Congratulations! You've arrived at
The Yahtzee! Page
This
page probably covers everything you need to know about the dice game,
Yahtzee, including;
What you need to play
Yahtzee Rules
Probability and Statistics
Yahtzee High Scores and Low Scores
Playing
Strategy
Tell
Us Your Yahtzee High Score - fill in this page
if you'd like to tell us your (honest) yahtzee high score
What
Is Needed to Play the Game
At the most basic, all you need is five dice, paper and a pen. And perhaps a calulator to save time on adding up the scores. Its basically similar to poker dice, but you try for a high score rather than gamble with chips - although you could be competitive about it if you play head to head.
One Step Up, you can buy a purpose made Yahtzee dice game available in most toy stores and all over the internet. These come with formatted scorepad and something to roll the dice into so they don't all fall on the floor.
You can also get a hand-held
electronic version (pic below) which do all the work including adding
up the score
you. One of these was used in the 100 game stats test described further
down the page. These machines are carefully programmed with the correct
yahtzee rules, including the most common mistake which made on multiple
yahtzees - take a look at the yahtzee rules link if you're not sure.
These
days, you can play the game on-line
too - click this link to see five places you can play. Or you can download a free version right here.
You can also get a CD-Rom version to play on your PC, marketed as Ultimate Yahtzee by MB / Hasbro.
Of course you'll need
to know the rules, so here
they are;
The Yahtzee Rules
(click this link)
Theoretical Probability of Rolling Certain Scores
It
seems very attractive
to try and calculate the probability of completing various target
scores (such as full house) from various starting positions,
but in fact its appalling hard to do because there are so many
combinations possible. The first roll is entirely random, but has
dramatic affect on
the subsequent chance of achieving a given roll, so there's no fixed
starting point for an analysis. Also, the chances are affected by what
has already been rolled. If you've used 5's and three of a kind
already, a start throw of 5-5-3-6-4 is much less likely to yield a good
result than it would at the start of a game.
The chance of rolling a yahtzee in one turn
been calculated* as 4.6% or about 1:22 but even that assumes that the
player is targeting a yatzee and doesn't get tempted to go for a
straight after the first roll, or
take a random full house after roll two. These are things that happen
in real games, so the real odds are a little less.
And this is just an analysis on one roll type, not taking into account
previous scores or choices of how to select a given roll. The attempt
to statistically assess the likelihood of acheiving a given total score
is imponderably difficult .
* References - Tim Fulford Cornell University if you want to look at the derivation for yourself. Tim in Feburary 2008 went on to produce this simplest yet version of the maths.
Highest
and Lowest Possible
The lowest possible score in a game is fairly subject to tackle. The
absolute low is 5 - a yatzee of ones taken as chance everything else
taken as zero. This would need a good chunk of luck and a deliberate
attempt at a low score, but it remains possible. In normal play, where
an experienced player is trying to get a high score, less than 150 is
unusual although all the way down to about 110 is occasionally
possible.
The highest score possible with no Yahtzee's is 325, then 375 with one,
and 100 more for every subsequent yahtzee.
Since you only get 13 rolls in a game (see the rules, not all
players realise that additional yatzee's don't give you extra rolls)
the high
score ever possible is 1575 = 13 yahtzee's including all full scores in
all other boxes.
In
normal play, by and experienced player trying for a high score, the
best without a yahtzee is around 270. This requires 4 of each number on
the top row (and a bonus of course), plus good quality 3 and 4 of a
kind, and all three of full house, small and long straight. Most times
a good score is in the 250 to 260 zone, maybe pushing to 270.
Highest with and without yahtzee throw
The maximum score you're likely to get in a game with no Yahtzee is
around 270, so you might reasonably expect
the high scores with 1, 2 and 3 Yahtzee's to be 320, 420 and 520.
However, not that many games get over 260, and you won't get many 2 and
3 Yahtzees games to experiment with. This might lead you to expect
these games to score lower - but there's another trick up the yahtzee
rules sleve!
Each Yahtzees after the first scores 100 bonus, but still must be taken under one of the other categories (you only ever get 13 scores per game, even if you get more than one yahtzee). Thus a Y of 6's could be taken as 6's (worth 36 plus pretty much gauranteeing the bonus) on top of the Yahtzee bonus. If the top row score is already taken you can take it as a full score on any of the bottom row categories. This multiple yahtzee scoring means you should be able to top 520 with a 3 yahtzee game.
Measured Probability of Achieving Certain Scores
In December 2007 Chris Young, a very experienced Yahtzee player, played 300 games of Yahtzee using an electronic hand held device (using the electronic device has the useful effect of gauranteeing the yahtzee rules were ruthlessly followed). The following stats were found
Number of Yahtzee's rolled = 105, or one every 2.85 games. This exactly matches quite well with the theoretical expectation.
Low Score - 127
Highest Score with no yahtzee - 277
Highest Score with 1, 2 and 3 yahtzees - 326, 437, 504.
Again, these closely match expectations
The most interesting thing to come from this trial was the probability of achieving and overall game score, shown by this table and graph
| Score At Least | Probability |
| 150 | 98% |
| 200 | 81% |
| 250 | 45% |
| 300 | 13% |
| 400 | 3% |
| 500 | 1% |
Computer Generated Scores
In
January 2008 Tim Fulford and Oliver Humpidge independantly wrote
alogrithms to simulate Yahtzee games. Oliver ran his script for 300,000
turns and found about 1:22 resulted in Yahtzee which matches theory
very closely. Tim ran his for an impressive 15 million and came up with
1:27, but his algorithm didn't seem so good at playing the game,
because it got a low score of just 37 which its doubtful if a
human player could do without deliberately aiming for a low score. Its
high score was 918. It also showed only 60% chance of scoring at least
200, compared to over 80% by human expert Chris Young.
Game
playing strategy
Strategy
depends firstly on what you are trying to
acheive. This is split into two targets
1. You are trying to hit the best ever score in your life
2. You are trying to get the highest score you can in this game - eg in
a head-to-head roll off.
Full Houses. If your trying for absolute top score. the plan is clearly
aimed at maximising the yatzee chance. So if you roll 4-4-4-2-2 on the
first roll, don't score it as a full house - hold the fours and roll
on. If you're just trying
to make the most of this match, take the full house - they can come
thick and fast sometimes but other times when you're left with it to
get near the end its very
hard to play for. One way to play for a full house is, say you get
2-2-6-6-5, hold the two's and sixes. This give you a 1:3 chance if you
have one roll left and 5:9 if
you have two rolls (1/3+(2/3*1/3)). If you
miss though, you end up with a poor roll.
The other way is to wait for one to crop up of its own accord, and this
normally works.
Straights. Its good to get the straights out of the way early, so you
can concentrate on going for gold. That long straight can be stubborn
if you need it late in the game. Always look out for 2-3-4 or 3-4-5 on
the first roll, giving you a very high chance of
getting a small straigth with two further rolls - because you have two
dice to roll and two target numbers.
The other good one to get first roll is 2-3-4-5, again two rolls and
two target numbers, but only one dice to work with. This is you best
chance of a long straight unless one pops right out of the bag.
Top row. The dilema is whether to go for the sub-total bonus. You need
three of every number, and don't be fooled into thinking that dropping
a 1 is OK. That still means you have to get four of something else.
Most times, you need to get four of either 4's
5's or 6's to get the bonus, then you can afford to drop on at least
one of the lower sets. So, the first 4 of a kind you get needs
to be taken as numbers, not as four-of-a-kind. Save that for your
second four roll.
A good strategy on the bonus is this; if you are trying to get the most
out
of the current game go for the bonus. You'll get it about 1:2 goes and
it will keep you up to a good average. However, if you want to go for
sheer max score, don't worry about it. Take your first good
three of a kind (eg, 5-5-5-6-4) as three of a kind and not (in this
case) as 5's. Likewise your first good four. You may still pull
off a
bonus anyway (although less often) so that when you do bag some
yatzee's the
possibility of a miracle high score is there. It'd be a shame to
finally
roll that 4 yahtzee run and have it coupled with a dodgy go and only
get 500.
Taking 5 6's as 6s.
In a head to head or best-score-this-game strategy, its worth taking a
high value yatzee as numbers and not as a Yatzee. Eg 6-6-6-6-6 could
be taken a sixes -
it virtually guarnatees the bonus so you score 30+35=65 - better
than 50 for the yatzee. Although you might be cursing if you get a
second
one and only get 50 instead of 100 for it