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Subject: Some Dragonwood Math rss

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Darren Kisgen
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A few comments/reviews on this website have argued that this or that strategy is clearly better than others. For example, I have read three reviews/comments that say that the Scream capture approach is clearly the best. Funny enough, another reviewer or two have commented that the Strike strategy is clearly best. Some say Enhancements are too powerful, while others say you shouldn’t really go for Enhancements. So I thought I would provide some of the mathematical calculations that went into the design of the game, which I think will help clarify whether these comments might be true, and might be of interest generally to some people. If you don’t want the details behind the design of the game however, please don’t keep reading. Some may consider what follows spoilers (I personally would).

Let’s start with the Scream argument (colors that are the same). This is not the easiest to use as some have suggested. However, it is true that in playtesting we did find that it is an approach that many first time players gravitate toward, especially children, because it is easiest for some people to identify. But I calculated several probabilities and also ran simulations in designing the game, and Scream is not the easiest to use. Take a simple case of 3 cards. The odds of getting 3 of the same color (for a Scream) are approximately 3.2%. The odds of getting 3 numbers in a row (for a Strike) are approximately 3.7%. So it is actually slightly harder to get a Scream than a Strike in this example, but they are pretty similar. But that is only half the equation. The other consideration is comparing that to the value you need to roll to capture a creature or an Enhancement. For 8 of the Dragonwood cards, the Strike capture value is lower than the Scream value, for 8 of the cards the Scream is lower than Strike, and for 9 they are the same. So there is an equal balance of the three that implies that in some cases the Strike will be easier and in some cases the Scream will be easier (in equal numbers).

I have excluded the Stomp from these calculations so far, because it is clearly harder to get the same number of cards for a Stomp than a Strike or Scream, but the significantly lower numbers required to capture when using the Stomp reflect this. For one comparison, the odds of getting at least 2 of a kind with 3 cards is approximately 19.6%. So it is significantly easier to get a 2 card Stomp than a 3 card Scream or Strike (with just 3 cards). For some cards, this makes the Stomp more appealing than either of the other 2 choices. For other cards, the advantage tilts the other way. This was the intent of the design of the game. Different cards are appealing for different approaches. As one example, a few cards have a 5 capture value for a Stomp and a 7 for a Strike or Scream or both. The probability of getting a 5 with 2 dice is 63.9% and the probability of getting a 7 with 3 dice is 72.2%. So it is easier to capture one of those cards if you can get the 3 cards for a Strike or Scream, but it is easier to get the 2 cards needed for a Stomp. So there is a tradeoff there, and the game was designed to hopefully give players a number of interesting tradeoffs as you play.

So far though I have only given odds for the case of 3 cards. You might wonder how the odds change when we draw up to a larger hand. So, for example, what are the odds of having at least 5 of a Strike or Scream with say 7 cards? This is a more complex probability calculation, but the odds of at least a 5 card Scream are approximately 1.2% and of a 5 card Strike is 5.3%. So a Strike is significantly easier to get for larger amounts of cards. This is one of the reasons the Orange Dragon is much harder to get with a Strike than a Scream. On the other hand, obviously with 6 cards in your hand you have a 100% chance of having at least a 2 card Scream, whereas a 2 card Strike is not guaranteed (though likely). This is one of the reasons the 3 point cards are a bit easier to get with Strikes. But again the best approach depends on the Dragonwood card you are trying to capture, which Enhancements you have, your overall strategy, etc.

Regarding a Stomp and 7 cards, the odds of getting 3 of a kind for a Stomp with 7 cards is 6.7%, which is in the same ballpark as getting 5 cards for a Strike, but easier. The dice have an average value of 2.5, so rolling 3 dice on average gives a total value of 7.5 and 5 dice gives a value of 12.5. Accounting for the somewhat easier ability to get a 3 card Strike, this implies a 12 for a Strike is about as hard to get as an 8 for a Stomp, for a difference of 4. For creatures valued 4 points or more (levels such that these kinds of hands matter), the median difference in a Strike and Stomp attack value is 3, which is close to 4. The reason the difference is lower than 4 however is that Enhancements disproportionately benefit Stomps (if you reduce attack values equally for all three techniques, the Stomp gets relatively easier the lower you go).

Regarding Enhancements, the value of Enhancements also depends on the situation. Take a simple example, the Magical Unicorn. The Magical Unicorn has the same capture values as the Fierce Jaguar, which is worth 3 points. So you can view capturing the Magical Unicorn as effectively giving up 3 points. The question is, is this worthwhile? Well, in one case - if the game is going to end soon - it does not. You likely won’t have time to make up that loss in points. But how about toward the beginning?

The Magical Unicorn allows you to add 1 to any capture attempt. The average difference in capture values between creatures that differ by 1 victory point is approximately 1.7 capture points. So the Magical Unicorn allows you to gain a bit more than half a point per capture (0.59). So, if you are going to make 5 more captures in the game, you will roughly break even on the Magical Unicorn (noting that these captures would only be on creatures, since Enhancements can’t be used to get Enhancements). More than 5 and you benefit from the Magical Unicorn, fewer and you don’t. The Dragonwood deck contains 30 creatures (out of 42 cards). Taking a 3 player game as an example, you remove 10 out of 42 cards from the deck in the setup, which means you will remove on average about 7 creatures, leaving 23 creatures in the deck. This means that if all creatures are captured in a game, each player will get 7 or 8 creatures in the game. This indicates that the Magical Unicorn can definitely be beneficial (it wouldn’t be much fun if it couldn’t). But, to use it on the full amount of creatures you would need to get the Magical Unicorn at the beginning, which of course doesn’t happen all the time. And, it depends on the strategies of the other players and how quickly the orange and blue dragon are defeated (all creatures may not be captured in a game). And, more or fewer creatures may appear from game to game in general. And finally, even if you use the Magical Unicorn on say 7 more capture attempts, that will gain you a net advantage of about 2 points. That is significant, but hardly enough to guarantee a win. I conducted a similar analysis for the rest of the Enhancements. The goal was to make Enhancements appealing but not overwhelmingly so. And it very much depends on when they appear and the strategies of other players and your own use of the Enhancements.

I hope some find this interesting, and I am happy to answer any further questions on this (there were a lot more probability calculations that went into the game, for anyone that is interested). And note I am not trying to suggest that every card in the game has the perfect numbers. While I worked very hard to determine the numbers on each card in the game to make for interesting tradeoffs, I am sure someone could make the case that a certain number could be tweaked up or down 1 on a particular card. But I hope this clears up the question of whether certain strategies in general are clearly overpowered.

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Khexhu

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I've not formed a final opinion on this game yet. I'll buy the math even though during actual play it can often seem to not be that way (and hence I can understand why some feel the way they do about it despite the odds being correct).

My design question though is why did you choose to not allow players to draw a card on their turn (like so many other games) and then attack? And if requiring sacrificing the attack, if only to be different, then why just one card and not two or even more?

I'm not sure I buy the 20 minute suggested time on the box with the rules as-is. The lack of card drawing seems to make the game drag a bit especially if players decide to re-evaluate attack options before deciding to just draw again.

My other, far less important, question would be if you considered letting certain or even all creature cards have a special effect for them once won (possibly even merging in the item cards to that extent such that they are just one card). As-is the creatures can feel very similar, if not entirely themeless. I imagine the answer has to do with keeping the game simpler and accessible and I suppose merging the items with them would do away with part of the math your talking about. But I feel like I would have liked it a little more that way (As an adult anyway, our 8 year old son still asks to look at the "Helpful Bunny" card or whatever it's called just because he finds it so cute.)
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Darren Kisgen
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Thanks for your comments. Regarding the idea that you can draw a card and attack on your turn, someone else also suggested this variant in another post, and if you enjoy playing that way, I certainly encourage you to do so. The idea being that on your turn you draw a card, and then choose to either draw another card or attack on the same turn. This seems like a fine idea. Why did I design it the way I did? I wanted turns to go quickly, particularly with an eye toward families. If you can draw a card and then choose whether to draw again or attack on the same turn, a player’s turn will take longer as they make that decision. On the other hand, if you only are drawing or attacking, you can typically make that decision before your turn comes up again (I realize this may not always be the case as the choices in the landscape may change, but most of the time you have a good idea). Sure, drawing a card on your turn may not always be the most exciting thing to do on a turn, but it gives you (or more importantly, kids) something to do, and at least in games I have seen, drawing cards goes very quickly (for example, you might even have 2 rounds around the table where everyone draws a card, but that will likely take less than 20 seconds). And drawing just one card often gives you something new to think about. But again, if you prefer it the other way, it does not compromise any part of the game to play it that way, so I hope you play it the way you prefer.

As for how many cards to discard when you lose an attack, I wanted to encourage risk taking in the game without fear of being set back too much. Thus, not only do you only discard 1 card, but also it doesn’t have to be from the ones you are using for the attack. This was intentional. I did consider including some creatures that are more powerful and force you to discard 2 cards instead of 1 (right now that only comes up with the “Dragon Spell” variant). Perhaps that will make it into an expansion.

Regarding creatures with special powers, sure that would be a lot of fun. But I wanted to keep this simple, as you guessed. I’ve played a lot of fantasy tabletop games (Thunderstone Advance, Talisman, D&D Legend of Drizzt, Descent, Battlelore, Mice and Mystics, Claustrophobia, Dungeon Fighter, etc.), and there are a lot of interesting features in many of those games that would have been tempting to include, and many of those games are great if you want that added complexity. But for Dragonwood, I really wanted something that was simple enough you can grab it off the shelf, learn it quickly, and play a 20-minute game and still get that fantasy adventure feel.

And as for the playing time, I think the first couple of plays will probably take more like 30 minutes. But once you get the hang of it, it really should only take about 20 minutes.

I hope you enjoy the game!
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