Do I suck at yatzee? (Kind of long and most likely tricky)

[zinna]

A couple of weeks ago I was in Croatia for holiday and on my way home to the hotel I pass a casino with a big sign saying poker so I go in and ask if they offer any poker and they point towards a couple of video poker machines and Im on my way leaving when I seeing a couple of guys playing some game with money on their table so I go over and check it out. I approach the table and I can see that they are playing yatzee and Im thinking what heck I can play some yatzee if it isnt high stakes.

I ask what stakes they are playing and they explain in crappy english that they are playing for 2 kuna (about 0.4$) per point and you pay the diffrens between your score and the winners score and every one does that so there is only one winner. There are 4 players in the game if I join.

I join the game and order a beer and we are all playing and talking. After maybe 20 minutes or so the following happens: I and 2 of the other players are about even in score maybe 10 points diffrens or so and the last is probably trailing 40 points or so.

At this point I have completed 1 pair, 2 pair, small straight, full house, 3 of a kind, chance (not sure of the english term but its the one where you take the sum of your 5 dices and add up) ones (2 points), twos (8 points), threes (9 points) and fours (8 points). On my first roll I get 2 sixes but I cant get any more and Im now facing the decision on what I should erase (probably not the correct term but you will hopefully understand anyway) and I tell the guys who is writing down the points to remove my yatzee. He looks at me as Im the biggest retard he has ever met and ask me If I really want to erase my yatzee and I say: Yes remove my yatzee. He looks at me and shakes his head and removes it and the other guys start laughing and they say something in their home language that I dont understand and laugh even more.

Now the question: Is removing yatzee a really big mistake at this point? What should I have done otherwise? How many points am I winning/losing by removing my yatzee?

I understand that this isnt a standard question and that it might be very hard to answer but I would really like an answer since this has been bugging me for the last weeks.

Yes I know my english suck but Im from Europe so please have this in mind.

[LCposter]

I used to play yahtzee pretty frequency in high school, so at that time I had a good feel how often you'd hit a yahtzee. I haven't played in 15 years though, so I don't remember so well. I certainly remember getting 3 yathzees in a game several times, and even 4 yahtzees once or twice, so I think it probably must occur once every 20 rolls or so. Considering that you get 67.5 on average for the first yahtzee, and 117.5 on average for each subsequent yahtzee, you certainly don't want to scratch the yahtzee lightly.

I only remember scratching a yathzee near the very end of a game where I was down to only a few choices left, and in good shape to make the 35-point top section bonus (e.g. only needing 2 or 3 of a few numbers to complete). Since you will need at least 4 5's or 4 6's, it may be better to just give up on the top section bonus, take the 2 6's here, and keep the yahtzee alive. It's obviously much easier to make 4-of-a-kind/yahtzee when rolling for any number as opposed to specific numbers like 5 or 6. If it comes down to having to scratch yahtzee or 4-of-a-kind, I'm quite sure scratching yahtzee would be correct in that case. I'm sure there are many other situations where scratching a yahtzee is correct, so I wouldn't get too wrapped up in how they reacted in your game.

I hope others chime in because I think there are a lot of interesting strategy decisions in yahtzee.

[SamIAm]

I admit that I actually own this book:


but I haven't read it. [img]/images/graemlins/frown.gif[/img]
-Sam

[FlFishOn]

My feel is that a Yahtzee occurs about once per 25 turns or so but it occurs more often when you're trying to fill the top half of the card. Scratching it out with 4 rolls to go is likely a positive play. 6 rolls, I'd guess neutral.

[Siegmund]

Optimal strategies for maximizing your total score at Yahtzee have been around for quite some time (I remember writing a primitive version of same in the middle 90s). At http://svsoc1.win.tue.nl/~wstomv/misc/yahtzee/ you can analyze any position, practice against a perfectly-playing bot, etc.

If I understand your post correctly (there is no "one pair" or "two pair" in Yahtzee, but rather "3 of kind" and "4 of kind") -- you had 5s, 6s, large straight, and yahtzee left, and thrw 66xxx -- taking 0 for Yahtzee is a TINY bit better than 12 for 6s.

(If you are playing to win for a fixed stake, rather than playing 'per point', the strategy is harder to calculate.)

[SamIAm]

[ QUOTE ]
Optimal strategies for maximizing your total score at Yahtzee have been around for quite some time

[/ QUOTE ]
Note that maximizing your expected score is definitely not always the way to go. If you finish with 100pts, and I have 90pts and one roll left, I'd much rather get a 50/50 chance of 11pts than a sure-fire 8.
-Sam

[Siegmund]

Yes, I did slightly misread OP's post -- kind of odd to have only "winner vs. each other player" settlements, rather than pairwise settlements like chinese poker and almost every other 4-person game where margin of victory matters.

If they payoffs are based on something other than pairwise differences, yes, there are differences in strategy needed. (In your example, if it were a 2-player game, or if a third player had a score of more than 101, the guaranteed 8 would be clearly right - only when making 101 is enough to make you the winner of a multiway game is the 50/50 chance of 11 right.)

[Ibuprofen]

Wow this is crazy, I just rediscovered Yahtzee online at www.atari.com and have been playing it many times a day. Last night I was even thinking, "Man it'd be great if I could play this for money!" It's amazing that you found a game like that.

Anyway I'm no expect on the game but you really don't want to put a 0 in the Yahtzee field unless you almost have to. Also, since when does Yahtzee have a 1 pair and 2 pair? Maybe the game is different in Europe.

You probably should have had a few spots open, 4 of a kind, large straight, 5's and 6's. Maybe some others I'm missing, but if it were me I'd blank out large straight or 4 of a kind well before my Yahtzee spot.

[zinna]

Yes, in the european version (at least swedish and croatian) there is 1 pair and 2 pair if this makes any differens.

[MCS]

You can scratch out Yahtzees?