Did you win? Did you go bust? Do you think you chose a good strategy? Why not take a look at how you would do if you played through this scenario 100 times? We’ve added the $250 cap back in.

Multi-Run Betting Simulator (Capped at $250)

So what is the optimal fraction of your bank roll to bet? To calculate this, we use the Kelly criterion.²

The Kelly criterion provides a mathematically proven way to determine the optimal fraction of your bankroll to wager each time, so you can maximize your overall winnings in the simulations (and in real life). It does this by focusing on long-term growth rather than a single big win, balancing your gains against the risk of ruin. Put simply, if you know your chance of winning and the payout odds, the Kelly formula tells you exactly what percentage of your bankroll you should bet to see the fastest compound growth over many plays. For example, if a coin has a 60% chance to pay even money, the Kelly bet would be 20% of your bankroll every time. Over many bets, using Kelly leads to significantly higher final outcomes than betting arbitrary fractions or going all-in.

Kelly Bet Calculator

1. Haghani V, Dewey R. Rational Decision-Making Under Uncertainty: Observed Betting Patterns on a Biased Coin. arXiv [q-finGN]. Published online 2017. http://arxiv.org/abs/1701.01427 ︎
2. https://en.wikipedia.org/wiki/Kelly_criterion ︎

You can input multiple caffeine doses, specifying the amount and time of consumption. The tool also allows you to adjust key pharmacokinetic parameters, such as the time to peak concentration (Tmax) and caffeine’s half-life, for a personalized simulation.

Much of the logic for this tool comes from: White JR Jr, Padowski JM, Zhong Y, Chen G, Luo S, Lazarus P, Layton ME, McPherson S. Pharmacokinetic analysis and comparison of caffeine administered rapidly or slowly in coffee chilled or hot versus chilled energy drink in healthy young adults. Clin Toxicol (Phila). 2016;54(4):308-12. doi: 10.3109/15563650.2016.1146740. PMID: 27100333; PMCID: PMC4898153. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4898153

About This Tool

Skin cancer is typically excised in the shape of a “rhomboid” (as it is traditionally called, although it is not entirely rhomboid in the mathematical sense). Traditionally, the length to width ratio is 3:1.¹

To achieve a certain cure rate, a specific margin size is selected—generally 1 to 2 centimeters for melanoma, or 4 mm for basal cell carcinoma, among others. However, for certain neoplasms, such as atypical nevi, recommended margins are less clearly defined. This tool may prove helpful when considering whether to take a 2 or 4 mm margin for an atypical nevus.

This tool may also assist in selecting an appropriate treatment. Certain treatment modalities can achieve similar cure rates with smaller margins.

For instance, in the study “Clinical Characteristics of Basal Cell Carcinomas of the Vulva: An Institutional Retrospective Review” by Munoz et al., vulvar basal cell carcinomas were treated with either Mohs surgery using 3 mm margins or vulvectomy with 6 mm margins.²

Our tool shows that for a 1 cm basal cell carcinoma, vulvectomy results in a scar that is 38% longer and requires the removal of 89% more skin.

Calculating The Area of The Rhomboid

The area of the rhomboid was previously described by Tilleman et al as:

$A=\frac{d^2}{2}\times \left(\sqrt{a^2-1}+\arcsin \left(\frac{1}{a}\right)\right)$

Where a is the length to width ratio and d is the width (or the diameter of the circle). This can be derived from the below image. To do so, add the area of the circle to the area of four triangles (only one is pictured in the image), and then subtract the area of the sector of the circle occupied by the triangles.

1. Raveh Tilleman T, Tilleman MM, Krekels GA, Neumann MH. Skin waste, vertex angle, and scar length in excisional biopsies: comparing five excision patterns–fusiform ellipse, fusiform circle, rhomboid, mosque, and S-shaped. Plast Reconstr Surg. 2004 Mar;113(3):857-61. doi: 10.1097/01.prs.0000105338.66597.a0. PMID: 15108876. ↩︎
2. Muñoz G, Singla P, Hurst E, Council ML. Clinical Characteristics of Basal Cell Carcinomas of the Vulva: An Institutional Retrospective Review. Dermatol Surg. 2023 Jan 1;49(1):13-16. doi: 10.1097/DSS.0000000000003648. PMID: 36533789 ↩︎

You don’t have to use it for smoking though, you could also use it to see how much you would save by giving up your daily latte, or how much money you would have if you invested $5 every day for 10 years. To do this, you should set the cigarettes per day to 20 (1 pack).

Annual return on investment is set at 10%, based on the average annual S&P 500 performance over the past 100 years. Return on investment is calculated using the compound interest with daily contributions formula:

$A=p\times {\left(1+r\right)}^t+\frac{p\times {\left(1+r\right)}^t–1}{r}$