(poker) DICE Strategy ?

OK, let`s start with the rules: - is a game played with two players and 5 dice, each dice having 6 sides numbered as 1,2,3,4,5,6

- hand values are: 5 of a kind = 5 points , 4 of a kind = 4 points , full house = 4 points , straight (1,2,3,4,5 or 2,3,4,5,6) = 4 points

3 of a kind = 3 points , 2 pair = 2 points , one pair = 2 points , no pair and no straight = 1 point

- each player roll with all 5 dice and can hold any number of dice and have the right to re-roll only once with the un-holded dice

- in order to decide which player starts to roll first, each player roll one dice and the player with the highest roll starts to roll first

- after each player have rolled one series of rolls (one roll plus one re-roll if needed) with all 5 dice, a winner must be declared.

* if both players have made hands of equal value, the game is declared a tie, and a new game (with the same rules) have to start

NOW, this is where I need your help in order to know what dice to hold so I can maximize my overall chances to win the game:

Acting first

- if I have 2,3,4,5,5 - should I hold the pair of 5s or should I go for a straight ?

- if I have 1,2,3,5,5 - should I hold the pair of 5s or should I go for the straight ? (keep the pair I guess)

- if I have 1,1,2,5,5 - should I hold only one pair or both and go for the full house ?

- If I have 1,1,1,4,5 - should I hold the 3 of a kind plus another die or only the 3 of a kind ?

- If I have 1,3,4,5,6 - should I hold nothing, one die, or go for the straight ? (keep only one die I guess)

Acting last - When my opponent have already made a hand of 4 points value and I hold:

- 2,3,4,5,5 - should I hold 2,3,4,5, and go for either straight to send the game in a tie ?

- 1,2,3,5,5 - should I try my luck for the inside straight or keep the pair and hope for the best ?

- 1,1,1,4,5 - should I hold the 3 of a kind plus another die or only the 3 of a kind ?

- 1,3,4,5,6 - should I hold nothing, one die, or go for the straight ?

- When my opponent have already made a hand of 3 points value and I hold:

- 2,3,4,5,5 - should I hold 2,3,4,5, and go for the either straight or only keep the pair ?

- 1,2,3,5,5 - should I only keep the pair ? (I believe only keep the pair is right)

- 1,1,1,4,5 - should I hold the 3 of a kind plus another die or only the 3 of a kind ?

- 1,3,4,5,6 - should I hold nothing, one die, or go for the straight ?

- When my opponent have already made a hand of 2 points value and I hold:

- 1,3,4,5,6 - should I hold nothing, or only one die ?

Quote: PlayHunter

straight (small or large) = 4 points

What are small or large straights? In Yahtzee, a small straight is just 4 consecutive numbers, but you list going for a straight in your samples with a made small straight. I'll be gone and/or sleeping all day, so someone else might help you with this.

Quote: miplet

What are small or large straights? In Yahtzee, a small straight is just 4 consecutive numbers, but you list going for a straight in your samples with a made small straight. I'll be gone and/or sleeping all day, so someone else might help you with this.

Thank you for pointing this to me. - Yes, you are right .. I should specify, I`ll try to edit my original post to reflect this aspect too.

What I meant to say is that a Straight in this game is either 1,2,3,4,5 or 2,3,4,5,6. In both cases is composed of 5 dice, unlike Yahtzee.

I did the easy part: acting last. If I list 2 plays, the first one is better (trading wins and loses for ties the other way around.)
Acting last - When my opponent have already made a hand of 4 points value and I hold:

- 2,3,4,5,5 - should I hold 2,3,4,5, and go for either straight to send the game in a tie ?
Go for straight (Tie 72 lose 144)
Hold pair(win 1 tie 35 lose 180)

- 1,2,3,5,5 - should I try my luck for the inside straight or keep the pair and hope for the best ?
Hold pair(win 1 tie 35 lose 180)

- 1,1,1,4,5 - should I hold the 3 of a kind plus another die or only the 3 of a kind ?
Hold trips (win 1 tie 15 lose 20)

- 1,3,4,5,6 - should I hold nothing, one die, or go for the straight ?
Go for straight (tie 1296 lose 6480)
Hold none (win 6 tie 690 lose 7080)

- When my opponent have already made a hand of 3 points value and I hold:

- 2,3,4,5,5 - should I hold 2,3,4,5, and go for the either straight or only keep the pair ?
Go for straight (win 72 lose 144)
Hold pair(win 36 tie 60 lose 120)

- 1,2,3,5,5 - should I only keep the pair ? (I believe only keep the pair is right)
Hold pair(win 36 tie 60 lose 120)

- 1,1,1,4,5 - should I hold the 3 of a kind plus another die or only the 3 of a kind ?
Hold trips (win 16 tie 20)

- 1,3,4,5,6 - should I hold nothing, one die, or go for the straight ?
Go for straight (win 1296 lose 6480)
Hold none (win 696 tie 1200 lose 5880)

- When my opponent have already made a hand of 2 points value and I hold:

- 1,3,4,5,6 - should I hold nothing, or only one die ?
Hold none (win 1896 tie 5400 lose 480)

Miplet thank you so much !! This is of great help ! Can you do two more scenarios for acting last ? (sorry, forgot to add them)

Acting last:

When my opponent have already made a hand of 4 points value and I hold:

- 1,1,2,5,5 - should I hold only one pair or both and go for a full house ?

When my opponent have already made a hand of 3 points value and I hold:

- 1,1,2,5,5 - should I hold only one pair or both and go for a full house ?

Here is my final strategy table. The X's are the only changes in strategy from first to act. Any questions, just ask. Unless I messed up some where, going second has only a slight advantage. If this was a bet for $10000, the second to act would have an ev of $3.94.

hand	1st to act	1 point	2 points	3 points	4 points	5 points
5 of a kind	55555	55555	55555	55555	55555	55555
4 of a kind	44441	44441	44441	44441	44441	44441
full house	33322	33322	33322	33322	33322	33322 X
trips	33321	33321	33321	33321	33321	33321
2 pair	33221	33221	33221 X	33221	33221	33221 X
1 pair no straight	66321	66321	66321	66321	66321	66321
1 pair gut shot	66543	66543	66543	66543	66543	66543
1 pair open ended	55432	55432	55432 X	55432	55432	55432 X
straight	12345	12345	12345	12345	12345	12345 X
nothing	12346	12346	12346	12346	12346 X	12346

Again, Thank You very much miplet this is just BRILLIANT work ! Thank You so much once again !

One more question for this thread, considering before rolling these 5 dice for the first time, what is the probability of rolling:

- 3 of a specific kind ? (such as exactly 1,1,1,x,x for example, and not any 3 of a kind)

- a straight (any straight 1,2,3,4,5 or 2,3,4,5,6)

- 4 of a kind (any four of a kind)

Which is the order of these outcomes occurring considering that firstly you have to roll with all 5 dice, hold any if needed, and re-roll ?

Quote: PlayHunter

One more question for this thread, considering before rolling these 5 dice for the first time, what is the probability of rolling:

- 3 of a specific kind ? (such as exactly 1,1,1,x,x for example, and not any 3 of a kind)

- a straight (any straight 1,2,3,4,5 or 2,3,4,5,6)

- 4 of a kind (any four of a kind)

Which is the order of these outcomes occurring considering that firstly you have to roll with all 5 dice, hold any if needed, and re-roll ?

I don't understand the question. You want then odds of rolling straight in 2 rolls, given that is all you are trying to roll? Same with the 4 of a kind? will 5 of a kind count? Same questions for 3 of a kind.

Yes, if my goal is to make a straight that is the only thing I am trying to make and get points for, any other outcome being 0 points.

For example if my goal is to make 4 of a kind, and I finish with a fullhouse I will get 0 points. But if I roll 5 of a kind I will be rewarded with the same number of points for making 4 of a kind, because 5 of a kind also includes 4 of a kind which is my goal.

And yes, if I need 3 of a specific kind (1,1,1,x,x) and happens to roll 4 or 5 of 1, then that would count like 3 of my specific kind.

I am asking this because sometimes I have to choose which goal should I go for the next roll: a straight or a 4 of a kind ?

Some other times I have to choose my next goal to be: a straight or a fullhouse ?

Some other times I have to choose my next goal to be: a fullhouse or 4 o a kind ?

And some other times I have to choose between to set my next goal at rolling: 3 of a specific kind, or any 4 of a kind ?

And some other times I have to choose between to set my next goal at rolling: 3 of a specific kind, or a fullhouse ?

And some other times I have to choose between to set my next goal at rolling: 3 of a specific kind, or a straight ?

So what I need to know would be the odds (before to roll) of setting my next roll to achieve each of these outcomes in part:

- any 4 of a kind (5 of a kind will count as well just like rolling 4 of a kind)

- any straight (1,2,3,4,5 or 2,3,4,5,6 - both counting the same for reward)

- a fullhouse

- 3 of a specific kind

* Sorry that I was not clear in my last post ! Re-reading it now, I see that I did not even asked all I wanted to in that one.

I hope this post it is clearer and makes more sense .. but if still not, please let me know and I will try to re-formulate it again.

The denominator is 60466176. And the numerators are: straights 7784832, quads 7999776, specific 3 of a kind 10309926, full house 11270880 (11736576 if counting 5 of a kind)

Many thanks a lot again ! (this is what I needed) So the least occurring is a straight and the most occurring is a full house ? - So if I am to choose my next goal between a full house and 3 of a specific kind, I should choose to set my next goal for rolling a full house ?

Quote: PlayHunter

Many thanks a lot again ! (this is what I needed) So the least occurring is a straight and the most occurring is a full house ? - So if I am to choose my next goal between a full house and 3 of a specific kind, I should choose to set my next goal for rolling a full house ?

You're welcome. Yep, full house is the easiest to get. The only thing that requires a non-intuitive strategy is going for the straight. If your first roll is only made up of 6's and/or 1's, keep nothing. Otherwise hold 1 of each from 2 to 5 and just one 6 or 1 if you have it. If you start with a five of a kind in 2's to 5's, you would still hold one of them.

ps the numbers in my previous post assume that you can keep everything on the first roll. If for some strange reason you can't, they will be slightly lower for straights and full houses

Thanks for the tip on straights ! Yes, after the first roll everything can be held, from none - up to all five dice. Many thanks once again !

One more scenario: - if only straights and quads (including 5 of a kind) get points (4 points each), and all other outcomes (including full houses) get zero points, and I have rolled 1,1,2,3,5 should I hold the pair and go for a quad or 1,2,3,5 and go for the straight ?

(I am pretty sure this case is hold the pair and go for a quad because going for the straight I get one die to roll my number, while going for a quad I get 3 dice to roll 2 numbers, which means I have 1,5 dice to roll my number .... but I ask just to be 100% sure)

Quote: PlayHunter

One more scenario: - if only straights and quads (including 5 of a kind) get points (4 points each), and all other outcomes (including full houses) get zero points, and I have rolled 1,1,2,3,5 should I hold the pair and go for a quad or 1,2,3,5 and go for the straight ?

(I am pretty sure this case is hold the pair and go for a quad because going for the straight I get one die to roll my number, while going for a quad I get 3 dice to roll 2 numbers, which means I have 1,5 dice to roll my number .... but I ask just to be 100% sure)

Go for the straight (36/216) not quads (16/216)

Oh, :-) I am really bad at math. (but, I am really glad I asked) Thank you very very much once again ! :-)