[ View Thread ] [ Post Response ] [ Return to Index ] [ Read Prev Msg ] [ Read Next Msg ]

BGonline.org Forums

OT - Yahtzee Problem - Rollout

Posted By: Stick
Date: Saturday, 17 December 2011, at 10:47 p.m.

In Response To: OT - Yahtzee Problem (Stick)

I either though people would be more familiar with the game or that the math behind it would be more obvious/interesting for backgammon players.

Again, this is my opponent's last turn no matter what he gets. If he rolls for aces and scores in that box his game is over. If he rolls for yahtzee and misses he'll have to zero out the aces box. If he rolls for yahtzee and gets it, he still has to fill in the aces box.

Scenario #1 - Rolling for the Yahtzee

First, the easy scenario, roll for the Yahtzee. If he makes his yahtzee he'll win regardless of what I do on my turn. If he misses his yahtzee he'll lose since he's already behind on the scorecard. The odds of him making a yahtzee needing one four over two rolls is equal to 11/36 or ~30.5% of the time. (odds of him not rolling a four over two rolls is 5/6 * 5/6 or 25/36)

Scenario #2 - Rolling for the aces

The second scenario he rolls for the aces. I know it feels like if he goes for aces that he should automatically almost get at least one more with two rolls of four dice left but that's not the case. The odds of him not getting another ace and therefore losing immediately is (5/6)^8 or 390625/1679616 which is ~23%. Therefore he loses 23% of the time immediately.

Now, of the ~77% of the time he makes his top by rolling at least one more ace he still has to worry about me making a small straight. If I make my small straight on my last turn of the game I win. I'm a small favorite to make a small straight on one turn when that's all I'm shooting for, about 53%. That means going for the aces overall will win ~36% of the time.

There is another scenario or two worth briefly thinking about, such as rolling for the yahtzee on the first roll and then switching to go for aces if you miss. The most obvious problem here of course is that you're also throwing back the ace so when you don't yahtzee or roll the ace again on that one turn you're stuck needing two aces with five dice if you go that route.

I have also ignored going for the aces and making a yahtzee that way. The probability is so low it has no overall effect on the decision.

My opponent at the time went for the yahtzee and I told him I thought it was wrong. Oddly enough, he didn't make it and the game was mine!

Bored? Play games of Yahtzee online against yourself:

Interface #1

There other places to do it with difference interfaces but that's the one I go with. If you're interested in improving your game this link gives you a hand on what you should roll for to score the optimal score. The biggest fallback of things like this is that you aren't playing against anyone and that can often change your decisions during a game.

Stick

Messages In This Thread

 

Post Response
Your Name:
Your E-Mail Address:
Subject:
Message:

If necessary, enter your password below:

Password:
 

 

[ View Thread ] [ Post Response ] [ Return to Index ] [ Read Prev Msg ] [ Read Next Msg ]

BGonline.org Forums is maintained by Stick with WebBBS 5.12.