Yahtzee theory

[AdamM]

I have a friend who says Yahtzee is pure luck.
I'm asserting that you can apply some of the same princuiples as you can to poker to give an edge.

The example I've given though is way beyond my maths.
Please help me work this out.

you have two spaces left to fill, the large straight and the four of a kind.
your first roll is 1,2,4,5,5
Can we work out if the correct strategy is to take two rolls at the 3 with the single dice (which I make a 1/3 chance of hitting), or do we keep the two and roll for the four of a kind on .

A factor probably needs to be that the large straight awards 40 points, but the four of a kid will award 20 points, plus the value of the fifth dice (average 3.5 presumably) but on the occasions we make a bonus Yahzee, we get that 23.5 plus a 50 bonus.

anyone brave enough to take this on for me?

[Laxie]

I'm going for the 4 of a kind, but that's probably wrong.

[Jon MW]

lol it's largely luck but there's definitely game theory behind it where you can maximise your points by taking the right options at the right time.

I don't think I can be quite interested enough to work out how much luck you'd need to overcome perfect strategy but I'd assume it wouldn't be that high.

[AdamM]

I appreciate the edge is quite small, but I'm now interested in this specific problem.
I gave it a shot, but my brain started sweating.

[AdamM]

and I guess it'd also be interesting (well, kind of) to also work out the same but with a first roll of 2,3,4,5,5 making you up and down on the large straight

[Doobs]

and I guess it'd also be interesting (well, kind of) to also work out the same but with a first roll of 2,3,4,5,5 making you up and down on the large straight

Must be best to go for the high straight with low as back up? 

Your mate think poker is random too?

[Acidmouse]

I play a bit online and the good players know what score to take and when to gamble,  lots of tactics and thinking tbh.  I am sure there is game theory math online somewhere

[AdamM]

Assume this is the last two slots.
Short straight, fives on the top, all gone.

She's not a poker player, but think she accepts the skill factor in poker.

[Doobs]

It is straight probability and not really game theory.  Probability of hitting open ender with one throw is 1/3. 

Probability of two more in one throw of 3 dice is 1/6^2 x 5/6 x 3, which is much lower.

Etc.

[Tal]

It is straight probability and not really game theory.  Probability of hitting open ender with one throw is 1/3. 

Probability of two more 5s in one throw of 3 dice is 1/6^2 x 5/6 x 3, which is much lower.

Etc.

This.

(Also got rid of that five of spades thing that really winds me up - sorry!)

[Simon Galloway]

Used to be several people in the workplace with electronic yahtzee games, so there were lots of bets/challenges comps.  Without overdoing the maths, there was definitely an edge to be had.  Chasing the bonus Yahtzee (100 points) was the gambit, and better players were more readily prepared to put zero's in their 1's or 2's in the top half as required.  2,3,4,5,x was a pretty good roll, small straight locked up and a mathematical fav to make the long straight in 2 rolls.  Other than that, chase the yahtzee ftw as default, but similar to golf matchplay, be prepared to deviate according to how the opponent is faring.

[Tal]

http://www.math.cornell.edu/~mec/2006-2007/Probability/Yahtzee.htm

There are loads of others if you give it a quick Google.

[Claw75]

on the occasions we make a bonus Yahzee, we get that 23.5 plus a 50 bonus.

I'm useless as far as this kind of maths is concerned. Isn't a bonus yahtzee 100 points though? I'd be giving that a shot. Would probably go for the high straight if i was open ended. Really fancy a game now - it's been years!

[AJR14]

I play a bit online and the good players know what score to take and when to gamble,  lots of tactics and thinking tbh.  I am sure there is game theory math online somewhere

Online yahtzee?! This thread may have just made my social life take a hit. What sites are best and do you play for money or just fun v other people?

Used to play with family all the time, but havent played for ages.