How long is long run?
In the long run, a card counter with advantage will win. In the short term, luck will play a big role. But in the long run probability will win. But how long is long run?
Consider a card counter playing a
single deck game (Dealer hits Soft 17, no Double after
The following table shows the probability of reaching your goal for a given period of time. It also gives the Standard Deviation. If E is your expected earnings per hour and S is your standard deviation, then there is a 67 % chance that your actual earnings/hour will be between E – S and E + S. There is a 95% percent chance that your actual earnings/hour will be between E – 2 S and E + 2 S. There is almost a 100% chance that your actual earnings/hour will be between E - 3 S and E + 3 S.
The following table is based on 100 rounds per hour. 8 hours per day. 40 hours per week and 23 days per month.
Expected Earnings = 39.0 $/hour
|
Time |
Probability of Earning at least 0 $/hour |
Probability of Earning at least 50 % of expected earnings
(19.5 $/hour) |
Probability of Earning at least 90 % of expected earnings
(35.1 $/hour) |
Standard Deviation |
|
1 hour |
55.9 % |
53.0 % |
50.0 % |
273.8 $/hour |
|
2 hours |
58.1 % |
54.1 % |
50.4 % |
193.8 $/hour |
|
1 day |
65.6 % |
57.7 % |
51.2 % |
97.2 $/hour |
|
2 days |
71.3 % |
60.7 % |
51.9 % |
68.7 $/hour |
|
1 week |
81.1 % |
66.9 % |
53 % |
43.2 $/hour |
|
2 weeks |
89.6 % |
73.4 % |
54 % |
30.6 $/hour |
|
1 month |
97.5 % |
83.4 % |
56.3 % |
20.5 $/hour |
|
2 months |
100 % |
90.7 % |
58.5 % |
14.3 $/hour |
|
6 months |
100 % |
99.3 % |
67.9 % |
8.2 $/hour |
|
1 year |
100 % |
100.0 % |
74.6 % |
5.8 $/hour |
|
2 years |
100 % |
100.0 % |
82.6 % |
4.1 $/hour |
|
5 years |
100 % |
100.0 % |
93.2 % |
2.6 $/hour |
|
10 years |
100 % |
100.0 % |
97.8 % |
1.9 $/hour |
|
20 years |
100 % |
100.0 % |
99.7 % |
1.4 $/hour |
|
50 years |
100 % |
100.0 % |
100.0 % |
0.9 $/hour |
If you play for 1 month, you are almost certain not to lose money. But you do not have guarantee of reaching 90% of your expected earnings even if you play for 2 years. A good expectation to have is 50 % of your theoretical expected earnings. Thus if your expected earnings is 39 $/hour, you should have a good chance of earning at least 19.5 $/hour if you play for 2 months.