Columnist; Science and Academics
Lotto America is a lottery game offering a rollover jackpot and fixed prizes, as well as a multiplier add-on. It is similar in structure to Powerball, but with fewer numbers in both pools and a much lower second-tier prize.
Category
Lotto America is a combinatorial lottery game drawing from two pools: six numbers drawn from 1 – 52 (the base draw) and one number from 1 – 10 (the Star Ball).
Size of the draw: 5 + 1 = 6.
Size of a played line: 6.
Cost of a line: $1.
The game has one add-on: The All Star Bonus feature (for an additional $1), in which you can multiply your base prize. The multiplier is drawn automatically for each ticket before the number draw from 5 multipliers (2x, 3x, 4x, 5x). The multiplier applies to all prizes except the jackpot.
Prizes
There are nine tiers of prizes in the base draw, defined as matching 1 to 6 numbers (one is for the Star Ball and two for a base ball and the Star Ball). They are all fixed prizes, except the top prize (6 numbers matched), which is a rolling-over.
The prizes do not increase uniformly from the lowest to the highest. There is an abrupt jump between the first two tiers, i.e., from jackpot to $20,000, as well as between the second and the third tier, i.e., from $20,000 to $1,000, also for the corresponding odds of winning.
Lotto America was launched in February 1988 under the name of Lotto*America and is available in 16 jurisdictions. Photograph credit: Mehaniq / Shutterstock.com.
The odds of winning
The odds of winning with one line range from 1 in 25,989,600 (for the jackpot) to 1 in 17 (for the lowest tier). The overall odds of winning any prize are 1 in 7.61. The overall odds of winning any money prize in the base draw are 1 in 9.63.
The same odds apply if the All Star Bonus feature is activated.
In the next table are noted the odds of winning each possible amount, by taking into account the prize odds and the multiplier odds. These should be interpreted as a priori odds, before any information is available (before the ticket is printed).
| Prize | Ways to win it | Odds |
|---|---|---|
|
Jackpot |
Match 5 + 1 |
1 in 25,989,600 |
|
$100,000 |
Match 5 and 5× |
1 in 30,802,489 |
|
$80,000 |
Match 5 and 4× |
1 in 23,101,867 |
|
$60,000 |
Match 5 and 3× |
1 in 9,240,747 |
|
$40,000 |
Match 5 and 2× |
1 in 6,160,498 |
|
$5,000 |
Match 4 + 1 and 5× |
1 in 1,179,670 |
|
$4,000 |
Match 4 + 1 and 4× |
1 in 884,752 |
|
$3,000 |
Match 4 + 1 and 3× |
1 in 353,901 |
|
$2,000 |
Match 4 + 1 and 2× |
1 in 235,934 |
|
$500 |
Match 4 and 5× |
1 in 131,074 |
|
$400 |
Match 4 and 4× |
1 in 98,306 |
|
$300 |
Match 4 and 3× |
1 in 39,322 |
|
$200 |
Match 4 and 2× |
1 in 26,215 |
|
$100 |
Match 3 + 1 and 5× |
1 in 25,645 |
|
$80 |
Match 3 + 1 and 4× |
1 in 19,234 |
|
$60 |
Match 3 + 1 and 3× |
1 in 7,694 |
|
$40 |
Match 3 + 1 and 2× |
1 in 5,129 |
|
$25 |
Match 3 and 5× OR Match 2 + 1 and 5× |
1 in 1,080 |
|
$20 |
Match 3 and 4× OR Match 2 + 1 and 4× |
1 in 802 |
|
$15 |
Match 3 and 3× OR Match 2 + 1 and 3× |
1 in 321 |
|
$10 |
Match 3 and 2× OR Match 2 + 1 and 2× OR Match 1 + 1 and 5× OR Star Ball only and 5× |
1 in 107.0 |
|
$8 |
Match 1 + 1 and 4× OR Star Ball only and 4× |
1 in 85.0 |
|
$6 |
Match 1 + 1 and 3× OR Star Ball only and 3× |
1 in 34.4 |
|
$4 |
Match 1 + 1 and 2× OR Star Ball only and 2× |
1 in 23.0 |
Surprisingly, the odds of winning $100,000 are lower than the odds of winning the jackpot, and the odds of winning $80,000 are close to those.
This phenomenon is common across lotteries with pre-draw multipliers with uneven probabilities, where prizes of a lower amount can become rarer than the jackpot when viewed a priori. That does not mean they are harder to win after the multiplier has already been drawn.
Average win and fairness
The next table lists the average win for each money prize in the base draw (no multiplier applied):
| Prize tier | Prize amount | Average win |
|---|---|---|
|
Match 5 + 1 |
Jackpot |
Jackpot : 25,989,600 |
|
Match 5 |
$20,000 |
$0.006926 |
|
Match 4 +1 |
$1,000 |
$0.009042 |
|
Match 4 |
$100 |
$0.008138 |
|
Match 3 + 1 |
$20 |
$0.008319 |
|
Match 3 |
$5 |
$0.018717 |
|
Match 2 + 1 |
$5 |
$0.031195 |
|
Match 1 + 1 |
$2 |
$0.068634 |
|
Match Star Ball |
$2 |
$0.118064 |
For an average jackpot of $11.46 millions*, the average win is $0.44097.
One way to interpret this table is that over the long run, a win in the Match 4 + 1 tier is distributed as $0.009042 average win per line played (assuming the prize is won with the relative frequency of about 1 in 110,594 draws).
The next table lists the fairness of each prize relative to its probability:
| Prize tier | Prize amount | Fairness |
|---|---|---|
|
Match 5 + 1 |
Jackpot |
- |
|
Match 5 |
$20,000 |
0.69% |
|
Match 4 +1 |
$1,000 |
0.90% |
|
Match 4 |
$100 |
0.80% |
|
Match 3 + 1 |
$20 |
0.79% |
|
Match 3 |
$5 |
1.50% |
|
Match 2 + 1 |
$5 |
2.51% |
|
Match 1 + 1 |
$2 |
3.55% |
|
Match Star Ball |
$2 |
6.27% |
For an average jackpot of $11.46 millions*, its fairness would be 44.09%. However, this only applies in the circumstance where such a jackpot is actually won, as rollovers actually mean zero prizes in this tier.
*Note: The average jackpot was chosen as the average of the jackpots won since 2017.
Lotto America's $1 price point has kept it popular, even when competing with billion-dollar-jackpot giants like Powerball and Mega Millions. Photograph credit: Ringo Chiu / Shutterstock.com.
Expected value and house edge
The precise expected value of the Lotto America game cannot be obtained, as the first-tier prize is variable. It is yet relevant to estimate it in two cases, associated with two assumptions:
a) The first case is taking the jackpot amount as zero (case justified by a long series of draws when the jackpot is not won, given its probability).
b) The second case is taking an average amount for the jackpot won over a period of time (in this case, since the game launched in 2017).
In case a), the expected value is −$0.730965, or –73.10% as a percentage of the line cost. The house edge of the game is 73.10%.
In case b), the expected value is −$0.289995, or –29.00% as a percentage of the line cost. The house edge of the game is 29.00%.
One way to interpret this is that, in case a) you are expected to lose on average $0.73 at every $1 invested, over the long run.
The above values correspond to the base play.
With the All Star Bonus feature activated:
In case a), the expected value is −$1.234540, or –61.73% as a percentage of the line cost. The house edge of the game is 61.73%.
In case b), the expected value is −$0.793570, or – 39.68% as a percentage of the line cost. The house edge of the game is 39.68%.
This means that, in case a) you are expected to lose on average $1.23 at every $2 invested, over the long run.
Final remarks
With a relatively decent second-tier prize and a cost of only $1 per line, Lotto America is suitable for group play.
Although the odds of winning are far higher than in Powerball (about 11 times for the jackpot and about 4 times for the second-tier prize), the house edge is not much different between the two games.
Activation of the All Star Bonus reduces the house edge of the game when we don't consider the jackpot.
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