%	1184
100	2,793	0.07%	2.00%	2,087	0.05%	84.20%	706
101	2,674	0.07%	1.90%	2,240	0.06%	84.30%	434
102	2,448	0.06%	1.80%	2,258	0.06%	84.30%	190
103	2,315	0.06%	1.80%	2,398	0.06%	84.40%	-83
104	2,084	0.05%	1.70%	2,589	0.07%	84.50%	-505
105	1,998	0.05%	1.70%	2,532	0.06%	84.50%	-534
106	1,740	0.04%	1.60%	2,546	0.06%	84.60%	-806
107	1,700	0.04%	1.60%	2,591	0.07%	84.60%	-891
108	1,593	0.04%	1.50%	2,665	0.07%	84.70%	-1072
109	1,491	0.04%	1.50%	2,649	0.07%	84.80%	-1158
110	1,455	0.04%	1.40%	2,687	0.07%	84.80%	-1232
111	1,392	0.04%	1.40%	2,507	0.06%	84.90%	-1115
112	1,385	0.04%	1.40%	2,400	0.06%	85.00%	-1015
113	1,301	0.03%	1.30%	2,375	0.06%	85.00%	-1074
114	1,298	0.03%	1.30%	2,375	0.06%	85.10%	-1077
115	1,269	0.03%	1.30%	2,179	0.05%	85.10%	-910
116	1,338	0.03%	1.20%	2,166	0.05%	85.20%	-828
117	1,319	0.03%	1.20%	2,103	0.05%	85.20%	-784
118	1,286	0.03%	1.20%	2,056	0.05%	85.30%	-770
119	1,332	0.03%	1.10%	2,007	0.05%	85.40%	-675
120	1,292	0.03%	1.10%	1,850	0.05%	85.40%	-558
121	1,306	0.03%	1.10%	1,751	0.04%	85.40%	-445
122	1,334	0.03%	1.00%	1,676	0.04%	85.50%	-342
123	1,360	0.03%	1.00%	1,607	0.04%	85.50%	-247
124	1,384	0.04%	1.00%	1,496	0.04%	85.60%	-112
125	1,465	0.04%	0.90%	1,489	0.04%	85.60%	-24
126	1,440	0.04%	0.90%	1,347	0.03%	85.60%	93
127	1,408	0.04%	0.90%	1,227	0.03%	85.70%	181
128	1,451	0.04%	0.80%	1,247	0.03%	85.70%	204
129	1,477	0.04%	0.80%	1,195	0.03%	85.70%	282
130	1,439	0.04%	0.80%	1,170	0.03%	85.80%	269
131	1,547	0.04%	0.70%	1,042	0.03%	85.80%	505
132	1,455	0.04%	0.70%	972	0.02%	85.80%	483
133	1,414	0.04%	0.70%	942	0.02%	85.80%	472
134	1,380	0.04%	0.60%	897	0.02%	85.80%	483
135	1,454	0.04%	0.60%	858	0.02%	85.90%	596
136	1,311	0.03%	0.50%	822	0.02%	85.90%	489
137	1,208	0.03%	0.50%	757	0.02%	85.90%	451
138	1,128	0.03%	0.50%	770	0.02%	85.90%	358
139	1,115	0.03%	0.50%	717	0.02%	85.90%	398
140	1,062	0.03%	0.40%	689	0.02%	86.00%	373
141	912	0.02%	0.40%	624	0.02%	86.00%	288
142	858	0.02%	0.40%	657	0.02%	86.00%	201
143	831	0.02%	0.40%	719	0.02%	86.00%	112
144	748	0.02%	0.30%	641	0.02%	86.00%	107
145	684	0.02%	0.30%	614	0.02%	86.00%	70
146	549	0.01%	0.30%	579	0.01%	86.10%	-30
147	479	0.01%	0.30%	591	0.02%	86.10%	-112
148	460	0.01%	0.30%	588	0.02%	86.10%	-128
149	402	0.01%	0.30%	526	0.01%	86.10%	-124
150	380	0.01%	0.30%	545	0.01%	86.10%	-165
151	314	0.01%	0.20%	504	0.01%	86.10%	-190
152	301	0.01%	0.20%	475	0.01%	86.10%	-174
153	284	0.01%	0.20%	458	0.01%	86.20%	-174
154	247	0.01%	0.20%	405	0.01%	86.20%	-158
155	247	0.01%	0.20%	425	0.01%	86.20%	-178
156	223	0.01%	0.20%	365	0.01%	86.20%	-142
157	196	0.01%	0.20%	353	0.01%	86.20%	-157
158	207	0.01%	0.20%	343	0.01%	86.20%	-136
159	179	0.00%	0.20%	328	0.01%	86.20%	-149
160	153	0.00%	0.20%	332	0.01%	86.20%	-179
161	158	0.00%	0.20%	323	0.01%	86.20%	-165
162	159	0.00%	0.20%	307	0.01%	86.20%	-148
163	135	0.00%	0.20%	291	0.01%	86.20%	-156
164	130	0.00%	0.20%	273	0.01%	86.20%	-143
165	133	0.00%	0.20%	269	0.01%	86.30%	-136
166	123	0.00%	0.20%	256	0.01%	86.30%	-133
167	132	0.00%	0.20%	247	0.01%	86.30%	-115
168	120	0.00%	0.20%	233	0.01%	86.30%	-113
169	145	0.00%	0.20%	252	0.01%	86.30%	-107
170	122	0.00%	0.20%	236	0.01%	86.30%	-114
171	123	0.00%	0.20%	238	0.01%	86.30%	-115
172	126	0.00%	0.10%	246	0.01%	86.30%	-120
173	107	0.00%	0.10%	280	0.01%	86.30%	-173
174	120	0.00%	0.10%	271	0.01%	86.30%	-151
175	113	0.00%	0.10%	271	0.01%	86.30%	-158
176	128	0.00%	0.10%	301	0.01%	86.30%	-173
177	93	0.00%	0.10%	302	0.01%	86.30%	-209
178	98	0.00%	0.10%	344	0.01%	86.30%	-246
179	104	0.00%	0.10%	359	0.01%	86.30%	-255
180	101	0.00%	0.10%	377	0.01%	86.40%	-276
181	95	0.00%	0.10%	418	0.01%	86.40%	-323
182	71	0.00%	0.10%	371	0.01%	86.40%	-300
183	76	0.00%	0.10%	413	0.01%	86.40%	-337
184	55	0.00%	0.10%	453	0.01%	86.40%	-398
185	72	0.00%	0.10%	445	0.01%	86.40%	-373
186	73	0.00%	0.10%	483	0.01%	86.40%	-410
187	82	0.00%	0.10%	509	0.01%	86.40%	-427
188	75	0.00%	0.10%	514	0.01%	86.40%	-439
189	74	0.00%	0.10%	512	0.01%	86.50%	-438
190	56	0.00%	0.10%	542	0.01%	86.50%	-486
191	78	0.00%	0.10%	498	0.01%	86.50%	-420
192	69	0.00%	0.10%	484	0.01%	86.50%	-415
193	91	0.00%	0.10%	533	0.01%	86.50%	-442
194	81	0.00%	0.10%	448	0.01%	86.50%	-367
195	76	0.00%	0.10%	433	0.01%	86.50%	-357
196	80	0.00%	0.10%	442	0.01%	86.50%	-362
197	94	0.00%	0.10%	416	0.01%	86.60%	-322
198	81	0.00%	0.10%	407	0.01%	86.60%	-326
199	81	0.00%	0.10%	378	0.01%	86.60%	-297
200	94	0.00%	0.10%	395	0.01%	86.60%	-301
201	92	0.00%	0.10%	334	0.01%	86.60%	-242
202	122	0.00%	0.10%	363	0.01%	86.60%	-241
203	103	0.00%	0.10%	388	0.01%	86.60%	-285
204	97	0.00%	0.10%	327	0.01%	86.60%	-230
205	99	0.00%	0.10%	310	0.01%	86.60%	-211
206	125	0.00%	0.10%	335	0.01%	86.60%	-210
207	108	0.00%	0.10%	357	0.01%	86.60%	-249
>207	2,646	0.07%	0.10%	534,214	13.36%	100.00%	-531568

By the way, with your poor B.S., you'd be much better off taking this Martingale system to baccarat and betting the Banker each time, since there the house edge is just over 1%.

Hope this helps!

Dog Hand

DogHand –

You completely did what I was looking for! Thank you for taking the time to put all that together for me. I had to see it in black and white. The actual numbers were what I needed to understand it.

Thanks to everyone else for their input.

Some of us ONLY learn things in black and white. I believe NOTHING unless I can see the data.