Digital Debunking: The Loaded Dice Advantage

When the bullfrogs stop croaking on a summer night, the vacuum of noise is almost deafening. You awaken from a hazy half-sleep, aware of a presence just outside. You moved off the grid to escape other people, but most of all, to escape your past. Every bump in the night is a reminder that that history could come knocking again at any moment.

You grip the baseball bat under the mattress and slowly but deliberately push open the creaky wooden door.

Greeting you is an unmarked manilla package about the size and shape of a postcard. There are two small square-shaped bumps in the upper left corner where the return address should have been. Your better judgement says to chuck it into the lake, but the pull of the unknown is too great.

With a resigned sigh, you tear open the padded envelope revealing a hand-written note and two six-sided red die. From the looks of it, they seem to be from a high-end casino. The letter reads,

 

One last job – and when I say this is the big one, you know I mean it.

Take them on a ride at the craps table. Distract casino security long enough for the crew to secure the big score.

I’ve got confidence in you kid. We leave for Atlantic City at sunrise.

         – Sergio

 

Confidence. Sergio had first crossed your path ages ago on the Las Vegas strip. In those days you were a confidence man, a grifter of the highest order. It’s where you honed your sleight of hand skills; the type of trick perfect for placing a set of loaded dice on the craps table without raising the suspicion of casino security. Amazing how skimming a few bucks out of a tourist’s pocket with three-card monte can turn into casino heists and nearly a decade lost inside a federal penitentiary. But when Sergio asks if you’re in, he already knows the answer. All that’s left to do now is get to work.

Three hours until daybreak. You were always a hopeless gambler when you played it straight. The casino has its thumb on the scale anyway, so no harm getting things back to level… well, maybe tilt it just a little bit more so in your direction.

In craps, if you can guess the outcome of the dice roll, you win. And if you know the outcome before you roll, you win big.

You’ll need to load the dice, adding a minuscule amount of weight to influence the roll. Inserting the head of a tiny nail in the pips of the dice could be enough to throw off its equilibrium and make the number opposite the weight come up more often than random chance. But weigh the sides too much and you blow your cover. The dealers in Atlantic City are no rubes.

You need precision. No time for trial and error. Common sense tells you that you should weigh the side opposite the number you want to roll, but simulation and optimization software lets you model whether weighing additional sides would yield an even better outcome. To roll a ‘one,’ do you just load the six side or would weighing other sides further increase your odds of winning?

In Altair InspireTM, you quickly create the geometry; a 19mm cube per Vegas standards. Not every casino rounds off the edges, but thankfully Sergio sent you a sample. A 1mm radius on the edges perfectly matches the die in the envelope. The final step is to add the pips on the dice geometry; cylindrical plugs set into the die. You set the entire die to plastic nylon material but set the plug material on the “six” side to steel to mimic where you’ll insert the nail heads to load the dice.

To set up the dynamic simulation of the dice roll, you next turn to Altair MotionViewTM, where you can accurately model the dice as it rolls across the table and caroms off the wall.

 

Dice roll video rendered in Altair InspireTM Studio

 

Now, the most important step – which sides of the dice to load. By leveraging the integration between MotionView and Altair HyperStudyTM, you can run an Design of Experiment (DoE) study across multiple rolls to determine which side or sides have the most influence on a certain outcome when weighted.

In order to get really accurate predictions across multiple rolls, you have to consider the human factor. It would be impossible to recreate the exact speed and rotation every time when throwing dice by hand, so with each roll, you vary the initial conditions. Every run should have slightly altered set of inputs – tweaks to the initial velocity and alterations of the die orientation.

The results of the optimization study are surprising. Logic would tell you that just placing the weight on the six side would be the best way to roll a ‘one.’ The simulation shows this to be true (2.5 times more likely than baseline), but HyperStudy’s DoE findings also show that placing weight on the two and four sides as well as the six side yield an even better result. Loading these three sides make it a full three times more likely that the roll will land on ‘one’ than if you used an unloaded die. Optimization actually uncovers a hidden treasure trove of information; an extra advantage that could be the difference between a big score or a trip back to the big house.

Influence of loading by side on likelihood of rolling a ‘one’

The DoE study also shows that weight on the three side has the most negative affect on the outcome of rolling a ‘one.’ Making the three-side lighter could further improve your odds, but the only way to do this would be to remove material on that side – too easy to spot by a careful dealer or pit boss.

You can see the sky beginning to turn a soft pink hue. Time is running short. You fix your smallest bit to your hand-held drill and begin loading the three sides of your die.

Just as you carefully paint the last embedded metal pip with whiteout and gingerly blow it dry, you hear the roar of an airplane overhead. As the sun crests over the horizon, the seaplane elegantly lands on the glassy lake. The hatch swings open and Sergio pulls his aviator sunglasses slightly down the crook of his nose and winks. “Grab your tux. It’s time to get to work.”

If you want to show off a party trick at home and have some simple tools, a loaded die will definitely give you an advantage. And if you’re looking to gain a product development advantage, HyperStudy can be the key to discovering hidden performance advantages through design exploration and optimization. It automatically creates intelligent design variants, manages runs, and collects data. Users are then guided to understand data trends, perform trade-off studies, and optimize design performance and reliability.

But as far as high-stakes heists go, we recommend leaving that work to a professional hustler.