Recent studies on the Dice Race Problem and its connections

Guy Louchard. "Recent studies on the Dice Race Problem and its connections." Mathematica Applicanda 44.1 (2016): null. <http://eudml.org/doc/293197>.

@article{GuyLouchard2016,
abstract = {The following type of dice games has been mentioned and/or studied in the literature. Players take turns in rolling a fair die successively, each player accumulating his or her scores as long as the outcome 1 does not occur. If the result 1 turns up, the accumulated score is wiped out, and the turn ends, that is the player gives the die to the next player. At any stage after a roll, the player (she, say) can choose to end her turn and bank her accumulated score. The winner is the first player to reach some xed target n 2 N. We present some new results on optimal strategies and winning probability in a one or two players game. For just one player there is no competition of course, and in this case we suppose that the player simply wants to minimize her total expected number of tosses over all possible banking strategies.},
author = {Guy Louchard},
journal = {Mathematica Applicanda},
keywords = {dice game, threshold strategy},
language = {eng},
number = {1},
pages = {null},
title = {Recent studies on the Dice Race Problem and its connections},
url = {http://eudml.org/doc/293197},
volume = {44},
year = {2016},
}

TY - JOUR
AU - Guy Louchard
TI - Recent studies on the Dice Race Problem and its connections
JO - Mathematica Applicanda
PY - 2016
VL - 44
IS - 1
SP - null
AB - The following type of dice games has been mentioned and/or studied in the literature. Players take turns in rolling a fair die successively, each player accumulating his or her scores as long as the outcome 1 does not occur. If the result 1 turns up, the accumulated score is wiped out, and the turn ends, that is the player gives the die to the next player. At any stage after a roll, the player (she, say) can choose to end her turn and bank her accumulated score. The winner is the first player to reach some xed target n 2 N. We present some new results on optimal strategies and winning probability in a one or two players game. For just one player there is no competition of course, and in this case we suppose that the player simply wants to minimize her total expected number of tosses over all possible banking strategies.
LA - eng
KW - dice game, threshold strategy
UR - http://eudml.org/doc/293197
ER -