GrogNerd. My apologies for saying "odds" when I should have said "probability".
Yes, 1 *to* 1 is the same thing as 1 *in* 2.
But my ticket wasn't giving odds. It was giving probabilities.
Probability with 1 ticket: 1 in 4. (Odds: 1 to 3)
Claimed probability with 2 tickets: 1 in 2. (Odds: 1 to 1)
This is *WRONG*!!! The actual probability is 7 in 16. (Odds: 7 to 9)
Then it gave the preposterous probabiltiy with 6 tickets as: More than 1 in 1 (Odds: Better than certain.)
In actuality the actual probabilty is 4-5 (Odds: 4 to 1) [Actually 3,267 in 4,096 and 3,267 to 729].
There. Does that clarify?
Whether probability or odds, you can't add them. If flipping heads is 1 in 2 (50%), then one could incorrectly conclude flipping the coin twice for a head would be 2 in 2 (100%). Obviously wrong. But if the odds are 1 to 1, one could incorrectly conclude flipping for one coin would be 2 to 1 (66%). Not so obviously wrong.
(The actual probability is 3 in 4 or in odds 3 to 1. (HH, HT, TH vs. TT))