Gambling debt cascades

What it is

The MathWorks Math Modeling Challenge is a 14-hour problem set for high school teams. The 2026 competition’s third problem asked about the spread of legalized sports betting and what it does to household finances. This page covers my portion of our team’s submission: a model of how gambling losses turn into debt, and how often that debt ends in bankruptcy.

The answer takes the form of a 9-state Markov chain. A person occupies one state per month — from recreational betting, through elevated spend, credit drawdown, a revolving balance, minimum payments, delinquency and charge-off, to bankruptcy — with a separate recovery state that leads back toward the top. The question the model is built to answer is not “how many gamblers go bankrupt” but “how many more go bankrupt than would have without the chasing behaviour”, which is why every scenario is run against its own counterfactual.

How it works

The ladder is the model. Each month, the population vector is multiplied by a transition matrix whose entries are monthly probabilities calibrated from consumer-credit data, so a cohort spreads across the states over time rather than following any one path.

Loss chasing enters as a hazard multiplier, λ, applied to four forward deterioration edges: credit drawdown into a revolving balance, revolving into minimum payments, minimum payments into delinquency, and delinquency into charge-off. Each boosted hazard is capped, and the added probability mass is taken from staying put first, then from recovery, then proportionally from the rest of the row, with the row renormalized after each edge. λ = 1.14 is the calibrated gambling scenario; λ = 1.00 leaves the matrix untouched and is the counterfactual.

The chain is non-homogeneous in the scenarios where the effective balance is re-estimated from the population each month: as more people sit in the high-balance states, the chasing pressure rises, and the matrix used next month is not the matrix used this month. On top of all of it sits a Monte Carlo layer that resamples both the transition parameters and the process itself, so the headline numbers come with intervals rather than a single point.

The simulation above is not a replay. It runs the chain in the browser, and a build-time test refuses to ship the site unless this port reproduces the notebook’s own committed outputs to within one part in a billion.

Calibration

The US transitions are built from the Federal Reserve’s G.19 consumer credit series, the New York Fed’s Household Debt and Credit report, FDIC data, CFPB complaint records, and US Courts bankruptcy filings. The UK side uses Gambling Commission statistics, Bank of England lending data, the FCA’s Financial Lives survey, and Insolvency Service figures.

The two calibrations do not behave the same way. The UK’s delinquency state drains faster into charge-off and its charge-off state is markedly more likely to end in insolvency, which is why the UK’s cumulative attributable risk comes out roughly twice the US figure on the same horizon. Switching the toggle above between US and UK changes only the matrix; everything else is held fixed.

Results

At 36 months, the attributable cumulative bankruptcy risk among at-risk gamblers is 0.22% across the two countries — about 1 in 456 — and that is the excess over the counterfactual, not the total. It splits as 0.20% for the US and 0.41% for the UK.

The conditional transitions are where the ladder shows its shape. Someone already in delinquency has a 13.2% chance of reaching bankruptcy within 24 months in the US and 20.3% in the UK. Someone in the state two rungs above them has well under 1%. The risk is not spread evenly down the ladder; it is concentrated almost entirely in its last few rungs.

The compounding layer makes the same point in money. A single $3,000 loss carried on a credit card, with no further gambling at all, accrues to about $8,600 of cost over ten years. With $200 a month of continued chasing on top, the same starting loss reaches roughly $55,000.

Our submission placed in the top 15% internationally.

Limitations

Three, stated as the report states them. The initial populations are calibrated assumptions rather than measured cohorts, so the absolute counts should be read as scale, not census. The counterfactual is scenario-based: it is the same model run with λ = 1.00, which is a clean comparison but not a causal identification strategy. And the Monte Carlo layer reflects parameter and process uncertainty, not structural uncertainty — it does not ask whether a nine-state ladder is the right shape for the problem in the first place.

The subject is real financial harm. The figures on the hillside are deliberately abstract — blocks on terraces, not people — and the numbers above are population rates rather than individual predictions.

States

S0	Recreational
S1	Elevated spend
S2	Credit drawdown
S3	Revolving balance
S4	Minimum payments
S5	Delinquency
S6	Charge-off
S7	Bankruptcy
S8	Gambling recovery