First to reach n game
Volkov, Stanislav LU
and Wiktorsson, Magnus
LU
(2026)
In Statistics and Probability Letters
235.
- Abstract
- We consider a game with two players, consisting of a number of rounds, where the first player to win rounds becomes the overall winner. Who wins each individual round is governed by a certain urn having two types of balls (type 1 and type 2). At each round, we randomly pick a ball from the urn, and its type determines which of the two players wins. We study the game under three regimes. In the first and third regimes, a ball is taken without replacement, whilst in the second regime, it is returned to the urn with one more ball of the same colour. We study the properties of the random variables equal to the properly defined overall net profits of the players, and the results are drastically different in all three regimes.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/080c9e3b-cd87-409e-905e-535460c1e345
- author
- Volkov, Stanislav
LU
and Wiktorsson, Magnus
LU
- organization
- publishing date
- 2026-08-01
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Gambler’s ruin problem, Rubin’s construction, Pólya’s urn
- in
- Statistics and Probability Letters
- volume
- 235
- article number
- 110713
- pages
- 8 pages
- publisher
- Elsevier
- ISSN
- 0167-7152
- DOI
- 10.1016/j.spl.2026.110713
- language
- English
- LU publication?
- yes
- id
- 080c9e3b-cd87-409e-905e-535460c1e345
- alternative location
- https://linkinghub.elsevier.com/retrieve/pii/S0167715226000775
- date added to LUP
- 2026-03-12 11:40:07
- date last changed
- 2026-03-16 09:35:26
@article{080c9e3b-cd87-409e-905e-535460c1e345,
abstract = {{We consider a game with two players, consisting of a number of rounds, where the first player to win rounds becomes the overall winner. Who wins each individual round is governed by a certain urn having two types of balls (type 1 and type 2). At each round, we randomly pick a ball from the urn, and its type determines which of the two players wins. We study the game under three regimes. In the first and third regimes, a ball is taken without replacement, whilst in the second regime, it is returned to the urn with one more ball of the same colour. We study the properties of the random variables equal to the properly defined overall net profits of the players, and the results are drastically different in all three regimes.}},
author = {{Volkov, Stanislav and Wiktorsson, Magnus}},
issn = {{0167-7152}},
keywords = {{Gambler’s ruin problem; Rubin’s construction; Pólya’s urn}},
language = {{eng}},
month = {{08}},
publisher = {{Elsevier}},
series = {{Statistics and Probability Letters}},
title = {{First to reach n game}},
url = {{http://dx.doi.org/10.1016/j.spl.2026.110713}},
doi = {{10.1016/j.spl.2026.110713}},
volume = {{235}},
year = {{2026}},
}