JLedesma_605

Timid strategy matrix initialization.

library(markovchain)

## Warning: package 'markovchain' was built under R version 4.2.2

## Package:  markovchain
## Version:  0.9.0
## Date:     2022-07-01
## BugReport: https://github.com/spedygiorgio/markovchain/issues

Start_Mat <- matrix(c(1,0,0,0,0,0,0,0,0,
                      .6,0,.4,0,0,0,0,0,0,
                      0,.6,0,.4,0,0,0,0,0,
                      0,0,0.6,0,.4,0,0,0,0,
                      0,0,0,.6,0,.4,0,0,0,
                      0,0,0,0,.6,0,.4,0,0,
                      0,0,0,0,0,.6,0,.4,0,
                      0,0,0,0,0,0,.6,0,.4,
                      0,0,0,0,0,0,0,0,1
                      ),nrow=9)

Start_Mat <- t(Start_Mat)
MarkovChain<- new('markovchain',transitionMatrix=Start_Mat)

Finding the absorbing state of the matrix probabilities.

absorptionProbabilities(MarkovChain)

##           1          9
## 2 0.9796987 0.02030135
## 3 0.9492466 0.05075337
## 4 0.9035686 0.09643140
## 5 0.8350515 0.16494845
## 6 0.7322760 0.26772403
## 7 0.5781126 0.42188739
## 8 0.3468676 0.65313243

##The probabilities of winning in the timid strategy is .0203 ```

For the bold strategy, Smith must win every game played and with a .4 probability of winning each game, the chances of getting out is \(.4^3\) or .064. Which is higher than .0203 making the bold strategy better.

JLedesma_605_HW10

2022-12-22

Timid strategy matrix initialization.

Finding the absorbing state of the matrix probabilities.

For the bold strategy, Smith must win every game played and with a .4 probability of winning each game, the chances of getting out is \(.4^3\) or .064. Which is higher than .0203 making the bold strategy better.