User Guide for HWSim

What is this?

This is a simulator of the calculator used for determining HealthyWager payouts at Healthy Wage.

Why do we need this?

A number or reasons.

The biggest one is that the calculator is cumbersome to use, and probably intentionally so. You have to enter pledge data scenarios one by one, and get payout offers one by one. You can get as many as you want, but it takes a lot of time to enter the different data combinations manually (number of pounds to lose, months to do it in, monthly payment).

Another issue is that you only get one chance to enter your gender, height, and current weight. You are required to create an account to see any detailed offers.

Once the account is created, changing the starting weight requires calling customer service and having them update the data or clear it.

You could enter a fake email and create a fake account if you wanted to run what-if scenarios with starting weight, height, and gender. After all, that’s what I did to figure out the formulas. But it’s still a time-consuming, cumbersome process. With this app, you can play with all the input in any way you want and get instant results.

Naturally, Healthy Wage conceals a lot of information from you. For instance, they don’t want to tell you the total investment amount directly, because it’s scary to look at for some.

But they also don’t want to tell you things like where the calculator switches from the “regular” formula to the “triple-bonus” formula, where you can get a huge payout increase by increasing your pledge by 1 pound or 1 month.

Also, they won’t tell you explicitly when you are “overbetting,” I.e. you are betting so much that your net gain exceeds some calculated limit that HW has set for you based on the pounds pledged, or possibly on BMI. When overbetting, you are pledging some dollars that do not earn any return from Healthy Wage. They only get returned to you if you win—and in some cases, they actually reduce the return on investment that the other dollars produce!

I have figured out where the betting limits are and the app will alert you to them, so that you do not breach them.

What are the mathematical equations in the calculator?

I will try to describe this as simply as I can.

There are two main formulas in the calculator. One is what I will call the “regular” payout formula and the other is what I will call the “triple-bonus” formula.

Regular payout formula—lower ROIs

The regular formula offers a return on investment (ROI) on your bet that can range between 11.1% and 194.12%.

The formula that Healthy Wage used to determine this ROI is complex, and at this time I do not know this exactly. But I do know enough about important elements of it to create my own version of it, which is accurate to within a couple of dollars when ROI is 60% or more. This is because I have identified linearities that I can exploit, which are in effect in this upper ROI subset.

For smaller ROIs, accuracy declines because there is some nonlinearity that I haven’t found the definition for, and so I have attempted to min mimic it with my own equations. But smaller ROI means smaller dollars, and so it isn’t as important as getting things right on the high ROI end of things.

Here are the trends which are important to understand in the regular formula:

With ROI above 60%, the logarithm of ROI increases linearly with percentage weight loss. This continues until ROI reaches 194.12%. At this point, pledging another pound shifts you into the triple-bonus formula, which causes ROI to jump strongly.
For a given ROI and percentage weight loss, the logarithm of ROI increases linearly with the number of months of the wager. This increase is slight, but it is there. In percentage points, each month added has a greater effect on ROI as ROI increases—but that comes naturally with the logarithmic relationship.
The parameters involved in the linearities are dependent on the starting body mass index (BMI). As starting BMI increases, ROI shifts up strongly. It is not quite a linear trend, but it is close to it.
Conversely, for a given ROI, the percentage weight loss required to achieve that ROI decreases with increasing BMI. The relationship is modeled well with a quadratic trendline equation.

With all of that information, I was able to define an ROI equation that takes in starting weight, pledged weight, and number of months. The ROI equation is accurate to within a percentage point or two for ROI of 60% or greater. It applies to any bet value that does not breach any of the Healthy Wage rules or trigger one of a number a net gain limiting effects (see below for more detail).

For small ROIs (less than 60%), there is a additional suppression effect on ROI that is non-linear—or at least I haven’t been able to define it yet. I try to model it in with a quadratic term to get close to what really happens. But in practice, anyone getting low ROI is usually a mildly overweight person who is not making a large pledge. Not a lot of money can be made with low ROI anyway, so it is less important to be super accurate with these type of bets.

The constants involved in the ROI equation are different for men and women. Women get higher ROI than men for the same BMI, pledged percentage, and time. They need to bet less aggressively than men in order to access the triple-bonus formula.

Triple-bonus formula—higher ROIs

For ROI above 194.12%, the triple-bonus formula supplants the regular formula. Instead of an ROI that is dependent on BMI, pledge size, and time; you have something much simpler.

The triple-bonus formula pays out a gain consisting of two values:

The total bet multiplied by 194.12%
A bonus proportional to the number of pounds pledged in excess of 10% of starting weight

The number of months you need doesn’t matter here. BMI doesn’t matter to the formula itself, except that BMI is a determinant in whether this formula gets triggered or not.

The ROI will vary with bet amount. It will be huge for minimum stake bets, and will decrease as the stake increases. But unlike the regular formula, which defines ROI across all bet values, in the triple-bonus formula ROI is just a value resulting from a calculation that is dependent directly on bet size and pounds pledged.

The bonus is larger for women than for men. Women get $6 per pledged pound in excess of 10% of starting body weight. Men get $3.20 for each of those pounds.

Net Gain Caps

Generally, you can’t put the rent money into Healthy Wage and retire on your weight loss.

The $10,000 prize limit is well-known. Of course, that includes getting your own money back.

But in almost all cases, if you are betting enough to get a $10,000 prize, you are putting a huge portion of your money at risk for no financial benefit. This is because Healthy Wage caps your net gain in several other ways. These are dependent on your weight pledge amount, but also your gender and possibly your BMI if it is fairly low.

If you bet too much, you will be giving Healthy Wage a lot of money and be fighting to get it back with zero return. That’s not a good thing to do. Fortunately, Healthy Wage offers other ways to put that money to work for the same weight loss that you are attempting with the Healthy Wager—see below to find out more.

The only people who can shoot for $10,000 without overbetting in this way are morbidly obese women who are pledging to lose hundreds of pounds in 18 months, and are making a maximum pledge. Generally they will bet $2,500-$3,000 and attempt to approximately triple it.

Outside of this demographic, the following net gain caps will impose themselves on a big-money player. HWSim tells you where these limits are and when you are breaching them.

Pledged-pounds net gain cap: This is based on the number of pounds a player pledges, but also a player’s gender, and whether or not the payout formula in effect is the regular or the triple-bonus formula. To wit:
- Men working in the regular formula (ROI 194.12% or less) can earn no greater than $16 times the number of pounds pledged. Thus, their total bet should be no greater than $16 times the number of pounds pledged, divided by the ROI in effect.
- Women working in the regular formula (ROI 194.12% or less) can earn no greater than $30 times the number of pounds pledged. Thus, their total bet should be no greater than $30 times the number of pounds pledged, divided by the ROI in effect.
- Men working in the triple-bonus formula (ROI over 194.12%) can earn up to $16 times the number of pounds pledged, plus a flat bonus of $3.20 times the number of pounds pledged in excess of 10% of their starting weight. For maximum net gain, the total bet should be no greater than $16 times the number of pounds pledged, divided by 1.9412.
- Women working in the triple-bonus formula (ROI over 194.12%) can earn up to $30 times the number of pounds pledged, plus a flat bonus of $6.00 times the number of pounds pledged in excess of 10% of their starting weight. For maximum net gain, the total bet should be no greater than $30 times the number of pounds pledged, divided by 1.9412.

BMI-Dependent net gain cap: For players with starting BMI in the low thirties or less (especially women) who are looking to drop into the low twenties or less:
- For women in the regular formula: net gain is limited to $800 if BMI is 29.6 or less. For BMI above 29.6, the net gain is limited to $500 times BMI, minus $14,000. Examples:
  - BMI 29.0: Max net gain is $800
  - BMI 30.0: Max net gain is $1,000
  - BMI 30.5: Max net gain is $1,250
  - BMI 31.0: Max net gain is $1,500
- If this figure is less than the pledged-pounds net gain cap, you should limit total bet size to this limit, divided by the ROI that is determined by other factors in the regular formula.
- For women in the triple-bonus formula, net gain is limited to $800 plus bonus for BMI of 29.6 or less; $500 times BMI minus $14,000, plus bonus, for BMI above 29.6.
  - Bet size should be limited to $800 / 1.9412 or $412 if your BMI is 29.6 or less.
  - If your BMI is above 29.6, calculate $500 times BMI and subtract $14,000; then divide that by 1.9412 to find the maximum bet size.
- For men, the above calculations are the same—but practically speaking, very few men will have to deal with this limit, because the pounds pledged limit will almost always be less.

$10,000 Max gain cap: this one is self-evident.

Minimum pledged pounds required to enter the triple-bonus formula

In HWSim, there is a graph that shows you what your net gain will be as a function of the number of pounds of weight your are pledging to lose, with the bet size you have chosen.

As more pounds are pledged, net gain goes up slowly at first, then more quickly, as ROI increases in the regular formula.

But as pledged pounds increase, eventually you jump into the triple-bonus formula. At that point, net gain makes a leap upward—this is caused by the bonus part of the triple-bonus formula kicking into effect.

After that, net gain rises slowly with more pledged pounds. The net gain is equal to 194.12% of the wager, plus a bonus that goes up only $3.20 and $6.00 per pledged pound for man and women, respectively.

What this means for you is if you are on a monthly budget, and set up an aggressive bet that places you in the triple-bonus formula, you may be able to trade off: you can reduce the pounds pledged and it will only cost you a few dollars in the bonus component of the net gain and prize.

Example: Female, 5’-5”, betting $100/month for 6 months. Starting weight 225 pounds, losing 50 pounds

This bet pays $1,329 in net gain and $1,929 prize. It is a triple-bonus formula bet. The bet-dependent component is $1,164.72 (194.12% of the $600 bet) and the bonus component is $165.00 ($6.00 times the difference between 50 pounds and 10% of the starting weight).

Reducing the pledge to 39 pounds reduces the net gain to $1,263.72. The $1,164.72 bet-dependent component remains the same, but the bonus drops by $66.00, to $99.00.

For a reduction of $66 in gain (and prize), you can reduce your burden by 11 pounds, which is a lot. Losing 50 pounds in 6 months is equivalent to a 0.96% drop, week over week. But losing 39 pounds in that time is only 0.73% drop, week over week.

But ease to 38 pounds is too costly for net gain if the bet stays at $100 per month. At 38 pounds, net gains is only $1,208.28. This is because the pledged pounds net gain cap is now breached.

To avoid this overbet situation at 38 pounds, the bet can be reduced to $98/month, which actually increases the net gain to $1,231.57! And HWSim alerts you to this!