Manipulate[
dirs={{1,100},{1,-100}};
gamblerinit={{0,1000}};
baseline={{0,0}};
Graphics[
{{Opacity[0.33], Dynamic@Line[If[1000000-Last[gambler][[2]]>0&&Last[gambler][[2]]>0&&!paused,AppendTo[gambler,Last[gambler]+RandomChoice[dirs]],gambler]]},
Red, PointSize[Large],Dynamic@Point[Last[gambler]]},PlotRange->{0,Full},Axes->True,AspectRatio->Full,ImageSize->1000],
{{gambler,gamblerinit},ControlType->None},
{paused,{False,True}}
]