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Neopets TCG

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Choose Article : Arena Probability

Article 1 - Arena Stat Probabilites

Be forewarned, the following article is going to make you very bored... unless that is you are interested in probabilites, or want to win the Neopets TCG. Yes, that's right, this article looks at the real mathematical principles behind the game, and if you really want to compete and win every game you play, it's stuff you are going to have to memorise!

The real meat of the Neopets TCG revolves around arena challenges. You tap your Neopet, and if your opponent has a Neopet in the same arena (and they usually do), you both roll a single 6-sided dice, add the result to your stat total for that arena, and the highest total wins. Winning challenges allows you to bank (or draw) cards, and simply put, the more challenges you win, the more likely you are to win the game.

The most important choices you will make in the game are what Equipment to equip to what Neopet, and whether or not to play an Item in a challenge.

Dice Tables

The following tables depict all the possible dice rolls that could be made in a hypothetical contest between an Aisha and an Eyrie. We aren't interested in their actual stats, we are simply interested in their relative stats. What we need to compute is what is the percentage chance we will win a certain contest when the Neopets have matched stats, when one Neopet has a one-point advantage, a two-point advantage etc.. I will explain why we need to know this later on.

The numbers down the left hand side represent the possible rolls for the Aisha (1-6) and the numbers along the top represent the possible rolls for the Eyrie. An A means that the Aisha wins, and an E shows a victory for the Eyrie. The X means that the rolls are tied, and the dice must be rolled a further time. As you can see, the line of E's along the bottom row shows you that when the Eyrie rolls a 6 and the Aisha doesn't, the Eyrie wins. The exact opposite is true for the line of A's down the right hand side of each table.

One initial observation is that after +5 there is no change in the percentage chance of winning a contest. If you are already up by a large margin, there is no point in boosting your stats any further, it simply does not change the odds of winning!

PROBABILITIES FOR +5 or greater (if the Aisha's stat for this arena is 5 points or more higher than the Eyrie's stat) 1 2 3 4 5 6 1 A A A A A A 2 A A A A A A 3 A A A A A A 4 A A A A A A 5 A A A A A A 6 E E E E E X A 30 E 5 X 1 Aisha : 30/35 0.8571 Eyrie : 5/35 0.1428 (86%) ---------------------------------------------------------------- PROBABILITIES FOR +4 (if the Aisha's stat is 4 points higher) 1 2 3 4 5 6 1 A A A A A A 2 A A A A A A 3 A A A A A A 4 A A A A A A 5 X A A A A A 6 E E E E E X A 29 E 5 X 2 Aisha : 29/34 0.8529 Eyrie : 5/34 0.1470 (85%) ---------------------------------------------------------------- PROBABILITIES FOR +3 1 2 3 4 5 6 1 A A A A A A 2 A A A A A A 3 A A A A A A 4 X A A A A A 5 E X A A A A 6 E E E E E X A 27 E 6 X 3 Aisha : 27/33 0.8181 Eyrie : 6/33 0.1818 (82%) ---------------------------------------------------------------- PROBABILITIES FOR +2 1 2 3 4 5 6 1 A A A A A A 2 A A A A A A 3 X A A A A A 4 E X A A A A 5 E E X A A A 6 E E E E E X A 24 E 8 X 4 Aisha : 24/32 0.75 Eyrie : 8/32 0.25 (75%) ---------------------------------------------------------------- PROBABILITIES FOR +1 1 2 3 4 5 6 1 A A A A A A 2 X A A A A A 3 E X A A A A 4 E E X A A A 5 E E E X A A 6 E E E E E X A 20 E 11 X 5 Aisha : 20/31 0.6451 Eyrie : 11/31 0.3548 (65%) ---------------------------------------------------------------- PROBABILITIES FOR +0 1 2 3 4 5 6 1 X A A A A A 2 E X A A A A 3 E E X A A A 4 E E E X A A 5 E E E E X A 6 E E E E E X A 15 E 15 X 6 Aisha : 15/30 0.5 Eyrie : 15/30 0.5 (50%) ----------------------------------------------------------------

Summary

Let us summarise the information in the above tables.

  • Equal Stats - 50% chance of winning
  • 1-point advantage - 65%
  • 2-point advantage - 75%
  • 3-point advantage - 82%
  • 4-point advantage - 85%
  • 5 (or more) point advantage - 86%

As you can see, the difference between equally-matched stats and a one-point advantage is 15%. The difference between a one-point and a two-point advantage is 10%, still a pretty substantial gain. The next point of increase drops our level of increase to 7%, then 3% and finally 1%. The difference between a 3-point advantage and a 20-point advantage, although it may seem like a huge amount, in terms of game-play it is only 4%.

For example, you have a Blue Kacheek with an Agility of 8. You are up against your opponent's Kacheek Shepherd with an agility of 11. Your chance of winning the contest is 18% (100 - 82, we use 82, as the opponent has a 3-point advantage).

Your opponent decides to play lots and lots of Kadoaties, as he thinks it's going to give him a bigger advantage. The Kacheek Shepherd's agility is now 20, increasing his advantage from 3 points to 12 points! In reality, his chance of winning a successful challenge has gone from 82% to 86%, a tiny increase. Those Kadoaties would be much better off being placed elsewhere!

Conclusion

To conclude, If you are winning by 3 or more in an arena, playing any more Items or Equipment will only increase the chances of you successfully winning a challenge by a maximum of 4%. Of course, playing more in anticipation of an opponent playing an item in the next round is still a good strategy.

To maximise your odds of winning, I suggest that you aim to be 2-3 points higher than your opponent's Neopets in all arenas, but no more. If you do have that kind of a margin, keep your Equipment in your hand just in case, and keep your Items in your hand ready to bank. Playing them on your Neopets is simply not going to be, statistically-speaking, worth the effort.

Nice effort Adam! Very thorough, but spelling needs a little work A-