Tri-State Heads or Tails Probability Calculations - Vermont Lottery

Order
No.
Multi-Hand
Probability Break-out Table
w1 w2 w3 w1+w2+w3 Probability of each of the Arrangements
189 5 1 2 8 8.1849E-07 * 3.7401E-01 * 8.0867E-02 = 2.4755E-08 Y
190 5 1 3 9 8.1849E-07 * 3.7401E-01 * 6.3842E-03 = 1.9544E-09 Y
191 5 1 4 10 8.1849E-07 * 3.7401E-01 * 1.6370E-04 = 5.0112E-11 Y
192 5 1 5 11 8.1849E-07 * 3.7401E-01 * 8.1849E-07 = 2.5056E-13 Y
193 5 2 0 7 8.1849E-07 * 8.0867E-02 * 5.3857E-01 = 3.5648E-08 Y
194 5 2 1 8 8.1849E-07 * 8.0867E-02 * 3.7401E-01 = 2.4755E-08 Y
195 5 2 2 9 8.1849E-07 * 8.0867E-02 * 8.0867E-02 = 5.3525E-09 Y
196 5 2 3 10 8.1849E-07 * 8.0867E-02 * 6.3842E-03 = 4.2257E-10 Y
197 5 2 4 11 8.1849E-07 * 8.0867E-02 * 1.6370E-04 = 1.0835E-11 Y
198 5 2 5 12 8.1849E-07 * 8.0867E-02 * 8.1849E-07 = 5.4175E-14 Y
199 5 3 0 8 8.1849E-07 * 6.3842E-03 * 5.3857E-01 = 2.8143E-09 Y
200 5 3 1 9 8.1849E-07 * 6.3842E-03 * 3.7401E-01 = 1.9544E-09 Y
201 5 3 2 10 8.1849E-07 * 6.3842E-03 * 8.0867E-02 = 4.2257E-10 Y
202 5 3 3 11 8.1849E-07 * 6.3842E-03 * 6.3842E-03 = 3.3361E-11 Y
203 5 3 4 12 8.1849E-07 * 6.3842E-03 * 1.6370E-04 = 8.5540E-13 Y
204 5 3 5 13 8.1849E-07 * 6.3842E-03 * 8.1849E-07 = 4.2770E-15 Y
205 5 4 0 9 8.1849E-07 * 1.6370E-04 * 5.3857E-01 = 7.2161E-11 Y
206 5 4 1 10 8.1849E-07 * 1.6370E-04 * 3.7401E-01 = 5.0112E-11 Y
207 5 4 2 11 8.1849E-07 * 1.6370E-04 * 8.0867E-02 = 1.0835E-11 Y
208 5 4 3 12 8.1849E-07 * 1.6370E-04 * 6.3842E-03 = 8.5540E-13 Y
209 5 4 4 13 8.1849E-07 * 1.6370E-04 * 1.6370E-04 = 2.1933E-14 Y
210 5 4 5 14 8.1849E-07 * 1.6370E-04 * 8.1849E-07 = 1.0967E-16 Y
211 5 5 0 10 8.1849E-07 * 8.1849E-07 * 5.3857E-01 = 3.6081E-13 Y
212 5 5 1 11 8.1849E-07 * 8.1849E-07 * 3.7401E-01 = 2.5056E-13 Y
213 5 5 2 12 8.1849E-07 * 8.1849E-07 * 8.0867E-02 = 5.4175E-14 Y
214 5 5 3 13 8.1849E-07 * 8.1849E-07 * 6.3842E-03 = 4.2770E-15 Y
215 5 5 4 14 8.1849E-07 * 8.1849E-07 * 1.6370E-04 = 1.0967E-16 Y
216 5 5 5 15 8.1849E-07 * 8.1849E-07 * 8.1849E-07 = 5.4833E-19 Y
Total of All Probabilities = 1.0000000
Win Both
Games
To calculate the probability of each tier one must add all the probabilities for a given w1+w2+w3. For example,
the number of ways of matching a sum of 4 is 15
.
Order
No.
w1 w2 w3
Probability of Matching "w1+w2+w3 =4"
w1
+w2
+w3
Probability of each of the arrangements
5 0 0 4 4 5.3857E-01 * 5.3857E-01 * 1.6370E-04 = 4.7483E-05
10 0 1 3 4 5.3857E-01 * 3.7401E-01 * 6.3842E-03 = 1.2860E-03
15 0 2 2 4 5.3857E-01 * 8.0867E-02 * 8.0867E-02 = 3.5220E-03
20 0 3 1 4 5.3857E-01 * 6.3842E-03 * 3.7401E-01 = 1.2860E-03
25 0 4 0 4 5.3857E-01 * 1.6370E-04 * 5.3857E-01 = 4.7483E-05
40 1 0 3 4 3.7401E-01 * 5.3857E-01 * 6.3842E-03 = 1.2860E-03
45 1 1 2 4 3.7401E-01 * 3.7401E-01 * 8.0867E-02 = 1.1312E-02
50 1 2 1 4 3.7401E-01 * 8.0867E-02 * 3.7401E-01 = 1.1312E-02
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