Hot Roll Slot Machine

Hot Roll Slot Machine – Hot Roll is a bonus feature added to various 3-reel slot machines by the maker IGT. In the case of this analysis, it is based on the classic Triple Double Diamond game. If the player gets the Hot Roll icon on all three reels, they will play the craps-based bonus game. In this game, the player will continue to roll two dice and win money, until he rolls the seventh, ending the bonus.

I played 284 spins of this game at the Golden Nugget on January 2, 2014. As I played, I recorded my game and uploaded the video to YouTube. This page documents my results and attempts to reverse engineer the game to show you how it’s programmed. In this type of game, with weighted reels, 284 spins is not enough to know exactly how IGT has arranged it. What you see on this page is my very educated guess.

Hot Roll Slot Machine

Based on my 284 spins, I tally up the reel stripping order and count how many times each reel stops in each position. The following table shows my results.

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The way three reel machines usually work is to pick one random number from each reel and map it somewhere on the reel strips, depending on how each stop is weighted. It is not uncommon for the total number of stops to reach a power of 2. I don’t know the exact number of stops for this game but for the sake of example I’ll assume it’s 2

The following table is my best estimate of actual reel weights. I combined trying to keep the ratio similar to the actual data and trying to achieve what I felt was a believable rendering of the game. You may recall that in my survey of Las Vegas penny slots that the Golden Nugget came in 48th out of 71, with a return rate of 90.85%.

The way the game would be programmed, based on these weights, would be to choose three random numbers from 0 to 255 (programmers always start counting at zero). It will then map those numbers to a specific stop on the reel according to the following width of each stop. The game would then place each reel in a pre-determined position on the center row.

From the table above, you can see that 222 on reel 1 is mapped to the empty space between the red 7 and the 3 bar. The 0 of reel 2 is shown on the first blank map, above the double diamond and below the red 7. The reels fold so that the red 7 at the bottom is above the blank at the top of the list. 175 of reel 3 will be drawn purple map 7. The result will be as follows.

Deconstructing Hot Roll

Based on the weights above, the following table shows the number of winning combinations for each with its reel 1 multiplier.

The following table shows the return combination for each win. Each cell in the main body of the table is the product of the win, multiplier, and number of combinations from the table above. The total number of possible combinations is 256

= 16, 777, 216. Dividing the total return combination in the lower right cell of 10, 717, 885 by the total number of possible combinations of 16, 777, 216 we get 63.88%. Therefore, with a single credit bet on the middle payline, the player can expect to return 0.6388 credits, without counting the bonus.

Since the reel stops are weighted, this analysis must be repeated for each payline. To prevent this page from being too long for the other 19 paylines I will just present the returns in the following table. Note the bottom right cell shows the average base game return of 68.69%.

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The following table shows the expected number of each type of win across all 20 paylines. The bottom right cell shows that the player can expect to win 1.46 per bet.

The following table shows the expected return for each type of win across all 20 paylines. The lower right cell shows that the player can expect 13.737592 credits from the line paying each bet. Dividing that by a bet of 20 units, the base game return is 68.688%.

The following table shows the frequency of each winning amount, after applying the multiplier, over all 20 paylines. The lower right cell shows a total win of 13.737592. Dividing this by 20, the total bet, results in a base game return of 68.688%.

The bonus rules are explained in the rules section above. Let’s start analyzing the bonus by solving for the average win per roll, assuming it’s not seven. The table below answers that question. The lower right cell shows an average win of 3.733333, seven can be taken.

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Next, what is the average number of rolls? If the probability of an event is p it will take on average 1/p trials to occur. The probability of rolling a seven is 1/6, so it takes an average of six rolls to occur. However, the player doesn’t win anything on the original line of seven, so there are fives that pay before sevens.

There is also a consolation prize of 7 for rolling a seven on the first roll. The value of that is (1/6) × 7 = 1.166667. So, the average win per bonus is 1.166667 + 5 × 3.733333 = 19.833333.

As a reminder, the bonus is triggered when the player gets three Hot Roll symbols anywhere on the screen. To find the probability of it happening on each wheel, we also need to check the empty stops immediately above and below the Hot Roll symbol that touches the middle payline. On reel 1 there are, 18 (blank) + 25 (Hot Roll) + 19 (blank) = 62 stops that if you touch the middle payline make the Hot Roll symbol appear anywhere on reel 1, giving you a chance of 62/256 = 0.242188.

The following table shows the probability of the Hot Roll symbol appearing on three reels and the product. The lower right cell shows a bonus chance of 1.13%.

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The total profit from the bonus is the chance of the bonus times when the average win. This product is 0.011308 × 19.833333 = 0.224279.

After all that, we showed the return of the base game is 68.688% and the return from the bonus is 22.428% for a total return of 91.116%. If the player bet less than 200 credits, thereby losing the most profitable coin, the return drops by 0.039% to 91.077%.

I would like to emphasize that I am not saying that this is an exact refund. This page is more of an exercise in slot machine design than solving a specific restoration of that one game. To get an exact return I would need to know the exact reel weights, which I don’t have. The first time I saw Hot Roll Poker was July 1, 2015 at the Suncoast in Las Vegas. The idea is simple. If a player doubles his bet he will qualify for multipliers based on the roll of two dice.

Hot Roll is an optional feature on top of three-, five-, and ten-play video poker. The feature rules are as follows.

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I caught these two and one of them developed into a full house. In a 9-6 Jacks or better game I played, two pairs paid 2x and a full house 9x. The bet per line was five coins and the multiplier was 11. So, the total winnings were 5×11×(4×2 + 1×9) = 55 × 17 = 935 coins.

Given that the probability of doubling is 1/6 and the multiplier ratio is 7, the total multiplier ratio is (1/6)×7 + (5/6)×1 = 12/6 = 2. Since the player has to double his bet, the return is exactly the same as the base pay table. Therefore, the restoration of normal video poker can be used for Hot Roll Poker.

The following tables show the games, pay tables, and returns for Hot Roll Poker. I was kindly provided by IGT, the game maker.

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