# What is the chance of getting another move after clearing the board? **URL:** \ **Category:** Gameplay Chat (PC/Mobile)\ **Created:** [January 4, 2018, 11:27am UTC](https://community.gemsofwar.com/t/what-is-the-chance-of-getting-another-move-after-clearing-the-board/34654 "2018-01-04T11:27:23Z")\ **Posts on this page:** 13\ **Page:** 1
**Author:** ![svechen](https://sea1.discourse-cdn.com/flex019/user_avatar/community.gemsofwar.com/svechen/32/8382_2.png) [@svechen](https://community.gemsofwar.com/u/svechen)\ **Post date:** [January 4, 2018, 11:27am UTC](https://community.gemsofwar.com/t/what-is-the-chance-of-getting-another-move-after-clearing-the-board/34654/1 "2018-01-04T11:27:23Z")
For the Math-Nerds 😉 Now that the exploders are really en vogue: What is the Chance of getting another move after clearing the complete board with an exploder (like Worldbreaker or Gorg or whatever)? ---
**Author:** ![Jainus](https://sea1.discourse-cdn.com/flex019/user_avatar/community.gemsofwar.com/jainus/32/34949_2.png) [@Jainus](https://community.gemsofwar.com/u/Jainus)\ **Post date:** [January 4, 2018, 12:35pm UTC](https://community.gemsofwar.com/t/what-is-the-chance-of-getting-another-move-after-clearing-the-board/34654/2 "2018-01-04T12:35:23Z")
Pinging @lyya who I believe can do these calculations in her head ---
**Author:** ![Amadan](https://sea1.discourse-cdn.com/flex019/user_avatar/community.gemsofwar.com/amadan/32/7653_2.png) [@Amadan](https://community.gemsofwar.com/u/Amadan)\ **Post date:** [January 4, 2018, 12:48pm UTC](https://community.gemsofwar.com/t/what-is-the-chance-of-getting-another-move-after-clearing-the-board/34654/3 "2018-01-04T12:48:44Z")
Oof. I feel like that’s probably some pretty nasty math. I mean, the chance of any four given skyfall gems being the same color is pretty simple; that’s just (1/7)^4, or 0.00042, or 0.042% (I’m pretty positive that the devs have said drop chances after the initial board setup are equally distributed, barring combo-breaker shenanigans). But in terms of applying that to any four given _consecutive_ orbs _anywhere_ on a full board skyfall? I mean, it’s not even 8AM and I haven’t gotten to coffee yet, but I can’t even begin to guess at how to quantify that. Best I can do is “something higher than 0.042%”. ;p ---
**Author:** ![Grundulum](https://avatars.discourse-cdn.com/v4/letter/g/82dd89/32.png) [@Grundulum](https://community.gemsofwar.com/u/Grundulum)\ **Post date:** [January 4, 2018, 1:29pm UTC](https://community.gemsofwar.com/t/what-is-the-chance-of-getting-another-move-after-clearing-the-board/34654/4 "2018-01-04T13:29:27Z")
Rather than calculating this analytically, I suspect it will be faster to do this numerically. Set up a Monte Carlo simulation to generate a million boards using the known gem probabilities (14% for the six colors and 16% for skulls, IIRC). Then determine how many of those contain a 4- or 5-match on them. This will be a lower limit, since cascades off 3-matches can lead to extra turns. But it should be _close_, at least. And I don’t really care to reproduce the entirety of the match detection and board spawning algorithm for this question. ---
**Author:** ![Shimrra](https://sea1.discourse-cdn.com/flex019/user_avatar/community.gemsofwar.com/shimrra/32/87_2.png) [@Shimrra](https://community.gemsofwar.com/u/Shimrra)\ **Post date:** [January 4, 2018, 2:34pm UTC](https://community.gemsofwar.com/t/what-is-the-chance-of-getting-another-move-after-clearing-the-board/34654/5 "2018-01-04T14:34:00Z")
And then redo it with the numbers altered by there being a storm in play. ---
**Author:** ![awryan](https://sea1.discourse-cdn.com/flex019/user_avatar/community.gemsofwar.com/awryan/32/74650_2.png) [@awryan](https://community.gemsofwar.com/u/awryan)\ **Post date:** [January 4, 2018, 4:00pm UTC](https://community.gemsofwar.com/t/what-is-the-chance-of-getting-another-move-after-clearing-the-board/34654/6 "2018-01-04T16:00:15Z")
If Famine is filled for the AI. You have a 0% chance of getting an extra turn. They do tend to happen more often when there is a color storm happening. If you don’t get an extra turn, there’s a 95% chance that the AI will get at least one 4 gem match from the board. ---
**Author:** ![Lyya](https://sea1.discourse-cdn.com/flex019/user_avatar/community.gemsofwar.com/lyya/32/3650_2.png) [@Lyya](https://community.gemsofwar.com/u/Lyya)\ **Post date:** [January 4, 2018, 4:32pm UTC](https://community.gemsofwar.com/t/what-is-the-chance-of-getting-another-move-after-clearing-the-board/34654/8 "2018-01-04T16:32:36Z")
I can’t solve this problem analytically. The chance of any 4 gems being of the same color are 1/(7^3), or 1 in 343, or about 0.29%. It’s not 1/(7^4) because the color of the first gem doesn’t matter. _Assuming that the outcome of results is independent_ then: there are 40 horizontal chances and 40 vertical chances at success (4-match), each with a probability of 1/(7^3). There are also L, T, and + shaped matches that would count as 5-matches. Each of the 36 3x3 block contains 9 such shapes, for a total of 324 chances of nonlinear 5-matches, at 1/(7^4) probability each. To fail them all would be (1 - 1/(7^3))^80) \* (1 - 1/(7^4))^324), which makes the chance of getting an extra turn: 1 - ((1 - 1/(7^3))^80) \* (1 - 1/(7^4))^324)) ~= 0.3083 ~= 30.83%. However, the premise is flawed, as these chances are not independent. If in any given row, gems ABCD are _not_ a 4-match, then the odds of BCDE being a 4-match are considerably lower, as the only chance they have at matching would require BCD to share a color. Thus you’d think the chance is considerably lower than 30.83%. _However_ however, none of this accounts for 4-matches from cascades, which are so complex that I wouldn’t know where to begin modeling. Ultimately, @Grundulum is correct, and a simulation is the best predictor of such a complex system. ---
**Author:** ![Bolatsi](https://sea1.discourse-cdn.com/flex019/user_avatar/community.gemsofwar.com/bolatsi/32/7182_2.png) [@Bolatsi](https://community.gemsofwar.com/u/Bolatsi)\ **Post date:** [January 4, 2018, 5:19pm UTC](https://community.gemsofwar.com/t/what-is-the-chance-of-getting-another-move-after-clearing-the-board/34654/9 "2018-01-04T17:19:11Z")
Stupid question incoming! Does the kingdom affect the probability of gem colors that drop / form? Isn’t Whitehelm more likely to have yellow gems dropping than the others or am I completely out of radar? ---
**Author:** ![Grundulum](https://avatars.discourse-cdn.com/v4/letter/g/82dd89/32.png) [@Grundulum](https://community.gemsofwar.com/u/Grundulum)\ **Post date:** [January 4, 2018, 5:22pm UTC](https://community.gemsofwar.com/t/what-is-the-chance-of-getting-another-move-after-clearing-the-board/34654/10 "2018-01-04T17:22:17Z")
It’s worse than that. Any L, T, or + shape has a significant chance to be part of a linear 4- or 5-match, since you already know that three consecutive gems are the correct color. This is absolutely solvable analytically, but there would be sooo many cases of overlap and double/triple/quadruple counting. Edit: @Bolatsi. As far as we know, kingdom and banner have no impact on drop rates. ---
**Author:** ![Slypenslyde](https://sea1.discourse-cdn.com/flex019/user_avatar/community.gemsofwar.com/slypenslyde/32/30373_2.png) [@Slypenslyde](https://community.gemsofwar.com/u/Slypenslyde)\ **Post date:** [January 4, 2018, 5:44pm UTC](https://community.gemsofwar.com/t/what-is-the-chance-of-getting-another-move-after-clearing-the-board/34654/11 "2018-01-04T17:44:07Z")
This could be answered with a really neat feature: It’d be cool to have a “player statistics” page that tracks little factoids like “number of gems exploded”, “turns played”, “number of extra turns”, etc. I want it to see if my average number of turns is significantly different from the CPU’s, but it could track things like this. I find it hard to characterize what counts as a “skyfall extra turn” though. I can make a good sounding definition like: > A greater-than-4 match occurring as at least the 2nd match of a turn where at least one of the gems involved was not on the screen at the time the match occurred. But I’m imagining a scenario where you trigger a 3-match that causes a skyfall 3-match that causes some gems that were already on the screen to make a 4-match. Hmm. Maybe the better definition is algorithmic: ``` 1. All gems start with a "from skyfall" flag set. 2. At the start of each turn, unset the flag for every gem. 3. When a match is made: 3.1 For each cascade past the first: 3.1.2 If a gem involved in this match has the "from skyfall" flag set, set a "skyfall involved" flag. 4. At the end of the turn: 4.1 If "skyfall involved" and "extra turn" are set, this was a skyfall extra turn. ``` Compare your total number of non-extra turns to this “skyfall involved” set of extra turns and we have our answer! I can’t see the devs ever implementing this kind of player-specific statistics page, but I can dream! ---
**Author:** ![Lyya](https://sea1.discourse-cdn.com/flex019/user_avatar/community.gemsofwar.com/lyya/32/3650_2.png) [@Lyya](https://community.gemsofwar.com/u/Lyya)\ **Post date:** [January 4, 2018, 6:25pm UTC](https://community.gemsofwar.com/t/what-is-the-chance-of-getting-another-move-after-clearing-the-board/34654/12 "2018-01-04T18:25:17Z")
After running 10 million trials with randomly generated boards, the Monte Carlo odds of getting a native (non-cascading) Extra Turn appear to be approximately 24.8%. This is assuming even distribution of all gem types, including skulls. ---
**Author:** ![Slypenslyde](https://sea1.discourse-cdn.com/flex019/user_avatar/community.gemsofwar.com/slypenslyde/32/30373_2.png) [@Slypenslyde](https://community.gemsofwar.com/u/Slypenslyde)\ **Post date:** [January 4, 2018, 6:31pm UTC](https://community.gemsofwar.com/t/what-is-the-chance-of-getting-another-move-after-clearing-the-board/34654/13 "2018-01-04T18:31:13Z")
Wow. That’s a lot higher than I expected, but it also explains a lot. ---
**Author:** ![Brat](https://sea1.discourse-cdn.com/flex019/user_avatar/community.gemsofwar.com/brat/32/35350_2.png) [@Brat](https://community.gemsofwar.com/u/Brat)\ **Post date:** [January 4, 2018, 9:40pm UTC](https://community.gemsofwar.com/t/what-is-the-chance-of-getting-another-move-after-clearing-the-board/34654/14 "2018-01-04T21:40:37Z")
Well… as a human maybe 1 in 4 odds… the AI has about a 95% rate it seems.