Spin Lotto

Spin Lotto is mathematically like the lottery, but skinned like a slot machine. It involved picking five numbers from 1 to 49 and a Star Ball (like the PowerBall) from 1 to 15. If the player super sizes his bet, he can multiply any wins involving the Star Ball, except the jackpot.

For all the rules and analysis, please see my new page on the game. I welcome all comments.

The question for the poll is would you play Spin Lotto? Multiple votes allowed.

Choice 5 should read, "Why did the uniforms change color, from orange to blue, on Orange is the New Black?" There is a limit to the number of characters.

I'm a little confused. Rule #3 states...

Quote:

3. The game will draw 15 balls, without replacement, from 1 to 49. These will be arranged in five columns of three rows each.

...and yet, in the OP screen shot, the numbers "4" and "42" appear twice suggesting each reel contains balls 1-49.

Quote: Gialmere

I'm a little confused. Rule #3 states...

Quote:
3. The game will draw 15 balls, without replacement, from 1 to 49. These will be arranged in five columns of three rows each.

...and yet, in the OP screen shot, the numbers "4" and "42" appear twice suggesting each reel contains balls 1-49.

First, I agree with Gialmere. The game draws 15 balls WITH replacement. That is clear in the explanation of the rules of the Gluck website, where it explains the payoff if you have, for example, picked the number 1 and then one of the lines comes out as 1-1-1-1-1.

So I suspect the return or house edge will need to be recalculated.

Also, from the tables on the WOO page dealing with the lucky star multiplier, I can't understand whether the analysis was done correctly. I note that when your star ball is in the middle row, there are 4 possible lines that can win, whereas when it is in the the upper or lowest row, there are only three possible ways to win a line.

There are 15 spots that can match your 5 numbers and you can have anything from 0 to 15 matches, although the most likely results will be 1X or 2X. Each spot has a 5/49 probability of being a match, independent of what happens with other spots.

Le's refer to the rows as A, B,C starting from the top row, and the columns as 1,2,3,4,5 starting with the left-most column.

A1 A2 A3 A4 A5
B1 B2 B3 B4 B5
C1 C2 C3 C4 C5

Spots B1, A2, C3, A4 and B5 have different properties than the other 10 spots because they each contribute to 4 lines, whereas the other 10 spots only contribute to 3 lines.

Define:
Power spots: B1, A2, C3, A4 and B5
Ordinary spots: A1,A3,A5,B2.B3,B4, C1.C2.C4,C5

When you have 2 -and only 2 -matches and both are in power spots

B1/B5 produces 4 lines with 2 matches each

A2/A4 produces 3 lines with 2 matches each and 2 lines with 1 match

B1/A2, B1/C3, B1/A4, A2/B5, C3/B5 and A4/B5 produce 2 lines each with 2 matches and 4 lines with 1 match

A2/C3 and A4/C3 produce only 1 line with 2 matches (and 6 lines with 1 match)

so that's an average of 2.1 lines with 2 matches and 3.8 lines with 1 match

When you have 2 -and only 2 -matches and both are in the same column

A1/B1, B1/C1, A2/B2, A2/C2, A3/C3, B3/C3, A4/B4, A4/C4, A5,/B5, B5/C5 will have No lines with 2 matches and 7 lines with 1 match.
A1/C1, B2/C2, A3/B3, B4/C4, A3/B3 will have No lines with 2 matches and only 6 lines with 1 match.

So, that is 0 lines with 2 matches and an average of 6.667 lines with 1 match.

For, now, I will punt on the other "2 matches" cases.

This methodological approach becomes very difficult when you have to work out the scenarios for when you have either 7 or 8 matches.

Quote: gordonm888

There are 15 spots that can match your 5 numbers and you can have anything from 0 to 15 matches, although the most likely results will be 1X or 2X. Each spot has a 5/49 probability of being a match, independent of what happens with other spots.

I dunno. I've been messing with it and, although duplicate numbers are fairly common, you never see them on the same column. I'm thinking each column is a slot reel with every ball being randomly generated for the three spots without replacement. So...

Quote: gordonm888

Let's refer to the rows as A, B,C starting from the top row, and the columns as 1,2,3,4,5 starting with the left-most column.

A1 A2 A3 A4 A5
B1 B2 B3 B4 B5
C1 C2 C3 C4 C5

...assume you picked numbers 1-5. If #1 lands on the A1 stop it cannot land on B1 or C1 and therefore their chances are reduced to 4/49. If, on the same spin, #2 lands on B1, then C1 is reduced to a 3/49.

If true, how does this affect the return% math?

P.S. It's not a burning issue so don't bother if it sounds tiresome, but thank you for your analysis above. I'm not a math wiz but find this stuff fascinating.

You guys are absolutely right that numbers can repeat. After playing for a while, I have never seen the same ball in the same column. This leads me to believe each column is drawn from a separate pool of 49 balls, without replacement.

That said, I redid the math under these rules and the odds turn out the same. I must admit I wasn't expecting that. I will have to think about an explanation in simple English why the odds are the same.

I noticed the same thing! Why is this happening?

I looked at my original spreadsheet and the formula would be that for if all 15 balls were drawn WITH replacement. Yes, I know I said "without replacement" on my site. As I try to think about it, my math without replacement didn't match that claimed in the help file of the game, but there was a match with replacement. So, I went with that, but forgot to update the rules. Sorry for the laziness.

Here is what the math would like like if the whole game were dealt without replacement.

Catch	Star	Pays	Combinations	Probability	Return
0	No	-	15,204,112	0.531552	0.000000
1	No	-	9,502,570	0.332220	0.000000
2	No	5	1,854,160	0.064823	0.324117
3	No	25	132,440	0.004630	0.115756
4	No	250	3,080	0.000108	0.026920
5	No	1,000	14	0.000000	0.000489
0	Yes	-	1,086,008	0.037968	0.000000
1	Yes	5	678,755	0.023730	0.118650
2	Yes	10	132,440	0.004630	0.046302
3	Yes	50	9,460	0.000331	0.016537
4	Yes	500	220	0.000008	0.003846
5	Yes	10,000	1	0.000000	0.000350
Total			28,603,260	1.000000	0.652967