Monthly-Dice

Dice as a ranking game

If you feel that any given single game of dice is a bit dull, you may find it more challenging to achieve a high "monthly" ranking. This is done by playing evaluation games - one allowed per day - with your best 7 scores used to calculate an average score for that month. Rank high enough, and you win gold for yourself and for the city!

BUT!! That is not what makes monthly ranking fun, in this writer's humble opinion. It is the fact that your strategy is no longer confined to a single game of dice… you now have to look at each single game as part of a long term goal. If you play cautious all month, you will probably average between 80 to 100. However, knowing that only 7 out of the 30 games only need to count, you can look for opportunities to go for some very high scoring games, knowing that even if you bomb 3 out of 4 times, you will still have 7 great scores after 28 days!

Where dice becomes truly exciting is when you embrace the fact that there is a measure of luck - and on any given day, that luck may swing greatly in your favour. Other days, it may be on your side, but you will need to employ the strategy to keep your score potential high. More often than not, you will end up with scores in the 40's (when all is against you) or high 70's or low 80's (and were just ONE resource away from getting the 30 point city). It is the intensity of missing those close calls and the thrill when you do break through those elusive 110+ scores that makes this game fun.

In brief, playing the "long game" of Dice is about risk vs. reward. The strategy comes in when you can identify spots where there are higher scoring opportunities when risk is low or can be lowered. So to expand the strategy guide into something to help your month long average, I will run through a sample game and discuss where strategies can be applied. After, we can look back and see what could have been done differently and judge how that may have helped or not.

CORE STRATEGY RECAP

Recall from the original strategy page that we want to build all the cities (for points), all the knights (for points and to help with building cities) and be "efficient", or use as many dice as we can per turn. Easier said than done without a few tricks up your sleeve, so with this in mind, lets begin.

EFFICIENT GOALS

So my first turn I have one of the "efficient" rolls:
01-start.jpg
a knight (ore, wool, wheat) and a road (wood, brick). This lets me use 5 dice this turn, only wasting 1 die. Note that I will only get two points for this. I could opt to build the settlement and get 3 points, but the settlement does not help me to achieve my initial goals that earn high scores, which are:

• build 4 cities
• build roads to all 4 cities
• build all 6 knights

My second turn starts out good - two wood and a brick.
02-Second-roll.jpg
I need only 1 more brick to get an "acceptable" roll. Some quick math says I have a 1/6 chance at getting another brick on a single die - so with 3 dice to roll, that is 3/6, or 50% to hit a brick. Plus, if I miss, I have a second 50% shot on roll 3. The odds of missing two 50/50's in a row is only 25%, so my odds on at least getting a double road out of this turn is 3:1 (for every four times I am in this situation, statistically I will succeed 3 times and fail once).

A double road is somewhat less efficient a result as it wastes two dice. Of course, I could "back door" a triple-road if I am lucky, or perhaps even a road/settlement. Even though a road/settlement is not one of my main goals as pointed out above, it gets us on the path of an "efficient" game that can lead to the highest of high scores - so while we may not plan to get this result, we will take it if it works out that way!

Thoughts and alternative results

So on this turn, based on the first dice role, I can choose a result that gives me great odds at staying "on course" with the main goals that acheive a high score, plus I give myself options to improve without any risk. Even in that 25% chance that I cannot hit my second brick, I can still get lucky on the 3rd roll and hit a wool/wheat for a settlement (which on a single roll could happen 13.6% of the time). This would slow down my road advancing, which could comprimise reaching all 4 cities. However, I can use the wood / brick Jokers later in the game to help me get a "triple road" role to make up for this, and stay on track for a 110 range score.

WHEN TO BUILD A CITY (EARLY)

So I managed to roll a brick and was able to build a double road. I have now connected to a city which means I now have to think about when I should "go for a city". In most games, you should expect to use your jokers (knights thatg you have built which can be used once to substitute a resource) to get cities. Only 3 of the knights help with cities so this means you have to build at least one "natural" city. The odds of rolling a natural city (the right 5 resources without needing a joker) in the 1st two rolls of a turn are not good, but it happens. When it does, it really sucks if you have no open city slot AND used a joker to fill it! So to keep your options open:

• Do not build a city if it is likely that you will need to use a joker - unless you have roads connecting to at least one other city that you could build on if you hit a natural city on a later turn
• If you happen to roll 4 to a city on roll 1, and have the joker for the 5th, you are about a 60% chance to get the city without needing that joker - this would be a low risk attempt and worth going for depending on your situation (what else can you build? Do you have other open cities?)
• If you don't have the joker, or if you only start 3 to a city, (jokers or not), this is too high risk early in the game. If you are only 4 to the city on roll two, you are maybe about 35% to hit your needed resource or a double-gold

Thoughts

4 to a city with the joker is an acceptable risk because you are still guaranteed the city. If you are lucky, you save your joker for later but if not, use the joker knowing that you still have many more turns to hit a natural city. On the other hand, with no joker, you run the risk of blanking your other roles. 60/40 is not good enough odds because, again, you don't guarentee a high score by succeeding this one time - but you likely ruin your shot at the higher scores if you don't.

RISK VS REWARD

So it's turn 3 and I run into a roll like this:

09-Turn-three.jpg

What should be selected? Well, there is 3 to a city, but we just covered why that is no good to pursue early in the game (it's agood reward, but the risk is too high). I could keep the two brick… then try to roll for two wood and perhaps even luck into a road/settlement? Well, it turns out that the odds of getting two exact items (like wood-wood) out of 4 dice are worse than 1 item from rolling 2 dice. The risk is only "medium", but the reward isn't so great without getting lucky enough to backdoor a road/settlement (very unlikely).
There are all three resources for a knight and also a brick. To get an efficient roll, I would want to get a wood or a double-gold from the last two dice. Again, the odds of that are better than 60%, so this is a low risk to get a decent reward.

My risk is low in this case because I already have a knight. I need knights for points and to further the core strategy of building all 6 knights. If I miss the road, this isn't great because 3 dice get wasted this turn and it slow down the road-building needed to access another open city. If it does happen, there is still time to get lucky and hit a 3x road road roll later, likely with the use of jokers(so all is not lost yet!). So to summarize, after the first roll of the turn, I elected to chooses the resources that gave me good odds to finish the turn with a great result: building the items I need for a high score and only wasting 1 die if I hit my roll. If I miss, I waste 3 dice, but this is better that the other choices that gave me far worse odds at success with a big hit to my chances at a good score if I missed.

Another variation of this roll would be a natural settlement 04-settlement.jpeg (wood, brick, wheat, wool, crap, crap). This is nice because we are 60%+ for the ore (to get a knight/road) and if it does not come in, we can opt for the settlement rather than just the road. Again, you will need settlements for the highest of high scores - but you also need to be very efficient and a settlement alone does not further the main scoring goals, plus it wastes two dice. There are also backdoor settlement/road possibilities. For example, if you hit a brick on roll 2, you could opt to keep that and roll 1 die on the 3rd roll for a 33% chance at a wood (bonus road) or an ore (knight/road instead).

Also good from an odds perspective is 11-3way-roll.jpg. In this case, you can hit wheat or wool and use the double gold for the knight/road, or you could hit wood and use the double gold for a 2x road. If you have two rolls left, you are 75% to hit one of those three (the hope, of course, is to hit the knight/road as it is more efficient).

An unfortunate roll would have been 05-Bad-roll.jpg. This forces you to have to roll a wool or most likely get stuck with a single road. While common strategy says "a road is better than a -2", a single road turn is 4 wasted dice and the path to a sub-100 score. However, if we had the wool joker, it would not be so bad.

Thoughts about taking gambles early in any given game

Gambling (going for a high risk, high reward roll) is not the usual way most people start a game. However, you may weigh thi in with your particular month long strategy. Since you only need 7 good games playing once a day all month, you may as well take higher risks if you already have 7 very good scored games. Perhaps you might take the attitude of "I will go for risky, high scoring games early in the month and be more conservative later if I don't get a a few stellar scores right away." In general, I usually let the first few rolls set the tone. If I have wasted 9 or more dice in the 1st 3 rools, this is going to be a bad game unless I get very lucky for most of the remainder. However, if I have only wasted two dice or less, I have a great start and need to make a choice. 1) I stick to a conservative risk/reward strategy and nurse that great start into a 105 to 111 score (unless hit a bunch of impossible rolls), or 2) I look for spots where I may have worse odds, but could make a few more "0 wasted dice" rolls for a 112 to 117 (or more!) score. Another variation of option 2 is to turn down better odds for a high risk/hi reward roll with a joker safety net (and hope my luck holds up later).

Note that by gambling I mean trying to get many 0 wasted dice rolls on early turns such as knight/knight or road/settlement or 3x road. I do not think gambling on completing cities when the 1st roll does not favour it is a good idea in any situation other than on the last turn with the 4th city still to go. There will almost always be a "better spot". You will rarley get "better spots" when a '4 out of 6' or '5 out of 6' to a 0-wasted dice roll comes up. You will need to decide if it is worth risking a ruined score for a shot at a rare high score.

TAKE BIGGER RISKS WHEN YOU HAVE A SAFETY NET

Just because acheiving one desired result is risky, it does not have to make the whole turn a risky one. Look for places where you can give yourself the potential to take alternative (and with luck, decent) results if it does not work out.

06-Options.jpg
On this role, I have ignored the strategy I used a few paragraphs up on virtually the same board. This is because I have two open cities and three potentially helpful jokers. My main goal is to give myself a chance at a natural city, but since I still have another blank city open (and I am on my way to a 3rd), I will not fret if I have to use a joker. I got lucky and scored a wheat and two ore rather than the less desirable "3 ore" or "2 what and 1 ore" when jokers might need to come in to play. Look at my potential here:
• I have both a wheat and ore joker, so of the 3 dice left, I need only roll a single ore or wheat to guarentee the city. This is a 2/6 x 3 dice = 6/6 chance (and while not really 100%, it is about as good as it gets, especially since I have TWO rolls to accomplish this)
• If I hit a wheat or ore, I am still about 35% to hit the other or a double-gold - of course I may also get really lucky and get the natural city on roll 2
• If I hit a wheat on roll 2, I could hit a wool/wool (doubtful) or a wool/blank and then use my wool joker instead for a high efficiency double-knight turn (although in this specific case I would not since I only have one knight left to activate)
• and if I end up very unlucky with 2 ore, a wheat and 3 bricks, I can still salvage the turn with my wool joker for a knight

WHEN TO THINK ABOUT MORE POINTS

Settlements are where you get the points needed for the stellar scores. You do not need to build any special roads to get to them, yet you can light them up for +3, +4 and if your game goes very well, +5 points as the opportunities.

What settlements do cost you is a turn. In a game with lots of turns getting eaten up with double-roads and single knights, this does not leave may turns left for building settlements. This is why when you can turn a double road into a back door road/settlement or use a joker for a double-knight, you open up turns to build settlements.

As my game winds on, I am on track to achieving the goals for a good score, but with no settlements, it is not looking like I will score big unless I get lucky. I only have three turns left and am still not connected to the last city, but with my wild joker still to use, I am confident that if I reach it, those 30 points will be mine.

Without settlements, my city/knight/road points only get me to 69 + 21 + 12 = 102. If I eek a few more roads out, I could look at a mid 100 score - and this is decent. For this game to hit a very high score, I am going to need two road/settlements and then a city. With only having 1 joker and 3 turns to work with, this will require incredible luck!

07-Near-the-end.jpg
Alas, my first two rolls this turn are crappy. I have to decide if I want to save two gold (for a single road) and try to roll a 2nd road to connect to my city. If I do that, I can use my last to turns to get a good 1st roll at a city… and on the other turn, I may be able to get a settlement. But once again, the odds of hitting two exact dice out of four is not great, so I am risking getting stuck with only a single road. At this point, I am out of back door options like building knights.

But I can end my turn here and simply build a settlement for points. Rather than gamble on the second road, I am going to take the "sure thing" option of the settlement (which I need for a better score), and gamble that I can hit a 2x road next turn and a city on my last roll.

In the end, I get the rolls I need (and indeed needed the last joker for my city) and I score a respectable 105.
10-Final-score.jpg

As far as month long scoring goes, I can look at this as a good "bottom" score for my eventual average. I considered the game to have been "slightly lucky" for me as I hit more that 60% of the 60/40 situations I was in. Thus, I can expect to do better when I inevitably have an even luckier game. If this had been an "average luck" game, I suspect I would not have made my 4th city and would have instead had to settle for building another settlement or two for a score in the 80's. So what could have made my game a bit more lucky and given me a better result? Take this turn:

08-No-space.jpg

On my second roll of my 11th turn, I hit a natural city but have no space to build it. If earlier in the game I got lucky and rolled a natural city, I may have saved my wheat joker. As a result, this may have allowed me to pursue a road/settlement turn having a wool/wheat joker back up. Take a 1st roll like this:

09-Risk-reward.jpg

I would have two more rolls to get the needed brick and ideally the needed wheat. If I don't get the wool, I am not worried about using this joker. If I don't get the wheat, I may feel that since I have already hit a natural city, I may want to take my chances at getting a second natural city and use the wheat now. Of course, I would also have to hit double-roads without using my wood/brick joker (not THAT hard to do) and a one or two 3x road, possibly using one or both jokers (That would require more luck, however).

This may seem like an awful lot of required luck - and you would be right. The point is not "try to get lucky more often". Rather, it is that when you do get those couple of lucky breaks, it sets you up to make skill-based decisions that can change a 80 point game into a 100+ game… and a 105 score into a 110+.

If I had managed to have my last city connected by the time I rolled that natural city, I would have been looking at all cities, 5 out of 6 jokers and a settlement finished with 3 turns left. The 1st turn would likely net me the last knight (and perhaps an extra road) for 6 or 7 points and the last two turns could easily turn out as settlements esp. with the wild card joker still in play. The settlements would have added 9 to my 105 score for a total of 114 (and possibly even 117 if the rolls were efficent and I also managed 3 more roads).

Some odds to keep in mind

(if you want to learn more about the math of dice odds, I Googled around and found this page: http://homepage.ntlworld.com/dice-play/Odds.htm)

Resources needed Dice available Rolls left % to succeed Notes
1 3 1 50% does not include a chance to hit double gold
1 3 2 75% does not include a chance to hit double gold
1 2 1 ~35% includes hitting double-gold
1 2 2 ~62% includes hitting double-gold
2 3 1 13.6% includes hitting double-gold
2 3 2 ~24% includes hitting double-gold
2 4 1 ~8% does not include a chance to hit 1 + double gold
2 4 2 30 to 40% Complex to calculate, but a fair estimation

Remember, just because your odds are 50% or better, you are never assured to make a roll. The only way you are 100% is if you get your desired result by roll 2. This does not happen often, so you will be faced with many of these 60/40 situations over the 15 turns in a game. If you must succeed at 5 (or so) key 60/40 rolls to ensure a good score, you will have to rely on luck alone. So try to turn as many of those 60/40's into 90%+ by having a joker as a back up and/or finding spots with multiple outcomes. If you get lucky now, you can save the joker. If not, you can always hope to get lucky later in the game when that needed joker is already used. And if you don't get lucky there either, hey, it is only 1 out of 30 games you can play all month - so over time, the odds do in fact favour playing with skill rather than relying on pure luck!

- Fleet

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