This is the second post about an investigation into the chances of breeding Twins in Dragonvale. Post 1 can be read HERE.
I’ve bred more than 150 twins, and added my data to the original from Axew. The tables and graph look like this.
The number of twins bred on attempts 6, 9 and 11 are outliers to the curve seen in the graph, and probably just due to the sample size. I can’t imagine game designers intentionally messing with the numbers this way. It would be a lot of work, for no gain. But the most noticeable thing is that there have been no attempts beyond attempt 19.
Twin Breed Cap at Attempt 19?
According to the expectations we artificially created, by setting the chance of Twins, from attempt 5 onward, to 15%, there is ~95% chance of breeding a Twin by attempt 19. That means approx every 20th Twin, would be bred on attempt 20 or beyond. You would expect about 12 of those by the time you bred 252 Twins, instead of the 0 that we actually have. Even if you increase the chances of Twins dramatically at the later stages, you should still see the occasional Twin occur later than 19 breeds. That does not seem to be the case.
And at this point, I would dearly love to hear from anyone keeping track, if they ever received a Twin after the 19th attempt.
The Expected Odds, Backwards
Previously we worked out what the expected odds, starting at the bump in chances at attempt 5, and just let them run their course. But, if breeding attempts are capped at 19, then we actually have an end point. And we can work out the odds backwards. There were 9 times when I hadn’t bred a Twin by attempt 18, and all 9 times I bred a Twin on the 19th. 9 times out of 9, means the breeding chance of getting a Twin on attempt 19 is 100%. There were 18 times when I hadn’t bred a Twin by attempt 17, and 9 times in 18 I bred a Twin on the 18th attempt. 9 times in 18 means the breeding chance of getting a Twin on attempt 18 is 50%. All the numbers look like this.
- 19 (9 of 9) – 100%
- 18 (9 of 18) – 50%
- 17 (6 of 24) – 25%
- 16 (7 of 31) – 22.5%
- 15 (7 of 38) – 18.4%
- 14 (8 of 46) – 17.4%
- 13 (14 of 60) – 23.3%
- 12 (15 of 75) – 20%
- 11 (9 of 84 (low)) – 10.7%
- 10 (18 of 102) – 17.6%
- 9 (16 of 118(low)) – 13.5%
- 8 (29 of 147) – 19.7%
- 7 (31 of 178) – 17.4%
- 6 (23 of 201(low)) – 11.4%
- 5 (42 of 243) – 17.2%
- 1 to 4 – 1%
We’ll ignore the percentages at 6, 9 & 11, as being outliers for the moment. Also the percentages at 1 to 4 are small, to affect game play, and 18, & 19 are huge out of necessity to reach a cap. The percentages now range from 17.2% at attempt 5 and 25% at attempt 17. 7 of them are 20% and below, and 3 are above 20% (13, 16 & 17). 13 seems like an outlier as well.
Second Guess of the Set Percentages
Averaging the odds from attempt 5 to attempt 15 returns an average of just under 17%. It seems odd that they wouldn’t use a round number, but let’s put it in for breeds 5 to 15. Then, if you wanted to equal chances for the last 4 attempts, you would give 25% for the 4th last, 33.33% for the 3rd last, 50% for the 2nd last, and 100% for the last. The odds look like this.
- 1 to 4 – 1%
- 5 to 15 – 17%
- 16 – 25%
- 17 – 33.33%
- 18 – 50%
- 19 – 100%
The New Expected Odds
The first 4 are the same as before. 1% of 100%, 1% of 99%, 1% of 98% & 1% of 97%. Then, it will be 17% of the remaining percentages from 5 to 15. Then the last 4 percentages are divided equally. It looks like this.
It makes the cumulative numbers work very well. We have the low percentage at the 6th attempt, which also drags down the cumulative numbers at the 7th attempt, but everything is in the green from that point on. Now to collect some more data, and see how things progress.
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