Casino Yahtzee is commonly described as a cross between Yahtzee and Bingo, and that is pretty spot on. The object of Casino Yahtzee is to score points by being the first one to “close” certain score rows and columns. The player with the most points once all score rows and columns are complete wins! Casino Yahtzee Dice Board Game Milton Bradley 1986 Excellent like New condition 3 dice are missing Vintage. Condition is 'Used' Casino Yahtzee Dice Board Game Milton Bradley Vintage 1986 Complete. Condition is 'Used'. Shipped with USPS First Class. How to get a Full House in Yahtzee: To obtain a full house in Yahtzee, you need to get 2 sets of identical dice. 1 set of 3 identical dice + 1 set of 2 identical dice. For example: 5, 5, 5, 2, 2 is a full house; 4, 4, 3, 3, 4 is also a full house (order of the dice does not matter) but 5, 6, 6, 1, 5 is not one (because of the 1).

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byMilton Bradley, E.S. Lowe, MB Spellen (1986) 2 to 4 8+ 45 minutes Designers Family 10 stars9 stars8 stars7 stars6 stars5 stars4 stars3 stars2 stars1 star Description From the back of the box: Casino Yahtzee combines the suspense of a gambling game with the strategy of Yahtzee. The challenge is to toss the dice and roll the numbers you need. Use chips to cover rows of numbers on your gameboard. Win points when you complete a row. Points can be scored across, down and diagonally. Use strategy too. Try to win the rows with the highest points by choosing the colored dice that can make it happen. Watch out for your opponents. If they roll the right numbers first, they can block you. Score the most points and win the game! Contents: 5 Special Dice: - 1 die: 1-6 - 1 die: 2-7 - 1 die: 3-8 - 1 die: 4-9 - 1 die: 5-10 1 Dice Cup 1 Dice Tray 4 Plastic Game boards with sliding tops Black Chips White Chips 1 Score Pad Instructions Game Discussions Add Comment You need to be logged in to comment. x Item: Item: Item: Comments (0) Marketplace No listings at the moment. Click here to list it for sale. Listing Date Listed By Price $ Item Condition Description Similar Games

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I think everyone knows how to play Yahtzee (please google the rules if you don't). You have 13 rounds of rolling dice to make 13 objectives which are awarded with different number of points. In each round you make an initial roll, hold 0 to 5 dice and roll the remainder, then hold 0-5 dice and and proceed with the final roll. You are trying to maximize the number of points you achieve at the end of all 13 rolls.
The tension in Yahtzee game strategy arises from the need to make decisions about which objective to pursue after seeing the outcome of the 1st and 2nd rolls in any given round. There are so many possible situations in Yahtzee, that I don't think anyone has ever calculated optimum strategy for the entire game. There are lots of websites with general strategy principles/rules but some of the strategy decisions when you have only a few rolls left still seem to be relatively unanalyzed.
So, I am starting this thread because this is the best damn forum to take some bites out of the Yahtzee strategy problem. And, if nothing else, we can pose some interesting problems for the math geeks on this forum to analyze.
To get us started, here is some information I've calculated on what occurs on the initial roll of 5 dice.

Permutations
Yahtzee (5oak)	0.0008
150
Full House	0.0386
1200
2 Pair + 1 Sing.	0.2315
3600
No Pair	0.0926
7776
240
No Pair Short Straight	0.0926
66 Pair Short Straight	0.0077
120
44 Pair Short Straight	0.0231
180
22 Pair Short Straight	0.0154
60
Total Short Straight	0.1235

And if you are chasing a single top category such as 6's, here are the probabilities I've calculated for the first roll.

Permutations
Five 6s	0.0001
25
Three 6s	0.0322
1250
One 6	0.4019
3125
TOTAL	1

Here are some problems to get us started:
Problem #1: There is only one round left, and you need to fill the FULL HOUSE line. What is the probability of being successful?
Problem #2 There is only one round left, and you need to fill the LONG STRAIGHT line with either 65432 or 54321. Your initial roll, unluckily enough, is a Yahtzee: 11111. Do you hold one dice and roll four dice? Or do you reroll all five dice? What is the strategy for the third roll? What is the expected probability of making a LONG STRAIGHT with this initial roll?
Problem #3 There are three rounds left. You need to fill 'THREES', 'SIXES' and 'FULL HOUSE'. You need 27 points between the 'THREES' and 'SIXES' to make the 35 point bonus for the top categories. The FULL HOUSE category is 25 points.
You first roll is: 66333. What should you do?
Including the 35 point bonus as appropriate, what is the EV in points for the last three rounds if you decide to :
- keep all five dice as a FULL HOUSE?
- keep the two 6s and reroll hoping to roll more 6s
- keep the three 3s and reroll hoping to roll more 3s
(I never said these would be simple problems.)
Any general comments on the Yahtzee Strategy problem are welcome as well!DRich

Do you have or have you read Olaf's Yahtzee book? He used to be a slot machine designer and BJ strategy guy.

No, I have never heard of it until this moment. I imagine that he has probably worked out all the expectations for most of the situational decisions that I am proposing.
I enjoy working on the mathematics of game strategies. Many of us have worked out the probabilities of many blackjack decisions even though books and the WOO site are available. The same is true for many casino games -many of us do the math ourselves. I was proposing that we do that for Yahtzee; if no one else is interested I'll just go ahead an do it myself unless I lose interest.FinsRulecharliepatrick

...Any general comments on the Yahtzee Strategy problem are welcome as well!

There's an interesting read at https://en.wikipedia.org/wiki/Yahtzee which describes some of the decisions. It looks a tough game to analyse.

There's an interesting read at https://en.wikipedia.org/wiki/Yahtzee which describes some of the decisions. It looks a tough game to analyse.

Thanks Charlie. I also found this viewchart presentation from the Netherlands Optimal YAHTZEE strategy . Its slow to get going, but the second half of it has some interesting analysis.gordonm888Here is some statistical information I found for the outcomes (without the Extra Yahtzee Bonus) when its your last turn and these are the single remaining Yahtzee hand category you are targeting.

Expected Value
Aces	6.49
4.21
Threes	6.49
8.43
Fives	6.49
12.64
15.19
4 of a kind	72.26
9.15
Short Straight	38.40
10.61
Yahtzee	95.40
23.33

This is from the link I referenced in my previous post.Amazing thread. Thanks for starting it.charliepatrick

Here is some statistical information...when its your last turn...

Yahtzee Slots

I can see the recursive approach, similar to how to do BJ. Also I noticed that One thru Sixes are always going to be X thru 6X, since it's just a matter of how many of 'what you want' you get multiplied by the value.
So I guess at N options to go you look at the {throw,# rolls left} and which dice to keep. Then like BJ look at where you're at and where you might land up and work out the EVs (or expected score). I suspect once you get going (programming wise) it's a matter of cranking a very big handle.
I feel a challenge looming!

I can see the recursive approach, similar to how to do BJ. Also I noticed that One thru Sixes are always going to be X thru 6X, since it's just a matter of how many of 'what you want' you get multiplied by the value.
So I guess at N options to go you look at the {throw,# rolls left} and which dice to keep. Then like BJ look at where you're at and where you might land up and work out the EVs (or expected score). I suspect once you get going (programming wise) it's a matter of cranking a very big handle.
I feel a challenge looming!

Parts of the problem involving the three rolls in a given round can be addressed by Markhov chains e.g., pursuing 6's, i.e. whenever you have one 6 you will roll four dice and the outcome probabilities for one, two, three, four, five 6's are always the same; when you start a roll with 2 sixes you will roll 4 dice and there will be another set of transiotion probabilities for two, three, four and five dice, etc.

Casino Yahtzee Instructions

Casino Yahtzee Instructions

The problem comes when you are rolling for Yahtzee or 4oak and you get say, two 6s on the first roll, but the second roll is three 4's, then you switch to fours. The rolls then switch to looking for 4s.

Casino Yahtzee Instructions Printable