English | 繁體中文
[GameLink] Disco Danny (NetEnt)
ReelSize: 3x3
Paylines: 5 Line
Provider: NetEnt
Features: Hold&Spin, FullReward
In the Hold&Spin feature, players can decide when to press SPIN according to their own game rhythm, which is also the origin of this name.
Most of the Hold&Spin featured games are 3x5 independent reels, each reel will only show the payout symbol or empty, after turning to the payout symbol or locked on the reel, until the full reel or the end of the free game.
The game generally starts with 3 free spins. As long as you win 1 payout symbol, the number of games will be reset back to 3 spins, so the number of spins you experience is different each free game.
First of all, the Markov matrix is not difficult to calculate. The difficulty lies in determining the state. If the state is set well, the subsequent calculations can reduce a lot of problems.
In this game, each reel will have 0~3 lock symbols, and then the remaining spins will be 0~3 spins. So there are 4*4*4*4=256 states in total.
After deciding the state, the next step is to calculate the probability of each state transition. The probability of transferring the number of scatter symbols for each reel is sorted out and represented by a red background in the spreadsheet.
There is one thing to pay attention to, when we define the state, we only consider the number of locked symbols on the reel, and do not consider the top, middle, and bottom of the locked position, so we must allow the transfer probability of these three situations are the same.
No matter where the lock symbol appears, the number of times it appears on the reel is the same, that is, the numbers in the three cases of orange and yellow backgrounds must be the same.
The next step is to calculate the probability of each state transition, because the number of spins after full is not important, so the states 253 to 256 can be deleted, the full game can only be represented by the state 252. The transfer matrix is represented by the green background area.
Then free game will initially have 3 scatter symbols, one for each reel, so the starting state is 84, and the starting state of the second round will start from 0, so play 18 (6*3) for these two situations And 27 (9*3) spins, which is the theoretical maximum number of free spins, you can get the probability of ending in each state. This is represented by a blue background.
Finally, calculate the average payout separately for the number of rounds of the free game, and then add them together to get the average payout of the free game. It is represented by a purple background.
Note: The reel strips used in the par sheet may not be the real strips of the game.
Parsheet_11 - Disco Danny (NetEnt)
[GameLink] Disco Danny (NetEnt)
ReelSize: 3x3
Paylines: 5 Line
Provider: NetEnt
Features: Hold&Spin, FullReward
Game Instructions
When talking about the feature of Hold&Spin, everyone may first think of the Lock It Link (WMS) series of games, but the series of gameplay is a little more complicated, so I chose another version that is more suitable for teaching.In the Hold&Spin feature, players can decide when to press SPIN according to their own game rhythm, which is also the origin of this name.
Most of the Hold&Spin featured games are 3x5 independent reels, each reel will only show the payout symbol or empty, after turning to the payout symbol or locked on the reel, until the full reel or the end of the free game.
The game generally starts with 3 free spins. As long as you win 1 payout symbol, the number of games will be reset back to 3 spins, so the number of spins you experience is different each free game.
Model Descriptions
Base Game
Base game is a general 5-line game. There is a golden scatter symbol to get the payout directly, and the payout of mix symbol. The payout symbol will only show a total bet of 10x or 20x, and a separate table is required.Free Game
Free game is more complicated. The symbol lock will use the Markov matrix, and you can replay another round after the reel is full, and there will be an extra multiplier when free game is over. The following will explain one by one.First of all, the Markov matrix is not difficult to calculate. The difficulty lies in determining the state. If the state is set well, the subsequent calculations can reduce a lot of problems.
In this game, each reel will have 0~3 lock symbols, and then the remaining spins will be 0~3 spins. So there are 4*4*4*4=256 states in total.
After deciding the state, the next step is to calculate the probability of each state transition. The probability of transferring the number of scatter symbols for each reel is sorted out and represented by a red background in the spreadsheet.
There is one thing to pay attention to, when we define the state, we only consider the number of locked symbols on the reel, and do not consider the top, middle, and bottom of the locked position, so we must allow the transfer probability of these three situations are the same.
No matter where the lock symbol appears, the number of times it appears on the reel is the same, that is, the numbers in the three cases of orange and yellow backgrounds must be the same.
The next step is to calculate the probability of each state transition, because the number of spins after full is not important, so the states 253 to 256 can be deleted, the full game can only be represented by the state 252. The transfer matrix is represented by the green background area.
Then free game will initially have 3 scatter symbols, one for each reel, so the starting state is 84, and the starting state of the second round will start from 0, so play 18 (6*3) for these two situations And 27 (9*3) spins, which is the theoretical maximum number of free spins, you can get the probability of ending in each state. This is represented by a blue background.
Finally, calculate the average payout separately for the number of rounds of the free game, and then add them together to get the average payout of the free game. It is represented by a purple background.
Simulation Result
File Download
Here is the par sheet of this game, if you are interested, you can download the par sheet file for research.Note: The reel strips used in the par sheet may not be the real strips of the game.
Parsheet_11 - Disco Danny (NetEnt)
基础游戏规则里面没有W,为什么要加上W的数量？
回覆刪除18局和27局是理论的最高局数，请问这个是如何得出的结论呢？
回覆刪除第一輪有6個空格，最慢每3局要出現一個鎖定圖標，所以最多玩6*3=18局。
刪除第二輪有9個空格，最多9*3=27局。
明白了，谢谢。还一个地方不是很明白，在绿色部分计算转移矩阵的时候，公式乘以R1,R2,R3概率后面再乘这个公式的意义是什么？IF(FLOOR(X$62/4,1)=FLOOR($R63/4,1),IF(X$62=$R63+1,1,0),IF(VLOOKUP(X$62,$R$62:$V$315,5,FALSE)=3,1,0))
刪除還要再乘上Spin次數的轉換，才是最後的機率。你可以試試看把這項移除會產生什麼變化？
刪除嗯，如果初始和结束的固定个数相同，那么如果（初始状态+1 = 结束状态），就为1否则为0；如果初始和结束的固定个数不同，就看结束状态的spin数剩余是3就为1否则为0。这段我自己理解了一下，但是不知道为什么要这也的计算。还望帮忙分析一下这部分？卡在这里实在不好理解清楚。
刪除因為狀態是由4個參數組成，[R1/R2/R3/Spins]，如果只考慮前三個參數，每列轉換機率會超過100%造成錯誤，這邊可以調整測試看看差異。
刪除博主你好！状态转移机率，R1从状态1~2，为什么是=SUM(G16:G17,G20:G21)/G13，不是=SUM(,G19:G21)/G13呢？还有从状态1~3，公式是=SUM(G19)/G13，没有看懂为什么要这么计算，我看类似R2,R3都是这样计算的。望解惑
刪除因為要從1~2，表示現在狀態是1，代表已經鎖定一格，可能是1-0-0/0-1-0/0-0-1其中一種。因為3種機率都相同，所以我這邊是直接使用第一種情況來計算的。
刪除假設現在是1-0-0，如果要變成狀態2，那就要出現第2格或第3格有鎖定的盤面，所以是[G16:G17,G20:G21]的這些組合；狀態1~3的概念也是一樣要從1-0-0變成1-1-1，只能靠0-1-1的組合，所以是[G19]
谢谢。还想请教一下，在round1的End减去了3，这里第一轮初始就有3个锁定的w，但是计算期望的时候不考虑这3个吗？按理这三个初始w是有倍数的，也应该考虑进去计算期望。
刪除因為初始3顆平均倍數跟新鎖定的算法不同，所以這邊沒有一起計算，在BaseGame的特色賠付有把初始3顆計算進去。
刪除我看博主你在BaseGame CF2的计算公式=Setting!E15+FreeGame!Q41+3*Setting!T5，这3*Setting!T5是指初始三个锁定的赔付吗？但我看游戏视频里这三个锁定赔付是X1~X50。不知道我是不是哪里理解错了
刪除初始3颗的倍数和新锁定都是1~50倍，请问这里的倍数和新锁定算法为什么不同呢？
刪除因為我不確定這兩種Scatter的平均倍數是否相同，所以我用不同的方式來計算，這邊是我模型的設計方式，不代表參考遊戲也是這樣做的。
刪除