Deconstructing Hot Roll

As I've said many times, I strongly believe that the player should have the right to know the rule of any casino game. That is usually the case. However, with slot machines, most players just stuff money in, hope to be amused for a while, and not lose too much of their hard earned dollar. Whenever I hear a slot player telling a story of a big win I always hear him/her remark "I had no idea why I won."

Partially for the reason, I've taken it upon myself to try to show my readers how slot machines are programmed. I presented various different deconstructions already. However, I've been overdue to do another one. For my latest one I went back to doing a three-reel game. This one is called Hot Roll. It features 20 paylines and a craps based bonus round.

So, please check out my page on Deconstructing Hot Roll. As always, I welcome all comments, questions, and corrections.

Also, my thanks to miplet for helping me confirm the math as well as for Lion's Share.

Here's a nit...I haven't read the whole page and probably won't get to...

Quote:

Hot Roll is a 3-reel slot by IGT.

I would add the word "machine"(or something)

And I would define who IGT is, distributor, manufacturer...whatever-I don't know, but let's choose distributor, then I would say...distributed by IGT

Hot Roll is a 3-reel slot machine distributed by IGT

and maybe add something to the end to make it flow a little better...like "that can be found at various casinos". So the whole thing would read like this:

Hot Roll is a 3-reel slot machine distributed by IGT that can be found at various casinos.

or

Hot Roll is a 3-reel slot machine distributed by IGT that can be found at various casinos in Las Vegas.

I'm almost positive I've seen Hot Roll tacked onto different base games as well, other than just Triple Double Diamond. (However, they were all visually similar, in the sense of it being a 3-reel, multi-line.)

Quote: Venthus

I'm almost positive I've seen Hot Roll tacked onto different base games as well, other than just Triple Double Diamond. (However, they were all visually similar, in the sense of it being a 3-reel, multi-line.)

It is. They had it on some other base games at the Golden Nugget.

Love Hot Roll!!! Good choice! Suggested changes below. There was a bit of a math oopsie. And some random copy/paste errors. :(

Hot Roll Pay Table
Event Pays
Three triple diamonds (20th payline) 100,000 20,000

***Note: All Paytables including this pay event need to be corrected, and returns adjusted in multiple places. Also may want to calculate return with all Triple Triple Triples being 1200X to determine non-max bet return.

9. If the player gets three Triple Diamonds on the 20th pay line, and makes a maximum bet, then he shall win 100,000 total credits, instead of the usual 1,200 times line bet for three Triple Diamonds. This jackpot is flat and not multiplied by the amount bet per line.




The total number of possible combinations is 256^3 = 16,777,216. Dividing the total return combinations in the lower right cell of 10,717,885 by the total possible combinations of 16,777,216 we get 63.88%.


After the Payline 1 Return Table:

Since the reel stops are weighted, this analysis must be repeated for each payline. To prevent this page from getting too long for the other 19 paylines I will just present the return in the following table. Note the bottom right cell shows an average return for the base game of 68.73%.
(Note: See below for return change details and the base game return needs to be changed in multiple locations)


These Three Tables:

Win Combinations over all 20 Paylines

The 15 combinations for Triple Triple Triple on line 20, are NOT summed into the totals. Total winning combos looks to be 24,500,900, not 24,500,885

Expected wins over all 20 Paylines
Possibly same issue as above table, but doesn't matter thanks to rounding.

Expected wins return over all 20 Paylines

Three triple diamonds 100000 20000 0.001125 0.017881 0.001125 0.017881
Three triple diamonds 1200 0.046941 0.048065 0.048065

That table may have had summing issues too, I'm not sure.

Win Summery Summary over all 20 Paylines
Win Count Expected Return
100000 20000 15 0.00000089 0.089407 0.017881

After paytable adjustments...new answers should be...

New max bet Base Return: 13.746532 cents per spin = 68.73% return for base spin

Non max bet Base Return: 13.729724 cents per spin = 68.65% return for base spin

So, the average win per bonus is 1.666667 1.1666667+ 5 × 3.733333 = 19.833333.

As a reminder, the bonus is triggered if the player gets three Hot Roll symbols anywhere on the screen. To determine the probability of it occurring on each reel, we also need to examine the blank stops immediately above and below the Hot Roll symbol that touch the center payline. For reel 1 there are, 18 (blank) + 25 (Hot Roll) + 19 (blank) = 62 stops that when touching the center payline make the Hot Roll symbol appear anywhere in reel 1, yielding a probability of 62/256 = 0.242188.

Final overall returns look to be (double check obv): 91.16% (max bet); 91.08% (non-max bet).

Quote: tringlomane

Final overall returns look to be (double check obv): 91.16% (max bet); 91.08% (non-max bet).

I don't understand the source of the increased return for max bet. By offering a special jackpot on the 20th line, players are incentivized to play max lines, but they don't have any choice in the matter.

So the return should be the same for any number of coins, assuming the top jackpot scales from 20,000 to 100,000 as you indicated. The way I understand the Wizard's write-up, it sounds like the return would actually diminish for betting additional coins per line.

Quote: gpac1377

I don't understand the source of the increased return for max bet. By offering a special jackpot on the 20th line, players are incentivized to play max lines, but they don't have any choice in the matter.

So the return should be the same for any number of coins, assuming the top jackpot scales from 20,000 to 100,000 as you indicated. The way I understand the Wizard's write-up, it sounds like the return would actually diminish for betting additional coins per line.

No, it's 100,000 credit award for Triple Triple Triple on line 20 when you max bet (5 credits per line). If you bet 1 credit per line, you just win 1200 on line 20. Bet 4 credits per line, you win 4800.

I'm pretty sure Wiz misread the fine print in the picture. I've played the game before, also if you zoom in on his picture enough, you can read the fine print. It's an eye test though.

Quote: tringlomane

No, it's 100,000 credit award for Triple Triple Triple on line 20 when you max bet (5 credits per line). If you bet 1 credit per line, you just win 1200. Bet 4 credits per line, you win 4800.

Perfect, thanks, I couldn't read the fine print.

In that case I'll complain about the poor incentive. They're enticing the player to cough up maximum coins, with only a negligible benefit :(

Quote: gpac1377

Perfect, thanks, I couldn't read the fine print.

In that case I'll complain about the poor incentive. They're enticing the player to cough up maximum coins, with only a negligible benefit :(

Yeah, I wonder how much it makes players play $1 vs. some other amount. Probably a lot since a lot of slotters are in the $1 range anyway...

Hell, it looks like max bet is 200 credits! So yeah, change 20,000 to 10,000.

Will edit post later if Wiz doesn't see this first. I gotta eat.

From the write-up:

Quote:

Per Nevada law, the outcome of each die is independent and each side has a 1/6 probability, as with real dice.

It's amusing that the representation of actual gambling implements forces them to generate honest outcomes.

That's probably not true online. I'm thinking of MyVegas, which admittedly is not real-money. The Frontier Fortune slot game, for example, uses representations of playing cards in the high-low bonus, and I doubt that it's programmed honestly. (I haven't played it recently. I should probably look again.)

Quote: tringlomane

Hell, it looks like max bet is 200 credits!

Good catch. I see it now on the glass. The penny slot players really get hosed when they succumb to the temptation of betting multiple coins per line.

Wheels can be still weighted, which is dumb.

Yeah, myVegas can give an outcome that is not representative of a standard deck.

Quote: tringlomane

There was a bit of a math oopsie.

That was my misunderstanding of the rules. I thought any jackpot on the 20th payline paid 100,000 coins. However, you're absolutely right that the 100,000 is based on a five ten-coin bet. Per bet, the win is 20,000. So I just fixed that and hopefully corrected all the pertinent places.

Thank you also for the copy/paste corrections and the suggestions on the added wording.

You definitely went beyond the call of duty with your proofreading. For that, I would be happy to buy you a drink or a meal sometime whenever you're in Vegas. Also note you are now recognized in the acknowledgment section at the bottom. Thank you very much!

Quote: Wizard

That was my misunderstanding of the rules. I thought any jackpot on the 20th payline paid 100,000 coins. However, you're absolutely right that the 100,000 is based on a five-coin bet. Per bet, the win is 20,000. So I just fixed that and hopefully corrected all the pertinent places.

Thank you also for the copy/paste corrections and the suggestions on the added wording.

You definitely went beyond the call of duty with your proofreading. For that, I would be happy to buy you a drink or a meal sometime whenever you're in Vegas. Also note you are now recognized in the acknowledgment section at the bottom. Thank you very much!

Thanks!!! But sorry I didn't watch your video first, which opened another can of worms. :( See PM for further corrections.

Quote: tringlomane

Thanks!!! But sorry I didn't watch your video first, which opened another can of worms. :( See PM for further corrections.

I didn't get any PM.

Quote: Wizard

I didn't get any PM.

Eh, I delayed it a bit. It's there now.

Maybe I'm missing something, but it appears you could increase the payout from the machine a whopping 5.856% by just playing 11 lines? That would get it up around 96% payout for a penny slot, which is not too shabby by slot standards. (taking advantage of pay lines 10 & 11). I wonder if that large bump is typical for the middle pay lines? That could be useful for something like a 5$ multi-line machine that might have a standard payout of 96.5% (maybe even make such a game advantage play after comps?)

Quote: brindle

Maybe I'm missing something, but it appears you could increase the payout from the machine a whopping 5.856% by just playing 11 lines? That would get it up around 96% payout for a penny slot, which is not too shabby by slot standards. (taking advantage of pay lines 10 & 11).

I noticed that as well, but it's mandatory to play all 20 lines. This is from the video:



It looks like the other four line selection buttons are disabled.

But payline differentials could be a factor in other games we don't know about.

Quote: brindle

Maybe I'm missing something, but it appears you could increase the payout from the machine a whopping 5.856% by just playing 11 lines? That would get it up around 96% payout for a penny slot, which is not too shabby by slot standards. (taking advantage of pay lines 10 & 11). I wonder if that large bump is typical for the middle pay lines? That could be useful for something like a 5$ multi-line machine that might have a standard payout of 96.5% (maybe even make such a game advantage play after comps?)

Unless something has changed, in Nevada the payout percentage is not allowed to be lower for a larger bet on the same game. Also, there can not be more than a 4% difference between the worst bet and the best bet on a game. I only bring this up because a game of mine was recently rejected because the minimum bet returned 89% and the max bet returned 94%. I ended up changing the minimum bet payback to 90% and it passed.

Quote: DRich

Unless something has changed, in Nevada the payout percentage is not allowed to be lower for a larger bet on the same game. Also, there can not be more than a 4% difference between the worst bet and the best bet on a game.

Does that law even apply to payouts that include progressive meters?

Edit: I don't see how it could. In any game with an uncapped progressive that requires max-bet to win it, the gap between the payout for min and max coins is unbounded.

Quote: AxiomOfChoice

Does that law even apply to payouts that include progressive meters?

Edit: I don't see how it could. In any game with an uncapped progressive that requires max-bet to win it, the gap between the payout for min and max coins is unbounded.

I think it may be legal to still have >4% difference, but it is a hassle because you need to have additional meters, and additional wager category SAS (slot accounting system) meters, which have frequently been implemented incorrectly. This would not apply to progressives; although the instantaneous return may be 4% greater than the base pay, they are interested in the long run return.

When I worked at GLI, I saw how multi-line virtual reels are constructed. Because many IGT games permit for the player to bet any number of lines, the return on the lines is kept identical. This is done by making the total weight of the symbol above or below any given symbol identical to the weight of that symbol. For instance, if you add up the weight of all 3-bar symbols on a reel, then the total weight of all the symbols above 3-bar symbols will be the same, and the total weight of all symbols below 3-bar symbols will be the same. Doing this ends up binding the weights of many symbols together. It is interesting to note that all of the symbol weights can be determined by only knowing what the Double Diamond and Hot Roll weights are.

Using the Wizard's data, I came up with the following reels, which result in a payback of 89.1% (89.17% at max bet). Of course, this could be off, but it probably won't be by much.

Reel 1	Weight	Reel 2	Weight	Reel 3	Weight
blank	4	blank	3	blank	2
Double Diamond	4	Double Diamond	3	Double Diamond	2
blank	4	blank	3	blank	2
Triple Diamond	4	Triple Diamond	3	Triple Diamond	2
blank	4	blank	3	blank	2
Purple 7	4	2-bar	3	1-bar	14
blank	4	blank	3	blank	14
Cherry	4	Cherry	3	Red 7	14
blank	4	blank	3	blank	14
3-bar	10	1-bar	17	2-bar	14
blank	16	blank	20	blank	14
3-bar	22	Purple 7	20	3-bar	14
blank	22	blank	20	blank	14
Hot Roll	22	3-bar	20	Hot Roll	14
blank	22	blank	20	blank	14
2-bar	22	Hot Roll	20	Purple 7	14
blank	22	blank	20	blank	14
Red 7	22	1-bar	18	1-bar	19
blank	22	blank	30	blank	36
3-bar	10	1-bar	18	1-bar	19
blank	4	blank	3	blank	2
1-bar	4	Red 7	3	Cherry	2

^^^

Interesting stuff. If I had to guess, your return answer sounds more realistic for a modern "penny slot". But since the game does require to play all twenty lines, do you think IGT may have not bothered to balance the reels similar to above since it really doesn't matter in this case? Unfortunately the only way to be more "sure" is to collect a bigger sample of symbols at 20 cents a whack. :(

Quote: tringlomane

^^^

Interesting stuff. If I had to guess, your return answer sounds more realistic for a modern "penny slot". But since the game does require to play all twenty lines, do you think IGT may have not bothered to balance the reels similar to above since it really doesn't matter in this case? Unfortunately the only way to be more "sure" is to collect a bigger sample of symbols at 20 cents a whack. :(

Yes, it is quite possible that they didn't balance the reels, since they lock you into playing all lines. In my years at GLI, I saw many video replicas of 3-reel games, in which they used the exact same balancing method, and actually re-used math from the original games. I imagine that they had a limited library of physical reel layouts and symbol weights, and once the balancing was complete, they were easy to re-use.

edit: I just saw, I'm at post 1000. I'll be due for an interview in 10 years!

More like 15+, but I am not a mathematician.

Re: 1000th post:

Quality >>>> Quantity.

Always look forward to reading your posts.

Still need to look at Betrock more too, haven't forgot, but I get easily distracted. :(

Quote: CrystalMath

Yes, it is quite possible that they didn't balance the reels, since they lock you into playing all lines. In my years at GLI, I saw many video replicas of 3-reel games, in which they used the exact same balancing method, and actually re-used math from the original games. I imagine that they had a limited library of physical reel layouts and symbol weights, and once the balancing was complete, they were easy to re-use.

edit: I just saw, I'm at post 1000. I'll be due for an interview in 10 years!

CM;

Me, I wish you'd post more often. Always worth reading what you have to say.

I'm quite confused when we start talking about the weight of the symbols on this particular game. I've read many times that a symbol cannot be weighted by more than six times the symbol next to it. It's even discussed on this website:

I have heard it is illegal for a slot machine to deliberately have too many near misses.

Both Wizard and CrystalMath's numbers violate this rule. Any opinions on what is happening here?

Quote: GLI-11

4.3.1(b) No Near Miss. after selection of the game outcome, the gaming device shall not make a variable second decision, which affects the result shown to the player. For instance, the random number generator chooses an outcome that the game will be a loser. The game shall not substitute a particular type of loser to show to the player. This would eliminate the possibility of simulating a 'Near Miss' scenario where the odds of the top award symbol landing on the payline are limited by frequently appear above or below the payline.

Quote: GLI-11

Rev 1.3 changes: 4.3.1(b) Near Miss. Removed the reference to award symbol ratio occurrence of 9:1 since the rule inhibited one type of technology disproportionately to all the others.

Quote: GLI-11

Rev 1.1 changes: 4.3.1(b) Reworded the Near Miss rule that requires the game to be arranged so that non-winning symbols on either side of the top award symbol do not occur more than a ratio of 9:1

So, it appears that GLI once mandated that the ratio be no more than 9:1 for top award symbols only. This rule no longer exists. There may be jurisdictions that have this regulation, though.

In my version, the weight of the non-winning symbols above and below the top award symbols are equal to the weight of the top award symbols, so it would pass the rule if required.

This is the only thing I could find from Nevada. They also state that the game cannot make a secondary decision. From this, I read that the probability of a symbol appearing must be constant.

Quote: NGCB

14.040(b)

For gaming devices that are representative of live gambling games, the mathematical
probability of a symbol or other element appearing in a game outcome must be equal to the
mathematical probability of that symbol or element occurring in the live gambling game. For other
gaming devices, the mathematical probability of a symbol appearing in a position in any game
outcome must be constant.