| Registrations | Advanced lottery win % | Regular lottery win % | Overall win % | Fail % |
|---|
Why multi-entry planning matters for H-1B hopefuls
The annual H-1B lottery is a defining bottleneck for skilled immigrants. Demand for cap-subject visas has surged far beyond the statutory limits of 85,000 slots, and recent registration cycles have seen hundreds of thousands of entries compete for those seats. Employers can submit only one registration per beneficiary, yet candidates sometimes line up multiple sponsoring companies in hopes of improving their odds. Until now, quantifying the value of that strategy has required spreadsheets or probabilistic modeling skills. This calculator fills the gap by translating the rules of the advanced-degree and regular lotteries into transparent percentages. By entering the number of other registrations in the market, the cap sizes, and the number of distinct employers ready to file on your behalf, you receive a clear view of how much each additional registration actually moves the needle.
The tool is designed for policy analysts, immigration attorneys, and international students alike. It assumes the official two-stage draw remains in place: a first lottery that allocates 20,000 visas to advanced-degree candidates and a second lottery that distributes 65,000 visas to the combined pool of everyone else plus any advanced candidates who were not selected initially. Because the registrations are effectively raffle tickets, the probability that none of your tickets are drawn follows a hypergeometric pattern. Capturing that nuance makes the output much more realistic than back-of-the-envelope percentages that treat each entry as independent.
Formulas behind the odds
Each lottery draw selects a fixed number of winners without replacement. If you hold k tickets in a pool of N total registrations and the agency draws m winners, the probability that you win nothing equals the number of ways the agency could pick winners from the remaining tickets divided by the number of ways it could pick winners from the entire pool. In MathML, the chance of a shutout is represented by the hypergeometric ratio
. Because the H-1B process uses two lotteries, an advanced-degree candidate must miss both draws to go home empty-handed. The overall failure probability therefore becomes the product of the no-hit probability in the first draw and the conditional no-hit probability in the second draw after the remaining pool size has changed.
The JavaScript implementation computes the logarithm of factorial expressions via a Lanczos approximation to the gamma function. This approach prevents overflow when the registration counts run into the hundreds of thousands. Once the calculator determines the probability of zero selections, it subtracts that value from one to obtain the success rate. It also computes the expected number of seasons required to win by inverting the overall success probability. If you indicate that you plan to try multiple consecutive years, the script raises the failure probability to the appropriate power to show the cumulative chance of eventually receiving a selection notice.
Working through the lottery stages
Consider how the two phases interact. Suppose there are 400,000 advanced-degree registrations from other candidates, 350,000 general-only registrations, and you can secure offers from two different cap-subject employers. In the first lottery, the total advanced pool is 400,002 tickets. Drawing 20,000 winners at random, the probability that both of your tickets lose is given by the combination ratio above. If both lose, they join the 380,002 other advanced tickets that remain, and the second lottery now contains those plus 350,000 general-only tickets. Because the second lottery also selects without replacement, we repeat the same computation with the updated totals. The calculator automates this cascading logic so you can focus on interpreting the implications rather than crunching numbers.
For candidates without a U.S. master’s degree, the analysis simplifies: you skip the first draw entirely and participate only in the regular lottery. The script therefore bypasses the advanced-degree math and computes a single hypergeometric probability. Even so, the table highlights how additional employer registrations continue to improve your odds, albeit with diminishing returns.
Worked example: a master’s graduate lining up two offers
Imagine Priya, who holds a U.S. master’s degree and finds two different consulting firms willing to sponsor her. She gathers data showing that last season USCIS received 409,000 advanced-degree registrations (excluding her potential entries) and 350,000 general-only registrations. She expects similar numbers this year. Plugging those counts into the calculator, setting the advanced-degree cap to 20,000, the regular cap to 65,000, and entering “2” for her registrations reveals an overall success probability of roughly 29%. The advanced lottery alone gives her a 9.8% chance of selection; if she misses there, the general lottery adds another 21.5% absolute chance. Her expected wait time—the reciprocal of the overall probability—is about 3.4 seasons. If she indicates that she’ll try four consecutive years, the cumulative chance of at least one win jumps to 73%, which is meaningful when planning life decisions around potential H-1B status.
The table beside the results reinforces how each additional job offer moves the needle. Going from one to two registrations raises her odds from 15% to 29%, a near doubling. Securing a third offer would push her probability to about 41%, but the marginal improvement from the third ticket is smaller than from the second. This diminishing return is the essence of risk diversification in the lottery context.
Comparison table: diminishing returns from extra registrations
To visualize the trend, the calculator produces a comparison table using the same market inputs but varying the number of employers willing to register you. A typical output might resemble the structure below. Values will update dynamically based on your numbers.
| Employers | Chance in advanced draw | Chance in regular draw | Overall success | Expected seasons |
|---|---|---|---|---|
| 1 | 9.8% | 15.7% | 15.7% | 6.4 |
| 2 | 19.0% | 23.4% | 29.1% | 3.4 |
| 3 | 27.0% | 31.0% | 41.2% | 2.4 |
| 4 | 34.0% | 38.2% | 51.5% | 1.9 |
The first column lists the number of employers. The next two columns show the marginal chances of being picked in each lottery stage, and the fourth column presents the combined probability. The final column converts that probability into an expected number of attempts. While the exact figures depend on your inputs, the pattern stays consistent: early additions produce large gains, while later ones taper off. This insight helps you decide how much energy to invest in courting multiple registrants.
Strategic insights and ethical considerations
Numbers are only part of the story. Multiple registrations are permitted only when each sponsoring employer has a genuine position and independent need for the beneficiary. Coordinated filings that lack bona fide job offers can trigger fraud investigations and denials for all associated companies. By quantifying the legitimate benefits of additional offers, the calculator encourages compliance: you can see the advantage of securing a small number of real opportunities without resorting to shell arrangements. The output also aids employers in setting expectations with candidates—especially those with limited immigration literacy—about why they might still miss out despite strong qualifications.
Policy makers and advocates can leverage the data to understand how changes to cap sizes or to the sequencing of lotteries would affect applicant behavior. For instance, if Congress increased the advanced-degree cap, the advanced lottery success column would climb proportionally, reducing the incentive to amass multiple employers. Conversely, if demand continues to soar, even large numbers of registrations may yield modest odds, underscoring the need for structural reforms or alternative visa pathways.
Limitations and assumptions
This calculator reflects the structure of the H-1B registration system as of 2025. It assumes that USCIS runs a single registration window, applies duplicate detection to disqualify identical submissions from the same employer, and allocates cap numbers randomly without favoritism. It also assumes that each of your registrations represents a legitimate, distinct employer willing to proceed through the full petition process if selected. The model does not account for subsequent petition denials, Requests for Evidence, or travel restrictions. Additionally, it treats the number of competing registrations as known inputs; real-world totals are uncertain until USCIS publishes them after the fact. You should therefore treat the results as planning estimates rather than guarantees. Finally, immigration rules evolve—always consult official guidance or a qualified attorney before making irreversible decisions based on projected odds.