赌徒输光问题的理论分析与模拟

1、模拟赌徒输光问题的输光概率和博弈持续时间的程序代码：ticp=0.3;a=10;z=5;l=0;m=0;generation=10000;num=0;for i=1:generation flag=1; z=5; while(flag) r = rand(); if r>1-p z=z+1; else z=z-1; end if z=0 l=l+1; flag=0; end if z=a m=m+1; flag=0; end endendwin=m/(m+l)lost=l/(m+l)toc求不同下的输光概率clearp=0.1:0.1:1;a=10;z=5; generation=100

2、00;for i=1:length(p)r=0;for j=1:generation m(j)=0;l(j)=0;flag=1;z=5;while(flag)r=rand(); if r<p(i) z=z+1; else z=z-1; end if z=0 l(j)=l(j)+1; flag=0; end if z=a m(j)=m(j)+1; flag=0; endendm(j)=m(j)/(l(j)+m(j);l(j)=l(j)/(l(j)+m(j);endlost(i)=mean(l);win(i)=mean(m);end动画模拟赌徒输光问题程序：fmat=moviein(30);

3、axis(-2 22 -2 22);hold on;a=20;u=10;p=0.5;%初始参数a,u,p;axis equalt=0:0.01:2*pi;y=5+0.3*sin(t);for i=0:a x=i+0.3*cos(t); fill(x,y,'b');endplot(u,u,5,7,'k');text(u,6,'leftarrow初始位置')plot(0,0,5,7,'k');text(0,6,'leftarrow赌徒输光了')plot(a,a,5,7,'k');text(a,6,

4、9;leftarrow赌徒大获全胜')x=u+0.3*cos(t);k=1;plot(-1,21,5,5,'b','LineWidth',2);fill(x,y,'r');fmat(:,k)=getframe;flag=1; %初始条件r=0;while(flag) r = rand() %产生一个随机数 if r<p u=u+1; %赌徒赢，向右移一格，代表赌本增加一 else u=u-1; %赌徒输，向左移一格，代表赌本减少一 end if u=0|u=a %游戏结束，赌徒输光 flag=0; end k=k+1; fill(x

5、,y,'b'); fmat(:,k)=getframe; k=k+1; x=u+0.3*cos(t); fill(x,y,'r'); fmat(:,k)=getframe;end不同下的博弈持续时间程序代码:clearp=0:0.01:1;a=20;u=10; generation=100;for i=1:length(p)k(i)=0;flag=1; r=0;for j=1:generation m(j)=0;while(flag)r=rand(); if r<p(i) u=u+1; else u=u-1; end if u=0|u=a flag=0;

6、end m(j)=m(j)+1;endflag=1;u=10;endk(i)=mean(m);endplot(p,k);hold onf=polyfit(p,k,16);plot(p,polyval(f,p),'r');legend('模拟的情况','用多项式对数据的拟合');title('p与赌博持续时间的关系');xlabel('p的变化');ylabel('赌博的持续时');当赌注发生变化时，求出不同下的博弈持续时间代码:clearp=0.5;a=20;u=10;generation=100;

7、b=1:0.1:10;for i=1:length(b)k(i)=0;flag=1; r=0; for j=1:generation m(j)=0;while(flag)r=rand(); if r<p u=u+b(i); else u=u-b(i); end u if u<=0|u>=a flag=0; end m(j)=m(j)+1;endflag=1;u=10;endk(i)=mean(m);endplot(b,k);hold onx1=ones(size(b)'x2=(1./b)'x=x1,x2;y=k'b1,bint,r,rint,stats=regress(y,x,0.05);plot(b,x*b1,'r'); legend(