The game I am referring to is highly similar to Black Jack. However, instead of cards equal to a certain value: pure integers are used.
The participant starts the game by rolling 1-100 as much as wanted. After adding each roll together, if the total passes 100 the participant loses, but if the number adds up to exactly 100, the participant wins.
If the participant hasn't lost, the host will roll until their total is greater than the participant's. If the host passes 100, the participant wins, otherwise the Host wins.
In this game if the participant only continues to roll when their total is less than 58, the odds of the participant winning each game is nearly 43%.
I simply want to know: How can you calculate the exact odds of winning each next game?
Example: Let's say H=Host wins, and P=Participant wins.
Order of winners: PHPHHP
What are the odds of Participant winning after the following has been displayed, and how could the odds continue to be calculated?
The participant starts the game by rolling 1-100 as much as wanted. After adding each roll together, if the total passes 100 the participant loses, but if the number adds up to exactly 100, the participant wins.
If the participant hasn't lost, the host will roll until their total is greater than the participant's. If the host passes 100, the participant wins, otherwise the Host wins.
In this game if the participant only continues to roll when their total is less than 58, the odds of the participant winning each game is nearly 43%.
I simply want to know: How can you calculate the exact odds of winning each next game?
Example: Let's say H=Host wins, and P=Participant wins.
Order of winners: PHPHHP
What are the odds of Participant winning after the following has been displayed, and how could the odds continue to be calculated?