Healthy Wage Calculator Example #1: Male / 270 / 6’1″ / 42″ Waist (Part 3)

In Part 1 we covered the 6- and 7-month bets to lose approximately 2 pounds per week, which pay out according to the regular formula; but with the 7 month bet offering better return on investment than the 6 month bet.

In Part 2 we covered the 8- and 9-month bets, with ROI increasing substantially but still paying according to the regular model. When we extended the 2 pound per week plan to 10 and 11 months, the supersize (summit) formula goes into effect, and the ROIs consisting of a near-tripling of the bet amount plus a flat bonus govern the payouts.

In this final part, we tailor the bet so that the summit formula stays in effect, but the pledge is reduced so that it is not nearly as onerous. This costs is some net gain, but the trading away of this gain for substantially easing the pledge can be highly attractive. We will consider this trade off for players on a budget, as well as for players willing to bet more to earn more.

Minimum weight pledge required to get into the summit formula

Assuming I want to lose weight no faster than the approximate 2 pounds per week that I have been maintaining for all these possible bets, the bet we are looking for is a 10 month bet, but it is less than 82 pounds—but just enough to enter the summit formula. In other words, 1 pound less and I would be in the regular formula, which has starkly poorer return on investment.

It turns out that 10 months / 76 pounds is a regular formula bet, and 10 months / 77 pounds is a summit formula bet.

At 76 pounds in the regular formula:

• An $11/month or $110 bet pays $212.59 gain, $322.59 prize; a 193.26% ROI
• A $63/month or $630 bet pays $1,216 gain, $1,846 prize; a 193.01% ROI (we bumped into the net gain ceiling a bit, so we lost about $3.23 here; but it’s still better than the $62/month gain of $1,198.24)

At 77 pounds in the summit formula, at the minimum -stake left end of the net gain plot:

• An $11/month or $110 bet pays $373.53 gain, $473.53 prize; a 339.57% ROI.

The 1-pound difference causes the $110 to be multiplied by 1.9412 instead of 1.9326. That component of the net gain is $213.53, only 94 cents more than the net gain at 76 pounds.

But now we have the vertical shift component of the summit formula net gain kicking in. That is $3.20 times the difference between the weight pledge and 10% of the starting weight of 270 pounds. That’s $3.20*(77-27) = $160.

So the net gain went up $160.94 with the addition of the 77th pound to the pledge.

At the other end of the plot, where maximum net gain (and the summit) is:

• A $63/month or $630 bet pays $1,382.96 gain, $2,012.96 prize; and a 219.51% ROI

The slope-multiplied portion of net gain is $1222.96, and the vertical shift portion is the same $160 in effect at minimum stake. The ROI here is less than at minimum stake because the slope-multiplied portion dwarfs the vertical shift at this bet size.

At $63/month or $660, the 77th pound has added $166.96 to the net gain.

Here are the differences in payout for different monthly payments, for a 10 month bet at 76 and 77 pounds:

• $20/mo, $200, 76 lb: Gain $386.53, Prize $586.53
• $20/mo, $200, 77 lb: Gain $548.24, Prize $748.24 (difference $161.71)

• $30/mo, $300, 76 lb: Gain $579.80, Prize $879.80
• $30/mo, $300, 77 lb: Gain $742.36, Prize $1,042.36 (difference $162.56)

• $40/mo, $400, 76 lb: Gain $773.06, Prize $1,173.06
• $40/mo, $400, 77 lb: Gain $936.48, Prize $1,336.48 (difference $163.42)

• $50/mo, $500, 76 lb: Gain $966.33, Prize $1,466.33
• $50/mo, $500, 77 lb: Gain $1,130.60, Prize $1,630.60 (difference $164.27)

• $60/mo, $600, 76 lb: Gain $1.159.59, Prize $1,759.59
• $60/mo, $600, 77 lb: Gain $1,324.72, Prize $1,924.72 (difference $165.13)

• $63/mo, $630, 76 lb: Gain $1.216.00, Prize $1,846.00 (the net gain ceiling in the regular formula has been reached)
• $63/mo, $630, 77 lb: Gain $1,382.96, Prize $2,012.96 (difference $166.96) (best net gain for 77 pounds of weight loss)

• ***$64mo, $640, 76 lb: Gain $1.216.00, Prize $1,856.00 (sucker bet, the extra $10 in the wager is earning nothing)***
• ***$64/mo, $640, 77 lb: Gain $1,381.63, Prize $2,021.63 (sucker bet, net gain is dropping after having added $10 to the wager)***

• ***$70mo, $700, 76 lb: Gain $1,216.00, Prize $1,916.00 (further along the sucker plateau )***
• ***$70/mo, $700, 77 lb: Gain $1,265.16, Prize $1,956.16 (most of the way down the sucker slope, pissed away most of the vertical shift bonus)***

• ***$80mo, $800, 76 lb: Gain $1,216.00, Prize $2,016.00 (ugh)***
• ***$80/mo, $800, 77 lb: Gain $1,232.00, Prize $2,032.00 (now on the net gain plateau, vertical shift bonus is long gone)***

Net gain / pledge trade-offs for budget bettors

For 10 months, it takes a 77 pound pledge to activate the summit model.

If you add pounds beyond this point, this will improve the net gain plot in two simultaneous ways:

1. It shifts the net gain slope vertically upward (by $3.20 per added pound for men, and $6.00 per added pound for women)
2. It extends the slope rightward, as the summit shifts to the right; which allows for more money to be bet and almost tripled (for men, each pound added allows for another $8.24 to be added to the total wager to potentially pick up $16.00 in new money; for women, the extra pound allows $15.45 to be added and pick up $30 in new money).

If money is no object, a man can make up to $11.24 for each extra pound and a woman can make up to $36 for each extra pound.

But if you are on a budget for your wager, and you are in the summit formula, adding weight to the pledge only gets you a $3.20 (men) or $6.00 (women) per pound added. You don’t get the benefit of moving the summit rightward and making it taller because you are not increasing your bet to move next to that enhanced summit.

So making the bet more onerous doesn’t get you much more money.

Previously I calculated gain and prizes for 10 months / 82 pounds. If I wanted to go for the biggest money, I would bet the money required to get on the net gain summits for those bets.

But if I was limited to, say, $50/month, I would stick with 77 pounds for both the 10 month bet. The 5 extra pounds on the 10 month bet only earn $16.00 more.

Those final 5 pounds may prove to be the toughest to lose, and with the relatively small prize enhancement associated with them it’s probably not worth the stress and strain to add them to the edge.

Here are comparisons between 77 pounds and 82 pounds for different monthly payments, when going for 10 months. Note the minimal differences—but also note what happens when the bet exceeds $65/month:

• $20/mo, $200, 82 lb: Gain $564.24, Prize $764.24
• $20/mo, $200, 77 lb: Gain $548.24, Prize $748.24 (difference -$16.00)

• $30/mo, $300, 82 lb: Gain $758.36, Prize $1,058.36
• $30/mo, $300, 77 lb: Gain $742.36, Prize $1,042.36 (difference -$16.00)

• $40/mo, $400, 82 lb: Gain $953.48, Prize $1,352.48
• $40/mo, $400, 77 lb: Gain $936.48, Prize $1,336.48 (difference -$16.00)

• $50/mo, $500, 82 lb: Gain $1,146.60, Prize $1,646.60
• $50/mo, $500, 77 lb: Gain $1,130.60, Prize $1,630.60 (difference -$16.00)

• $60/mo, $600, 82 lb: Gain $1.340.72, Prize $1,940.72
• $60/mo, $600, 77 lb: Gain $1,324.72, Prize $1,924.72 (difference -$16.00)

• $63/mo, $630, 82 lb: Gain $1,398.96, Prize $2,028.96
• $63/mo, $630, 77 lb: Gain $1,382.96, Prize $2,012.96 (difference -$16.00) (best net gain for 77 pounds of weight loss)

• $65/mo, $630, 82 lb: Gain $1,437.78, Prize $2,087.78
• ***$65/mo, $650, 77 lb: Gain $1.362.22, Prize $2,012.22 (CAUTION: THIS IS ON THE FALLING SLOPE OF THE SUMMIT AND IS A SUCKER BET. DO NOT MAKE THIS BET)*** (difference -$75.56)

• $68/mo, $680, 82 lb: Gain $1,479.98, Prize $2,159.98 (best net gain for 82 pounds)
• ***$68/mo, $680, 77 lb: Gain $1,303.98, Prize $1,983.98 (EVEN WORSE THAN $65/MONTH RUN AWAY RUN AWAY)*** (difference -$176.00)

• ***$69/mo, $690, (I don’t want to bother with this; you should have gotten the idea earlier about sucker bets—just don’t bet that much for either weight loss pledge PLEASE)***

Coda

That’s my example. More to come.