How Not to Win a Million Dollars: A Counterexample to a Conjecture of L. Breiman
نویسنده
چکیده
Consider a gambling game in which we are allowed to repeatedly bet a portion of our bankroll at favorable odds. We investigate the question of how to minimize the expected number of rounds needed to increase our bankroll to a given target amount. Specifically, we disprove a 50-year old conjecture of L. Breiman [1], that there exists a threshold strategy that optimizes the expected number of rounds; that is, a strategy that always bets to try to win in one round whenever the bankroll is at least a certain threshold, and that makes Kelly bets (a simple proportional betting scheme) whenever the bankroll is below the threshold.
منابع مشابه
On the oriented perfect path double cover conjecture
An oriented perfect path double cover (OPPDC) of a graph $G$ is a collection of directed paths in the symmetric orientation $G_s$ of $G$ such that each arc of $G_s$ lies in exactly one of the paths and each vertex of $G$ appears just once as a beginning and just once as an end of a path. Maxov{'a} and Ne{v{s}}et{v{r}}il (Discrete Math. 276 (2004) 287-294) conjectured that ...
متن کاملFrankl's Conjecture for a subclass of semimodular lattices
In this paper, we prove Frankl's Conjecture for an upper semimodular lattice $L$ such that $|J(L)setminus A(L)| leq 3$, where $J(L)$ and $A(L)$ are the set of join-irreducible elements and the set of atoms respectively. It is known that the class of planar lattices is contained in the class of dismantlable lattices and the class of dismantlable lattices is contained in the class of lattices ha...
متن کاملPredicting the Country Commodity Imports Using Mixed Frequency Data Sampling (MIDAS) Model
P redicting the amount of country imports toward assessing trade balance and its effect on the balance of payments (BOP) and finally money supply, general level of prices and the rate of economic growth is of paramount importance. Therefore, economic policymakers seriously need a model which cannot only predict the volume of imports well but also be capable of re...
متن کاملRole of Nitric Oxide in the Antipruritic Effect of WIN 55,212-2, a Cannabinoid Agonist
Introduction: For centuries, cannabinoids are known to be effective in pain relief. Itch is an unpleasant sensation that provokes a desire to scratch. Since itch and pain are two sensations sharing a lot in common, we aimed to investigate whether the cannabinoid agonist WIN 55,212-2 reduces serotonin-induced scratching behavior and also observe whether modulation of nitric oxide (NO) production...
متن کامل$L^p$-Conjecture on Hypergroups
In this paper, we study $L^p$-conjecture on locally compact hypergroups and by some technical proofs we give some sufficient and necessary conditions for a weighted Lebesgue space $L^p(K,w)$ to be a convolution Banach algebra, where $1<p<infty$, $K$ is a locally compact hypergroup and $w$ is a weight function on $K$. Among the other things, we also show that if $K$ is a locally compact hyper...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- CoRR
دوره abs/1112.0829 شماره
صفحات -
تاریخ انتشار 2011