% dice.m -----------------------------------------------------------
% Simulation of the Sam Loyd's Carnival Dice game:
% - You bet 1 dollar to play. You then roll 3 dice
% - If one six appears you get 2 dollars
% - If two sixes appear, you get 3 dollars
% - If three sixes appear, you get 4 dollars
% - Otherwise, you get nothing
% Is this a good bet to make?
% Three traces are created:
% - accumulated winnings
% - earnings per bet
% - expected earnings per bet
%
% The first two traces are displayed as they are computed, i.e. every time the
% dice are rolled, a new value is appended to the trace and the plot is updated
% so you can watch the function grow in real time.
%
% A second axis is added near the top of the figure to show the dice. For
% each die, a line with dots as markers is added for each of the six faces,
% with only one of these lines being visible at a time. A square patch is
% also added for each die for the visual effect.
% dice() - sets up simulation. No bets are placed until you click on a button.
% dice(n) - sets up simulation & makes n bets.
% dice(0) - sets up simulation & makes bets continously until you click stop.
% ----- Author: ----- Paul Mennen
% ----- Email: ----- paul@mennen.org
function dice(in1)
S.tr = plt(0,[0 0 0],'FigName','3 dice problem','Options','-Y-XTicks',...
'Xlim',[0 100],'Ylim',[-10,10],'YlimR',[-.15 .05],'Right',[2 3],'DisTrace',[0 1 1],...
'LabelX','# of bets','LabelY',{'Accumulated winnings' 'Earnings per bet'},...
'TraceID',{'Accum' 'per bet' 'expect'},...
'TraceC',[0 1 0; 1 0 1; .3 .3 .3],'AxisPos',[1 1 1.05 .85]);
c = get(gcf,'color');
S.ax = getappdata(gcf,'axis');
axes('units','norm','pos',[.5 .88 .38 .1],...
'color',c,'xcolor',c,'ycolor',c,'xlim',[0 5]);
patch([0 2 4; 1 3 5; 1 3 5; 0 2 4],[zeros(2,3); ones(2,3)],[0 .2 .3]);
S.tx = text(5.5,.4,' ','color',[0 .7 1],'fontsize',28);
cx = .5; cy = .5; e = .3;
for k = 1:3 % draw all possible rolls for each of 3 die
S.d(k,1) = line(cx, cy); % one dot
S.d(k,2) = line(cx+[-e e], cy+[-e e]); % two dots
S.d(k,3) = line(cx+[-e 0 e], cy+[-e 0 e]); % three dots
S.d(k,4) = line(cx+[-e e e -e], cy+[-e -e e e]); % four dots
S.d(k,5) = line(cx+[-e e e -e 0], cy+[-e -e e e 0]); % five dots
S.d(k,6) = line(cx+[-e -e -e e e e], cy+[-e 0 e -e 0 e]); % six dots
cx = cx + 2;
end;
set(S.d,'vis','off','linestyle','none','marker','s','color',[1 1 .5],...
'linewidth',3,'markersize',4);
S.sli = uicontrol('style','slider','value',0.95);
S.betC = uicontrol('CallBack',{@btn,S,1});
S.bet1 = uicontrol('CallBack',{@btn,S,0});
S.clr = uicontrol('CallBack',{@btn,S,-1});
set([S.bet1 S.betC S.clr S.sli],...
{'Position'},{[90 490 50 22]; [170 490 70 22]; [270 490 40 22]; [135 460 175 18]},...
'Units','Norm',{'String'},{'1 bet'; 'Continuous'; 'Clear'; '';});
text(-4.9,.15,'Speed','color',[.5 .5 .5]);
w = -6^3; % cost of placing all possible bets
w = w + 2*75; % 75 ways to win 2 dollar
w = w + 3*15; % 15 ways to win 3 dollars
w = w + 4*1; % 1 way to win 4 dollars
set(S.tr(3),'x',[0 1e9],'y',[w w]/6^3); % set earnings/bet expected value (trace3)
if nargin
if ~in1 btn(0,0,S,1); end; % for dice(0), click the continuous button
for k = 1:in1 btn(0,0,S,0); end; % otherwise click the 1bet button in1 times
end;
% end function dice
function btn(h,arg2,S,arg4) % button callbacks -------------------------------------------
if ~isfield(S,'betC') S.betC = h; end;
t = get(S.betC,'string');
set(S.betC,'string','Continuous'); % stop if it was running
if arg4==-1 % clear button comes here ---------
set(S.tr(1:2),'x',0,'y',0); % reinitialize the data and axis limits
set(S.ax(1),'xlim',[0 100],'ylim',[-10 10]);
set(S.ax(2),'xlim',[0 100],'ylim',[-.15 .05]);
return;
end;
if t(1)=='S' return; end; % If it was running (continuous) we are done
x = get(S.tr(1),'x'); xe = x(end); % single or continuous betting comes here
y = get(S.tr(1),'y'); ye = y(end);
y1 = min(y); y2 = max(y);
yr = get(S.tr(2),'y');
set(S.betC,'string','Stop');
while ishandle(S.betC)& strcmp(get(S.betC,'string'),'Stop')
if ~arg4 set(S.betC,'string','Continuous'); end; % do just one bet
set(S.d,'vis','off'); % turn all the faces off
r = ceil(rand(1,3)*6); % roll the 3 dice
set([S.d(1,r(1)) S.d(2,r(2)) S.d(3,r(3))],'vis','on');
r = sum(r==6); if ~r r=-1; end; % earnings for this bet
set(S.tx,'string',num2str(r)); % show the earnings
xe = xe + 1; x = [x xe]; % advance the x-axis by 1 bet
ye = ye + r; y = [y ye]; % add the earnings to accumulated winnings
set(S.tr(1),'x',x,'y',y);
xlim = get(S.ax(1),'xlim');
if xe > xlim(2) set(S.ax,'xlim',[0 xlim(2)+200]); end;
y1 = min(y1,ye); y2 = max(y2,ye);
set(S.ax(1),'ylim',10*[floor(min(y1,-10)/10) ceil(max(y2,10)/10)]);
yr = [yr ye/xe]; % add earnings/bet to line 2 on the right hand axis
set(S.tr(2),'x',x,'y',yr);
pause(1-get(S.sli,'value')); % adjust the speed of the loop
end;
% end function btn
