JBQ's spot on the Wild Wild Web
The musings of a French mathematician living in the heart of the American technology industry

Puzzle Quest helpers
While playing Puzzle Quest, I've wondered several times what could be the best way to spend my experience points. I order to be able to make the right choice, I've gathered a bit of data from within the game. This is
Those who are looking for a quick answer can skip all the way to the bottom of the page
quite a long article, and those who are looking for a quick answer can skip all the way to the bottom of the page where the last table contains numbers for each of the characters according to various growth strategies.

The first few relevant numbers are very basic: in Puzzle Quest, each character starts a level 1, gets 4 points of experience for each level, and I assume that the highest level that the character will get is 50 (because all the opponents in "Choose Opponent" mode have a level lower than 50, and because the top spell for each character requires level 50. I also assume that the character doesn't gain experience points other than by gaining levels (which isn't necessarily true as it is possible to buy experience points with gold coins). That means that there are 196 experience points to spend.

Let's start with the way the different characters can use their experience points:

EarthFireAirWaterBattleCunningMorale
Druid2132010
XP cost for Druid1312322
Knight0012213
XP cost for Knight3222131
Warrior1200321
XP cost for Warrior3123122
Wizard1320120
XP cost for Wizard2112323

It's worth mentioning that those numbers are spread identically for all characters, so that as a first approach we can establish a common set of basic strategies based on those numbers.

One basic strategy is to grow all the categories so that they all have the same rank. Spending all 196 points of experience that way (in addition to the equivalent of 14 points that the character starts with) will result in all categories growing to rank 15. Since that strategy spends more points
One basic strategy is to grow all the categories so that they all have the same rank.
in the categories that characters aren't strong at, it ends up spending most of the experience points in the categories that the character is weak in. In the end the sum of all the ranks is 105.

Another basic strategy is to spend the experience points evenly between all categories. Using all 196 experience points plus the 14 points that the character starts with, the end result is that two categories end up at rank 30, three at rank 15 and two at rank 10, i.e. the sum of all the ranks ends up being 125.

The third basic strategy is to play into the character's strengths, by spending experience proportionally to the speed at which each category grows, which boils down to spending 6 points in the categories where the character is strong for every 3 points in the categories where the character is average and 2 points in the categories where the character is weak. This results in getting up to rank 5 in the categories where the character is weakest, rank 13 in the medium categories and rank 51 for the strong categories, for a total of 151.

There are some other similar basic strategies based on the same data. It's possible to not touch at all the categories where the character is weakest, and to apply the three strategies above to the remaining categories. This gives the following results: growing all the ranks evenly brings them to 26 each (approximately), for a total rank of 130. Spending the same number of experience points in all medium and strong categories would bring them respectively to 21 and 40, for a total of 145. Spending it according to the
The strategies above are a good starting point
strengths would bring them approximately to 15 and 58, for a total of 163. Finally, the extreme approach would spend it all on the categories where the character is strong, bringing both of them around rank 100.

The strategies above are a good starting point. We are going to see below that they can be refined quite further based on the information that is available. As it turns out, each category has an impact on multiple aspects of the game, and each of those aspects grows differently as the character gains ranks. This table lists the aspects that are affected by each category, sorted by their growth pattern:

skilleffectmaxstart
lifextrawildresist
Earth Masteryadditional mana from Green Gemsmax Earth Mana (green)start Earth Mana (green)
N/Achance of extra turn when matching Green Gemschance of Wildcard when matching Green GemsN/A
Fire Masteryadditional mana from Red Gemsmax Fire Mana (red)start Fire Mana (red)
N/Achance of extra turn when matching Red Gemschance of Wildcard when matching Red GemsN/A
Air Masteryadditional mana from Yellow Gemsmax Air Mana (yellow)start Air Mana (yellow)
N/Achance of extra turn when matching Yellow Gemschance of Wildcard when matching Yellow GemsN/A
Water Masteryadditional mana from Blue Gemsmax Water Mana (blue)start Water Mana (blue)
N/Achance of extra turn when matching Blue Gemschance of Wildcard when matching Blue GemsN/A
Battleadditional inflicted damageN/AN/A
N/Achance of extra turn when matching Skullschance of Wildcard when matching SkullsN/A
Cunningadditional effect for Wildcards, additional Experience and Gold from defeated foesN/AN/A
N/Achance of extra turn when matching Gold Coinschance of Wildcard when matching Gold CoinsN/A
MoraleN/AN/AN/A
additional life pointschance of extra turn when matching Purple Starschance of Wildcard when matching Purple Starsadditional Spell Resistance

This following table lists the details of the seven different growth patterns for all ranks from 0 to 52 (notice that the values in italics were extrapolated, specifically the values in the "life" and "resist" patterns for ranks 28 and above. If my values turn out not to be correct, feel free to let me know.

rankeffectmaxstartlifextrawildresist
0+0%+0+0+00%0%+0%
1+5%+1+0+10.75%0.38%+0%
2+10%+1+0+31.5%0.75%+0%
3+15%+2+0+42.25%1.13%+0%
4+20%+2+1+63%1.5%+0%
5+24%+3+1+73.5%1.75%+0%
6+28%+3+1+94%2%+0%
7+32%+4+1+104.5%2.25%+0%
8+36%+4+2+125%2.5%+0%
9+40%+5+2+135.5%2.75%+0%
10+43%+5+2+155.75%2.88%+0%
11+46%+6+2+166%3%+0%
12+49%+6+3+186.25%3.13%+0%
13+52%+7+3+196.5%3.25%+0%
14+55%+7+3+216.75%3.38%+0%
15+57%+8+3+227%3.5%+0%
16+59%+8+4+247.25%3.63%+0%
17+61%+9+4+257.5%3.75%+0%
18+63%+9+4+277.75%3.88%+0%
19+65%+10+4+288%4%+0%
20+67%+10+5+308.25%4.13%+1%
21+69%+11+5+318.5%4.25%+1%
22+71%+11+5+338.75%4.38%+1%
23+73%+12+5+349%4.5%+1%
24+75%+12+6+369.25%4.63%+1%
25+76%+13+6+379.38%4.69%+1%
26+77%+13+6+399.5%4.75%+1%
27+78%+14+6+409.63%4.81%+1%
28+79%+14+7+429.75%4.88%+1%
29+80%+15+7+439.88%4.95%+1%
30+81%+15+7+4510%5%+1%
31+82%+16+7+4610.13%5.06%+1%
32+83%+16+8+4810.25%5.13%+1%
33+84%+17+8+4910.38%5.19%+1%
34+85%+17+8+5110.5%5.25%+1%
35+86%+18+8+5210.63%5.31%+1%
36+87%+18+9+5410.75%5.38%+1%
37+88%+19+9+5510.88%5.44%+1%
38+89%+19+9+5711%5.5%+1%
39+90%+20+9+5811.13%5.56%+1%
40+91%+20+10+6011.25%5.63%+2%
41+92%+21+10+6111.38%5.69%+2%
42+93%+21+10+6311.5%5.75%+2%
43+94%+22+10+6411.63%5.81%+2%
44+95%+22+11+6611.75%5.88%+2%
45+96%+23+11+6711.8%5.9%+2%
46+97%+23+11+6911.85%5.93%+2%
47+98%+24+11+7011.9%5.95%+2%
48+99%+24+12+7211.95%5.98%+2%
49+100%+25+12+7312%6%+2%
50+101%+25+12+7512.05%6.03%+2%
51+102%+26+12+7612.1%6.05%+2%
52+103%+26+13+7812.15%6.08%+2%

Let's look at the patterns:

In the "effect" column, higher ranks have a smaller impact than smaller ranks. That column is relevant for all categories except Morale. The "effect" grows by 5% per rank up to rank 4, 4% per rank up to rank 9, 3% per rank up to rank 14, 2% per rank up to rank 24, and 1% per rank above that. That means that from the pure point of view of the "effect", it's at least as effecive to grow a "weak" category up to rank 14 as to grow a "strong" category above rank 24.

The "max" and "start" columns go together, since they are both relevant for all four types of mana and not for any other category. "max" and "mana" grow evenly throughout the ranks, with the "max" growing by 1 for each odd
It's not a bad idea to grow the mana categories to values that are 1 more than a multiple of 4
rank and the "start" growing by 1 for each rank that's a multiple of 4. Because of this observation, I think that it's not a bad idea to grow the mana categories to values that are 1 more than a multiple of 4.

The "life" and "resist" columns are only relevant for the Morale category. The "life" grows by 1 on odd ranks and by 2 on even ranks, so that even ranks are slightly preferable. The "resist" pattern appears to grow by 1% for every 20 ranks, but since I haven't observed it above rank 27 I'm not actually sure that it does. Anyway, when investing in Morale, it's a good idea to plan to get just a bit above 20 or above 40.

Finally, the "xtra" and "wild" columns are relevant to every single category, where they affect the probability of getting extra turns and wildcards when matching the type of pieces of the board that is related to that category. "xtra" and "wild" grow slower and slower as the ranks get higher and higher. Notice that the value of "wild" is always exactly half the value of "xtra", so that everything that applies to "xtra" applies to "wild" with the same pattern. "xtra" grows by 0.75% for each rank up to 4, by 0.5% for each rank up to 9, by 0.25% for each rank up to 24,
Without looking at individual categories, aiming to get ranks around 4, 9 and 24 is a good general idea
by 0.125% for each rank up to 44 and by 0.05% for each rank above that.

It's worth mentioning that the "cutoff" points on the "effect" column and on the "xtra" and "wild" columns have several common values: 4, 9 and 24. Therefore, without looking at individual categories, aiming to get ranks around 4, 9 and 24 is therefore a good general idea.

Let's now look in detail at the various categories:

In the 4 mana-related categories, decent ranks to aim for are primarily 5, 9, 13 and 25, with 13 being slight less desirable than the other values. Those are ranks that efficiently use experience points. In the Battle and Cunning categories, the best ranks to aim for are 4, 9, 14 and 24, with (just like above) 14 being slightly less efficient. Finally, in the Morale category, 20, 22 and 24 are good ranks to stop at, and 40, 42 and 44 are similarly good. To a lesser extent, 4, 8 and 10 are also reasonable intermediate ranks to stop at on the way to getting the "good" values.

The basic experience models that we saw in the beginning can now be somewhat matched against the target ranks for each category
We now start to have a decent view on the "big picture". The basic experience models that we saw in the beginning can now be somewhat matched against the target ranks for each category.

The first basic strategy (grow all categories to rank 15) gets everything close to the magic values of 13 and 14 that we've just seen for all categories except Morale. This is therefore a reasonable basis for a more refined strategy, but as we've seen in the beginning it's not a very efficient way to spend experience as it spends quite a lot in the categories that characters are weak at.

The second basic strategy can also be looked at. It tends to stop the investment in the weak categories around 10, in order to grow the strong categories further. We've seen that 9 is a good rank to stop at in all categories except Morale, so once again we're going to have a reasonable fit.

The third basic strategy tended to stop the investment around 5 and 13
It is a reasonable fit for the ideal numbers we've seen
in the categories that the character isn't strong at, which means that just like the first and second strategies it is a reasonable fit for the ideal numbers we've seen, but as it tends to push some ranks to very high values it might not be a very balanced choice.

The fourth, fifth and sixth strategies also happen to get ranks that are close to the "good" values that we've seen above (26, 21, 40, 15). I won't go into deep details about those. Obviously, the seventh strategy with its unique emphasis gets very large values for two of the categories while leaving the other ones with very small values.

Last (but not least), the following table gives values for all 7 strategies adjusted for each of the 4 characters. It should be a good guideline for those who want to have the right numbers in their hands without having to use a calculator to get there. While I don't have enough playing experience to compare their real effect, I think that strategies 2, 3, 4 and 5 are worth trying, with my favorite being number 3, whereas strategies 1, 6 and 7 aren't probably quite as effective, and number 7 being probably the worst of all.

EarthFireAirWaterBattleCunningMorale
Druid (strategy 1)13131313141424
Druid (strategy 2)299291391422
Druid (strategy 3)455441341420
Druid (strategy 4)291292512424
Druid (strategy 5)411412112020
Druid (strategy 6)571531311420
Druid (strategy 7)961962122
Knight (strategy 1)13131313141340
Knight (strategy 2)913131338940
Knight (strategy 3)513131345460
Knight (strategy 4)125252530124
Knight (strategy 5)121212138140
Knight (strategy 6)113131364162
Knight (strategy 7)1222921100
Warrior (strategy 1)13131313141425
Warrior (strategy 2)933139291420
Warrior (strategy 3)545135411420
Warrior (strategy 4)129251292424
Warrior (strategy 5)141211412020
Warrior (strategy 6)155131551420
Warrior (strategy 7)197219522
Wizard (strategy 1)13131313141420
Wizard (strategy 2)133937139149
Wizard (strategy 3)135551134144
Wizard (strategy 4)252828251241
Wizard (strategy 5)214040211201
Wizard (strategy 6)136361131141
Wizard (strategy 7)296962121
Home page Related articles Posted on May 10 2007