Mad Hatters probabilities

[MrVan]

The recent 1.2 million coin win on Mad Hatters in the screenshots thread got me thinking.... I understand that on a standard slot the long term payout is the same no matter how many lines you play, but what about on a slot like Mad Hatters with an expanding wild symbol?

For example, lets say you play 5 lines and get a jackpot win of five wilds on line five (positions 3-2-1-2-3).

Because of the expanding reel, if you had been playing 15 lines you would have won on line 13 (3-2-2-2-3) and line 15 (3-2-3-2-3).

But.... what if you are only playing 13 lines? Even with the expanding wild in the middle, it is impossible for you to win the jackpot on more than two lines in one spin! So your maximum possible jackpot (not considering jackpot during free spins) is 40,000 x the line bet, while it is 60,000 x the line bet for playing just 2 more lines.

Another example, you play 15 lines and win the jackpot on line 1 (2-2-2-2-2), playing just 2 more lines would have tripled your jackpot win with additional wins on line 16 (2-2-1-2-2) and line 17 (2-2-3-2-2). So by increasing your bet by 13% you increase your potential max payout by 200%!

Consider getting five wilds on lines 8, 9, 10, 11, 26, 27, 28, or 30, even with the expanding reel you only will win the jackpot on one line, and five wilds on 2, 3, 18, or 19 will only win you two jackpots.

SO.... Right now I truly believe that playing 17 lines will give you a maximum return (EDIT- or at least better than 30 lines) on Mad Hatters. Can anyone prove me wrong mathematically??

Had the person in the screenshots thread been playing 18 coins an 17 lines (306 coin total bet), that win would have been over 2.16 million coins instead of 1.2 million.

[Zoozie]

SO.... Right now I truly believe that playing 17 lines will give you a maximum return (EDIT- or at least better than 30 lines) on Mad Hatters. Can anyone prove me wrong mathematically??

Yes, I can prove you wrong.
EV is the same no matter how many lines you play also with the expanding wild on reel3.


You need to define 'Maximum return'. With slots it is normally the EV or payout%.

I can prove the EV is still the same no matter how many lines you play also in the case with the expanding wild on reel 3. Actually it is the same proof as in the case without the expanding wild. Iterate through all combinations of the reels and realize two different lines will have excactly the same wins even with the expanding wild.

Just to confirm it I ran the simulation on the slot-simulator. I took Thunderstruck and then made reel3 all wilds and the simulator showed EV was independant on the number of lines. ( I tried 1,2,3,4,5,9,15,16,17,18,25). The payout for that slot was 606.34% btw.

You are right that adding just 1 more line can result in winning one more jackpot in same spin. But you only add this line in one of the few combinations where it actually does hit the jackpot. You need to add it to all combinations of spins, and it is just actually the same as any other line in EV.

You concluded that 17 lines is the minimum number of lines to win 3 jackpots in 1 spin. This probably right (didnt check). But it does not mean it has best EV.

In your measure it is 3/17 jackpots/line which is better than 1/15 jackpot/line. However it would be even better to just play 1 line, which would give you 1/1=1 jackpot/line. But playing bet 17 on just 1 line has the same betsize
but now 17/1=17 jackpot/line.

Remember the added cost for the extra lines. Basically more lines just decreases you variance. I prefer playing 5 lines on Isis for very high variance. Less than 5 is a little boring for me. But 5 is good.

Zoozie

[Alexandre]

Hi,

What is the slot simulator ?

Alex

[MrVan]

Thanks for the reply! I guess it does make sense that the payout % would be the same, but would the change of variance depend on the line layout?

To really simplify it, imagine two machines with three lines each, where machine #1 has the lines 1-1-1-1-1, 2-2-2-2-2, and 3-3-3-3-3, and machine #2 has the lines 2-2-2-2-1, 2-2-2-2-2, and 2-2-2-2-3. Wouldn't the variance on machine #2 be much higher because when any number between 1 and 4 symbols line up the win is tripled. and when a five line win finally hits it also includes two 4 line wins? I guess this is really what I was trying to figure out since I had a feeling that the payout % wouldn't be different.

[Zoozie]

What is the slot simulator ?

You can download it from this thread:
http://www.casinomeister.com/forums/...lities-18.html

[Zoozie]

Thanks for the reply! I guess it does make sense that the payout % would be the same, but would the change of variance depend on the line layout?

Yes, this is correct! Statistically this is called the co-variance.
If you have 5 wild on line 1, then you can not have 5 wilds on line 2 also. ( when wilds only occour once on each reel).

The size of the co-variance between two lines do depend on
1) The reels (the order of the symbols)
2) The definition of the 2 lines (even when they share no symbols they are co-related)

When the number of lines increase, so does the variance, but it is right that this increasement is not 'constant' or simple, they do matter on 1) and 2).

So this is not the same as multi-hand video poker where the variance increasement only depend on a very few factors besides the number of lines/hands.

Zoozie

[MrVan]

cool.... the reason I want to figure this out is because I feel a slot machine is the most fun to play when the variance is low and the line bet is high (i.e. few lines played). It would be interesting to see a graph of variance vs. # of lines, make a best fit line of the graph, and then find the points that are farthest below and above the best fit line to determine the lowest and highest variance/line combination.

[Zoozie]

It would be interesting to see a graph of variance vs. # of lines, make a best fit line of the graph, and then find the points that are farthest below and above the best fit line to determine the lowest and highest variance/line combination.

If you take 'Simulate'-mode in the slot-simulator it calculates the variance also.

However it takes a very long simulation time (hour at least) since the
variance converge very slowly. Since variance increases with bet naturally maybe a good measure would be variance/#lines since

Just change the number of lines for Thunderstruck etc. and run the simulate mode for different number of lines. Post the graph here if you make one

Zoozie

[paul02085]

I sure am glad we have wizards like Zoozie at this forum to help educate us about these issues

[jetset]

I'll join you in that sentiment, Paul - she makes a significant and valued contribution here imo.