Need help with strategy for a simple game for a book I am writing:

[rakbeater]

I hope this is the right forum to put this in. This is a strategy I am trying to fine tune for a book I am writing about the card game Pinochle.

Here are the rules:

Two player game - First player to 40 points wins. Game starts 0 points to 0 points.

Players alternate turns.

One turn consists of rolling one six-sided die (numbers 1-6) and adding that number to your score.

Here is where the strategy comes into play...

If your opponent rolls a 5 or 6, you have the option to keep your opponent from adding that number to their score and instead subtracting it from your score.

So if the score is 10 to 10 and your opponent rolls a 5, the score would be 15 to 10. You have the option to subtract that 5 instead of allowing your opponent to add to his score. That would make the score 10 to 5. You would be down 5 either way.

The strategy question is...in what score situations would you choose to subtract from your score instead of letting your opponent add to his score? Can you make a set of rules to guide your decision making process for each score situation?

 

[viraltux]

I would subtract whenever I am behind and allow him to add whenever I am ahead as long as doing so would not get him ahead...

I don't know the game but for what you say I don't think there is much to it, just keep the guy away from 40 when you're behind and allow him to get close to you when you're ahead. Am I missing something?

 

[rakbeater]

What about in situations where the score is tied or very close?

And at different points in the game (beginning, middle, end)?

 

[Stephen Tashi]

First player to 40 points wins.

The first player to get exactly 40 points or the first player to get 40 or more points?

 

[rakbeater]

The first player to get exactly 40 points or the first player to get 40 or more points?

I apologize, that part wasn't clear. First player to get 40 or more points. Thanks.

 

[viraltux]

What about in situations where the score is tied or very close?

And at different points in the game (beginning, middle, end)?

The rule still applies, think about it in the following example; imaging it is a football match and whoever has the highest score after 40 minutes wins, well, in that scenario if you are ahead you want the match to finish the sooner the better, and if you are behind you want the match to have more minutes so that you have more chances to recover.

So it does not matter what point of the game you're at; if after the addition/subtraction you are behind then you subtract, otherwise you add.

Just one more comment, in this analysis I am assuming that both players are equally good. If by subtracting or adding you end up in a tie but you are much better player, then you should subtract so that you have "more minutes" to beat the weaker opponent, inversely, if you are a weaker opponent it would be better for you to add so that you both are close to the end of the match and you can hope a stroke of luck might give you the final victory.