Tri-State Heads or Tails Probability Calculations - Vermont Lottery

The following breakout table describes all 216 arrangements, by Order Number and their corresponding
probabilities. The column “Win Both Games” is when an arrangement can win on both the Base Game and the
Multi-Hand Game. These Flags “Y” are used later on in the discussion of the over-all win in both games.
Order
No.
Multi-Hand
Probability Break-out Table
w1 w2 w3 w1+w2+w3 Probability of each of the Arrangements
1 0 0 0 0 5.3857E-01 * 5.3857E-01 * 5.3857E-01 = 1.5622E-01
2 0 0 1 1 5.3857E-01 * 5.3857E-01 * 3.7401E-01 = 1.0849E-01
3 0 0 2 2 5.3857E-01 * 5.3857E-01 * 8.0867E-02 = 2.3456E-02
4 0 0 3 3 5.3857E-01 * 5.3857E-01 * 6.3842E-03 = 1.8518E-03
5 0 0 4 4 5.3857E-01 * 5.3857E-01 * 1.6370E-04 = 4.7483E-05 Y
6 0 0 5 5 5.3857E-01 * 5.3857E-01 * 8.1849E-07 = 2.3741E-07 Y
7 0 1 0 1 5.3857E-01 * 3.7401E-01 * 5.3857E-01 = 1.0849E-01
8 0 1 1 2 5.3857E-01 * 3.7401E-01 * 3.7401E-01 = 7.5338E-02
9 0 1 2 3 5.3857E-01 * 3.7401E-01 * 8.0867E-02 = 1.6289E-02
10 0 1 3 4 5.3857E-01 * 3.7401E-01 * 6.3842E-03 = 1.2860E-03 Y
11 0 1 4 5 5.3857E-01 * 3.7401E-01 * 1.6370E-04 = 3.2974E-05 Y
12 0 1 5 6 5.3857E-01 * 3.7401E-01 * 8.1849E-07 = 1.6487E-07 Y
13 0 2 0 2 5.3857E-01 * 8.0867E-02 * 5.3857E-01 = 2.3456E-02
14 0 2 1 3 5.3857E-01 * 8.0867E-02 * 3.7401E-01 = 1.6289E-02
15 0 2 2 4 5.3857E-01 * 8.0867E-02 * 8.0867E-02 = 3.5220E-03
16 0 2 3 5 5.3857E-01 * 8.0867E-02 * 6.3842E-03 = 2.7805E-04 Y
17 0 2 4 6 5.3857E-01 * 8.0867E-02 * 1.6370E-04 = 7.1295E-06 Y
18 0 2 5 7 5.3857E-01 * 8.0867E-02 * 8.1849E-07 = 3.5648E-08 Y
19 0 3 0 3 5.3857E-01 * 6.3842E-03 * 5.3857E-01 = 1.8518E-03
20 0 3 1 4 5.3857E-01 * 6.3842E-03 * 3.7401E-01 = 1.2860E-03 Y
21 0 3 2 5 5.3857E-01 * 6.3842E-03 * 8.0867E-02 = 2.7805E-04 Y
22 0 3 3 6 5.3857E-01 * 6.3842E-03 * 6.3842E-03 = 2.1951E-05 Y
23 0 3 4 7 5.3857E-01 * 6.3842E-03 * 1.6370E-04 = 5.6286E-07 Y
24 0 3 5 8 5.3857E-01 * 6.3842E-03 * 8.1849E-07 = 2.8143E-09 Y
25 0 4 0 4 5.3857E-01 * 1.6370E-04 * 5.3857E-01 = 4.7483E-05 Y
26 0 4 1 5 5.3857E-01 * 1.6370E-04 * 3.7401E-01 = 3.2974E-05 Y
27 0 4 2 6 5.3857E-01 * 1.6370E-04 * 8.0867E-02 = 7.1295E-06 Y
28 0 4 3 7 5.3857E-01 * 1.6370E-04 * 6.3842E-03 = 5.6286E-07 Y
29 0 4 4 8 5.3857E-01 * 1.6370E-04 * 1.6370E-04 = 1.4432E-08 Y
30 0 4 5 9 5.3857E-01 * 1.6370E-04 * 8.1849E-07 = 7.2161E-11 Y
31 0 5 0 5 5.3857E-01 * 8.1849E-07 * 5.3857E-01 = 2.3741E-07 Y
32 0 5 1 6 5.3857E-01 * 8.1849E-07 * 3.7401E-01 = 1.6487E-07 Y
33 0 5 2 7 5.3857E-01 * 8.1849E-07 * 8.0867E-02 = 3.5648E-08 Y
34 0 5 3 8 5.3857E-01 * 8.1849E-07 * 6.3842E-03 = 2.8143E-09 Y
35 0 5 4 9 5.3857E-01 * 8.1849E-07 * 1.6370E-04 = 7.2161E-11 Y
36 0 5 5 10 5.3857E-01 * 8.1849E-07 * 8.1849E-07 = 3.6081E-13 Y
37 1 0 0 1 3.7401E-01 * 5.3857E-01 * 5.3857E-01 = 1.0849E-01
38 1 0 1 2 3.7401E-01 * 5.3857E-01 * 3.7401E-01 = 7.5338E-02
39 1 0 2 3 3.7401E-01 * 5.3857E-01 * 8.0867E-02 = 1.6289E-02
40 1 0 3 4 3.7401E-01 * 5.3857E-01 * 6.3842E-03 = 1.2860E-03 Y
41 1 0 4 5 3.7401E-01 * 5.3857E-01 * 1.6370E-04 = 3.2974E-05 Y
42 1 0 5 6 3.7401E-01 * 5.3857E-01 * 8.1849E-07 = 1.6487E-07 Y
43 1 1 0 2 3.7401E-01 * 3.7401E-01 * 5.3857E-01 = 7.5338E-02
44 1 1 1 3 3.7401E-01 * 3.7401E-01 * 3.7401E-01 = 5.2318E-02
Win Both
Games
4 - 10