Abstract
Cushing and Stewart (2024) is a wonderfully elegant mathematics research paper that includes the result that a minimal lottery design of only 27 tickets is all you need to be guaranteed a win in the U.K. National Lottery. Cushing and Stewart's paper generated significant global media coverage in 2023/2024. Judging from most reader comments left on popular news web sites, however, many readers did not understand the practical implications of the research work. So, I give many observations that were understandably missing from the original mathematics paper. For example, and most importantly, under no circumstances whatsoever should you gamble using the actual number choices published by Cushing and Stewart; you must instead apply a cypher to them first, as described and argued here. I also point out that you have a notably higher probability of winning prizes at the lowest tier with the Cushing-Stewart 27-ticket strategy than with a random-number 27-ticket strategy. This advantage is, however, perfectly counterbalanced by notably fewer expected within-tier prize wins across those 27 tickets when a win does occur in that prize tier. The net effect is that the Cushing-Stewart strategy has the same expected payoff as a random-number strategy. (The standard deviation of expected payoffs across prize tiers is also the same.) Unlike Cushing and Stewart, I use only high-school level mathematics (that you may skip over if you are interested only in the key takeaways). The low level of the mathematics used here make this an excellent pedagogical paper for high-school or freshman math/stats students. I also give pointers to time-tested millionaire wealth-building advice without the use of lotteries. I also give several directions for future research, including empirical and theoretical research questions.