Search arXivSearch

arXiv · 1801.02959

Does it Pay to Buy the Pot in the Canadian 6/49 Lotto? Implications for Lottery Design

Abstract

Despite its unusual payout structure, the Canadian 6/49 Lotto is one of the few government sponsored lotteries that has the potential for a favorable strategy we call "buying the pot." By buying the pot we mean that a syndicate buys each ticket in the lottery, ensuring that it holds a jackpot winner. We assume that the other bettors independently buy small numbers of tickets. This paper presents (1) a formula for the syndicate's expected return, (2) conditions under which buying the pot produces a significant positive expected return, and (3) the implications of these findings for lottery design.

Explore related subjects

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Steven D. Moffitt, William T. Ziemba. 2018-01-05. Does it Pay to Buy the Pot in the Canadian 6/49 Lotto? Implications for Lottery Design. https://arxiv.org/abs/1801.02959

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

Testing for Monotone Equilibrium Strategies in Games of Incomplete Information

This paper develops a unified framework for testing monotonicity of Bayesian Nash equilibrium strategies in unobserved types in games of incomplete information. We show that, under symmetric independent private types, monotonicity of differentiable equilibrium strategies is equivalent to monotonicity of a quasi-inverse strategy identified from observed actions. This allows the problem to be reformulated as testing a countable set of moment inequalities involving unconditional expectations. We propose a Cramer-von Mises-type statistic with bootstrap critical values. The method accommodates covariates and game heterogeneity. Monte Carlo simulations demonstrate finite-sample performance, and an application to procurement auctions illustrates cartel detection.

econ.EM

Ordinal Distributional Change and Conservative Transition Benchmarks: Measurement, Identification, and Inference

Repeated cross-sections reveal changes in ordinal distributions but not the transitions producing them. I axiomatically characterize a threshold-weighted probability metric for ordinal change from threshold-crossing principles. For any threshold-additive ordinal geometry, the discrepancy coincides with the Wasserstein--1 distance induced by that ground metric and measures minimum displacement; its optimizing plans define conservative transition benchmarks. With missing outcomes, I derive sharp identified sets for the discrepancy and endpoint-conditioned benchmark plans. I develop finite-sample-valid projection inference using randomized Monte Carlo calibration and global search with an almost-sure convergence guarantee. Applied to Arab Barometer data, the framework documents a robust shift toward broader and more regular remittance receipt in Lebanon. The discrepancy interval remains well separated from zero after allowing for item nonresponse and sampling uncertainty, while benchmark bounds provide strong numerical evidence that least-displacement restructuring excludes movement toward less frequent receipt and requires reassignment from nonreceipt to recurrent receipt.

econ.EM

A Stochastic Nested Fixed Point Algorithm for Large-Scale BLP Estimation

We develop a stochastic nested fixed point (SNFP) estimator for random coefficients logit demand models that updates model parameters using stochastic gradients and performs demand inversion one market at a time. Relative to the conventional nested fixed point (NFP) estimator, SNFP substantially reduces memory requirements and computational cost, making estimation feasible in very large datasets. We establish the large-$T$ (number of markets) asymptotic properties of the estimator under regularity conditions. We also characterize the effect of sharing one block of simulation draws across markets and show how to correct for it. Monte Carlo simulations show that the SNFP estimator achieves statistical accuracy comparable to the NFP estimator, and in our benchmark a single online pass estimates a model with 100 million markets in about 5.5 hours. An empirical application using scanner data further demonstrates the practical advantages of SNFP for large-scale demand estimation.

econ.EM