Dragon's Lair (NES)/any%(ntscu) - Revision history

Ktwo: /* RNG-analysis of 6-puff fights */

2023-08-14T07:56:53Z

‎RNG-analysis of 6-puff fights

Ktwo: /* Alternative Singe fight ("6-puffer") */

2023-08-14T07:46:38Z

‎Alternative Singe fight ("6-puffer")

Ktwo: /* Alternative Singe fight ("6-puffer") */

2023-08-14T07:42:45Z

‎Alternative Singe fight ("6-puffer")

Ktwo: /* Level 4 - Dragon's Lair */

2023-08-14T07:41:53Z

‎Level 4 - Dragon's Lair

Ktwo: /* Alternative Singe fight ("6-puffer") */

2023-08-14T07:41:27Z

‎Alternative Singe fight ("6-puffer")

Ktwo: /* RNG-analysis of 6-puff fights */

2023-08-13T07:29:46Z

‎RNG-analysis of 6-puff fights

Ktwo: /* RNG-analysis of 6-puff fights */

2023-08-12T20:31:38Z

‎RNG-analysis of 6-puff fights

Ktwo: /* Level 4 - Dragon's Lair */

2023-08-12T16:51:21Z

‎Level 4 - Dragon's Lair

Ktwo: /* RNG-analysis of 6-puff fights */

2023-08-12T14:41:41Z

‎RNG-analysis of 6-puff fights

Ktwo: /* Level 4 - Dragon's Lair */

2023-08-12T14:38:54Z

‎Level 4 - Dragon's Lair

@@ Line 381: / Line 381: @@
 * CL to NCL3 - 17%
-One cannot reasonably know in real-time the RNG-values, or even which RNG-loop the game is in. However, by simulating the smoke pattern for all possible seeds (so each element in the three possible NCLs (1-3)), combined with how likely it is for the game to be in each NCL, it's possible to calculate the probability of a specific pattern.<br /><br />
+There is no in-game cue indicating which RNG-loop the game is in, so this information is unknown in a real-time attempt. However, by simulating the smoke pattern for all possible seeds (so each element in the three possible NCLs (1-3)), combined with how likely it is for the game to be in each NCL, it's possible to calculate the probability of a specific pattern.<br /><br />
 ''Note: When looking at where the different RNG-pairs in the "carry loops" enter the "non-carry loops" when releasing R, some NCL-pairs are more common "entrance points" than others. However, since R will anyways in real-time be released at different points during the jump to the Singe fight, this feature will be averaged out (at least to some extent). A full investigation taking this into account adds a layer of complexity and has not been done. In the analysis below, it has therefore been assumed that each RNG-pair in a loop has equal chance of being the first in the "puff sequence".''<br /><br />

@@ Line 364: / Line 364: @@
 # If the jump into the fight was late, Dirk needs to be re-positioned one movement pixel to the left. So quickly turn around, move once and then turn back. This can be easier said than done. If the correct x-position is not achieved, it will turn into a 7-puff fight.
 # Rise when the first smoke puff passes by above
-# Buffer one small and two big jumps, while attacking and then duck upon landing
+# Buffer one small and two big jumps and then duck upon landing
 # This action is the most critical with this method in terms of execution. Throw two axes, the first one needs to connect with the baby dragon on the first frame it has a hitbox. Visually, the axe will fly past the baby dragon, but then disappear against Singe's belly. The baby dragon will then disappear some time after the second axe connected (making it look like it just despawned).
 # Rise and make a small jump. This will have to be done without delays after point 6. If there was a delay somewhere of one game frame in steps 6 or 7, there will not be enough time to finish the fight in 6 puffs and it will turn into a 7-puff fight. If the delay is bigger, Dirk will not have enough time to jump over the next smoke puff (with the method described in this section).
-# Two big jumps and then finally a small jump forward, all of them while attacking, to finish the fight.
+# Two big jumps and then finally a small jump forward to finish the fight.
-The fight with this method finishes one game frame before Singe blows the 7th puff, hence why step 4 and onward need to be without any delays, or else a 7th puff (low) is needed to finish the fight. In the 7-puff fight, step 7 and 8 should be replaced by "''buffer a small jump, two big jumps (over puff 5 and 6) and a big forward jump (over puff 7)''". A 7-puff fight is at best 45 frames slower than the 6-puff fight.<br /><br />
+Method 2 finishes one game frame before Singe blows the 7th puff, hence why step 4 and onward need to be without any delays, or else a 7th puff (low) is needed to finish the fight. In the 7-puff fight, step 7 and 8 should be replaced by "''buffer a small jump, two big jumps (over puff 5 and 6) and a big forward jump (over puff 7)''". A 7-puff fight is at best 45 frames slower than the 6-puff fight.<br /><br />
 A pre-requisite for attempting a 6-puff fight in a speedrun is to practice the execution. For this purpose, it's recommended to apply e.g. the game genie codes APEGLEPV and APEGGEPV, which bypasses the RNG's dependence on player inputs. Entering the Singe fight on the same frame will therefore lock Singe into the same pattern. The following save states (for FCEUX and Powerpak) start from right before Singe, [[File: Dragon's_Lair_(USA)_Singe_RNG_manip.zip]]. They require a modified ROM, either by having applied the mentioned game genie codes (or patch a ROM by changing instructions $C003 and $C004 to 0x18). Save state 1 is for method 1 (L, L, L, H, L, L) and save state 2 for method 2 (H, L, L, H, L, L). For the patterns to work, you need to move right without delay and enter the fight by making a small jump.<br /><br />

@@ Line 361: / Line 361: @@
 If jumping later than what's described in method 1, a different puff pattern and approach are needed. This method is a second slower than method 1:<br />
 # The jump into the fight is pixel-perfect. There are good visual cues for identifying if the jump was done on the right pixel. If the jump was correct, the first axe will look like it's almost flying past Singe, but then connects between his chin and belly. If the jump was too late, the two axes will connect with Singe's head. The fight is unwinnable with the needed puff pattern from this position. See point 3 for how to mitigate.
-# Duck and buffer two axe throws (if the jump into the fight was very early, the first axe throw can miss the dragon, so it's recommended to throw a 3rd axe for safety in this case).
+# Duck and buffer two axe throws
 # If the jump into the fight was late, Dirk needs to be re-positioned one movement pixel to the left. So quickly turn around, move once and then turn back. This can be easier said than done. If the correct x-position is not achieved, it will turn into a 7-puff fight.
 # Rise when the first smoke puff passes by above

@@ Line 65: / Line 65: @@
 # Buffer an attack when the level begins, take a few steps forward and jump and then attack again mid-air
 # Attack once before the egg, move forward and jump when Dirk is in front of the egg and finally attack once more mid-air
-# This baby dragon can be jumped over if it has a low take-off angle. A delay of at least 60 frames is then needed. The fastest way to do this is by throwing twice (55f) and then pause movement for one game frame (5f). An alternative and slightly slower method is shown in the linked video. Ducking and jumping costs 70f, but avoids having to rely on a pause in the movement. The jump over the dragon must be done from the last pixel of the platform.
+# This baby dragon can be jumped over if it has a low take-off angle. A delay of at least 60 frames is then needed. The fastest way to do this is by throwing twice (55f) and then pause movement for one game frame (5f). An alternative and slightly slower method is shown in the linked video. Ducking and rising costs 70f, but avoids having to rely on a pause in the movement. The jump over the dragon must be done from the last pixel of the platform.
 # Just buffer two attacks when landing after having jumped over the 3rd dragon. The 4th dragon will always fire before disappearing, so quickly jump up to the next platform.
 # Try to start attacking this baby dragon as soon as possible to avoid that it fires a second volley onto the platform Dirk is on

@@ Line 360: / Line 360: @@
 https://vimeo.com/852463029<br />
 If jumping later than what's described in method 1, a different puff pattern and approach are needed. This method is a second slower than method 1:<br />
-# The jump into the fight is pixel-perfect. There are good visual cues for identifying if the jump was done on the right pixel. If the jump was correct, the first axe will look like it's almost flying past Singe, but then connects between his chin and belly. If the jump was too late, the two axes will connect with Singe's head. The fight is unwinnable with the needed puff pattern from this position. See point 3 for how to mitigate. If the small jump was early, see method 1.
+# The jump into the fight is pixel-perfect. There are good visual cues for identifying if the jump was done on the right pixel. If the jump was correct, the first axe will look like it's almost flying past Singe, but then connects between his chin and belly. If the jump was too late, the two axes will connect with Singe's head. The fight is unwinnable with the needed puff pattern from this position. See point 3 for how to mitigate.
 # Duck and buffer two axe throws (if the jump into the fight was very early, the first axe throw can miss the dragon, so it's recommended to throw a 3rd axe for safety in this case).
 # If the jump into the fight was late, Dirk needs to be re-positioned one movement pixel to the left. So quickly turn around, move once and then turn back. This can be easier said than done. If the correct x-position is not achieved, it will turn into a 7-puff fight.

@@ Line 389: / Line 389: @@
 A few observations:
-* To jump over the 6th puff as shown for this method, you need to start pressing right before the high/low check for the 6th puff has been done. The simulation result for the 6th puff will therefore not be accurate in a real-time attempt (unless when having to mitigate and go for a 7-puff fight). The area for the 6th puff has therefore been colored differently.
+* Right needs to start to be pressed for the jump over the 6th puff before the high/low check has been done. The simulation result for the 6th puff will therefore not be accurate in a real-time attempt. The area for the 6th puff has therefore been colored differently.
 * There is a positive bias for the first puff, where a bit over half of them will be low.
 * Except for puff 4, there is significant negative bias for the remaining puffs.

@@ Line 333: / Line 333: @@
 https://www.youtube.com/watch?v=goEf5-qU7ZA<br /><br />
-<u>Alternative Singe fight ("6-puffer") - method 1</u><br />
+===Alternative Singe fight ("6-puffer")===
-https://vimeo.com/853932259<br />
 The standard approach to fight Singe is by standing on the left side of the screen and dodge and attack as best as one can, which is also the method shown in the video of the whole level. A very good fight in a real-time attempt can then be done in 15 or so smoke puffs (each one separated by the 145 frame delay).<br /><br />
-An alternative way of approaching the fight is to trade the (relative) safety of staying on the left side for maximum aggressiveness by staying close to Singe. This can shorten the fight down to a "6-puffer" by being able to land 3 axes every big jump, as well as adding some small jumps (with time for 2 attacks). The downside is that all 6 puffs need to be of the right kind (= L, L, L, H, L, L) and the execution can also be somewhat tight. The video above shows the fight, but here is a breakdown of it:
+An alternative way of approaching the fight is to trade the (relative) safety of staying on the left side for maximum aggressiveness by staying close to Singe. This can shorten the fight down to a "6-puffer" by being able to land 3 axes every big jump, as well as adding some small jumps (with time for 2 attacks). The downside is that all 6 puffs need to be of the right kind and the execution can also be somewhat tight.<br /><br />
-# The first small jump before the fight begins can be done from two different pixels. If jumping from one of the correct pixels, one of the two axes will hit Singe and one will miss. If you jump too early, none of the axes will connect. This is still a winnable situation, but turns it into a 7-puff fight (see below). Jumping later can also work out and is described in the section below ("method 2").
 # Duck upon landing and kill the baby dragon.
 # Rise and make a big jump over the 1st smoke puff.
@@ Line 345: / Line 355: @@
 # Crouch (under the 4th puff) and attack twice to take out the baby dragon. Then rise. These actions can all be buffered upon landing after step 5.
 # Wait briefly and then buffer a big jump (over the 5th puff), a small jump and a big forward jump (over the 6th puff). Jump too early and Dirk will land on the 5th puff. Jump too late and there will not be enough time to jump over the 6th puff. The latter case can be difficult to identify visually in real-time, but assuming it's done, it's possible to mitigate by turning it into a slower, but still 6-puff fight. In that case, skip the short jump between puff 5 and 6. Instead, initiate the big jump over puff 6 earlier and then finish off Singe with a small forward jump.
-<br />
+<br /><br />
-−
-As mentioned above, some of the mistakes can be mitigated by aiming for a 7-puff fight. The 7th puff must then be a low one and point 7 changed to "''big jump (over the 5th puff), a small jump, a big jump (over the 6th puff) and finally a big forward jump (over the 7th puff).''". This is a little over one and a half second slower than a 6-puff fight. If Singe has not been defeated by the 7th puff, another baby dragon will spawn together with the 8th puff.<br /><br />
-<u>Alternative Singe fight ("6-puffer") - method 2</u><br />
+<u>Method 2 (H, L, L, H, L, L)</u><br />
 https://vimeo.com/852463029<br />
-If jumping later than what's described in method 1, a different puff pattern (H, L, L, H, L, L) and approach are needed. This method is a second slower than method 1:<br />
+If jumping later than what's described in method 1, a different puff pattern and approach are needed. This method is a second slower than method 1:<br />
 # The jump into the fight is pixel-perfect. There are good visual cues for identifying if the jump was done on the right pixel. If the jump was correct, the first axe will look like it's almost flying past Singe, but then connects between his chin and belly. If the jump was too late, the two axes will connect with Singe's head. The fight is unwinnable with the needed puff pattern from this position. See point 3 for how to mitigate. If the small jump was early, see method 1.
 # Duck and buffer two axe throws (if the jump into the fight was very early, the first axe throw can miss the dragon, so it's recommended to throw a 3rd axe for safety in this case).
@@ Line 361: / Line 369: @@
 # Two big jumps and then finally a small jump forward, all of them while attacking, to finish the fight.
-The fight with this method finishes one game frame before Singe blows the 7th puff, hence why steps 4 and onward need to be without any delays, or else a 7th puff (low) is needed to finish the fight. In the 7-puff fight, step 7 and 8 should be replaced by "''buffer a small jump, two big jumps (over puff 5 and 6) and a big forward jump (over puff 7)''". Getting a 7th puff with method 2 is slightly less punishing than with method 1. It's at best 45 frames slower than the 6-puff fight.<br /><br />
+The fight with this method finishes one game frame before Singe blows the 7th puff, hence why step 4 and onward need to be without any delays, or else a 7th puff (low) is needed to finish the fight. In the 7-puff fight, step 7 and 8 should be replaced by "''buffer a small jump, two big jumps (over puff 5 and 6) and a big forward jump (over puff 7)''". A 7-puff fight is at best 45 frames slower than the 6-puff fight.<br /><br />
 A pre-requisite for attempting a 6-puff fight in a speedrun is to practice the execution. For this purpose, it's recommended to apply e.g. the game genie codes APEGLEPV and APEGGEPV, which bypasses the RNG's dependence on player inputs. Entering the Singe fight on the same frame will therefore lock Singe into the same pattern. The following save states (for FCEUX and Powerpak) start from right before Singe, [[File: Dragon's_Lair_(USA)_Singe_RNG_manip.zip]]. They require a modified ROM, either by having applied the mentioned game genie codes (or patch a ROM by changing instructions $C003 and $C004 to 0x18). Save state 1 is for method 1 (L, L, L, H, L, L) and save state 2 for method 2 (H, L, L, H, L, L). For the patterns to work, you need to move right without delay and enter the fight by making a small jump.<br /><br />

@@ Line 397: / Line 397: @@
 * Of the patterns getting past puff 3, puff 4 and 5 have a very high probability of being high and low, respectively. The probabilities are so high that the aggregated probability even gets in front of the expected value after puff 5 (4.9% iso 3.1%)! This effect is pretty clearly not by game design, but just "how it ended up to be". NCL1-3 only consist of 201 elements. The number of possible start seeds is then greatly reduced when we get to puff 4 (17 possible seeds) and 5 (12 possible seeds), so a few "lucky" outcomes are all that's needed for the probabilities to be greatly off, which appears to be the case here.
 * The effect reverses for puff 6, which has a much lower probability of being low than expected
-* Based on the above, one can maximize the probability of getting the TAS pattern by accepting the probabilities up to puff 5. During the jump before puff 6, one should however press R to scramble the RNG-values. This should lead to a probability closer to 50% for the 6th puff, instead of the 27% that will result from not pressing R. If this is done, the chance of getting the necessary pattern should increase considerably, so well worth doing!
+* Based on the above, one can maximize the probability of getting the right pattern by accepting the probabilities up to puff 5. During the jump before puff 6, one should however press R to scramble the RNG-values. This should lead to a probability closer to 50% for the 6th puff, instead of the 27% that will result from not pressing R.

@@ Line 338: / Line 338: @@
 An alternative way of approaching the fight is to trade the (relative) safety of staying on the left side for maximum aggressiveness by staying close to Singe. This can shorten the fight down to a "6-puffer" by being able to land 3 axes every big jump, as well as adding some small jumps (with time for 2 attacks). The downside is that all 6 puffs need to be of the right kind (= L, L, L, H, L, L) and the execution can also be somewhat tight. The video above shows the fight, but here is a breakdown of it:
-# The first small jump before the fight begins can be done from two different pixels. If jumping from one of the correct pixels, one of the two axes will hit Singe. If you jump too early, none of the axes will connect. This is still a winnable situation, but turns it into a 7-puff fight (see below). Jumping later can also work out and is described in the section below ("method 2").
+# The first small jump before the fight begins can be done from two different pixels. If jumping from one of the correct pixels, one of the two axes will hit Singe and one will miss. If you jump too early, none of the axes will connect. This is still a winnable situation, but turns it into a 7-puff fight (see below). Jumping later can also work out and is described in the section below ("method 2").
 # Duck upon landing and kill the baby dragon.
 # Rise and make a big jump over the 1st smoke puff.
@@ Line 344: / Line 344: @@
 # Big jump over the 3rd puff
 # Crouch (under the 4th puff) and attack twice to take out the baby dragon. Then rise. These actions can all be buffered upon landing after step 5.
-# Wait briefly and then buffer a big jump (over the 5th puff), a small jump and a big forward jump (over the 6th puff). The first jump in this step needs to be initiated (game) frame-perfectly and is therefore the most sensitive part of the fight. Jump too early and Dirk will land on the 5th puff. Jump too late and there will not be enough time to jump over the 6th puff. The latter case can be difficult to identify visually in real-time, but assuming it's done, it's possible to mitigate by turning it into a slower, but still 6-puff fight. In that case, skip the short jump between puff 5 and 6. Instead, initiate the big jump over puff 6 earlier and then finish off Singe with a small forward jump.
+# Wait briefly and then buffer a big jump (over the 5th puff), a small jump and a big forward jump (over the 6th puff). Jump too early and Dirk will land on the 5th puff. Jump too late and there will not be enough time to jump over the 6th puff. The latter case can be difficult to identify visually in real-time, but assuming it's done, it's possible to mitigate by turning it into a slower, but still 6-puff fight. In that case, skip the short jump between puff 5 and 6. Instead, initiate the big jump over puff 6 earlier and then finish off Singe with a small forward jump.
 <br />
@@ Line 363: / Line 363: @@
 The fight with this method finishes one game frame before Singe blows the 7th puff, hence why steps 4 and onward need to be without any delays, or else a 7th puff (low) is needed to finish the fight. In the 7-puff fight, step 7 and 8 should be replaced by "''buffer a small jump, two big jumps (over puff 5 and 6) and a big forward jump (over puff 7)''". Getting a 7th puff with method 2 is slightly less punishing than with method 1. It's at best 45 frames slower than the 6-puff fight.<br /><br />
-A pre-requisite for attempting a 6-puff fight in a speedrun is to practice the execution. For this purpose, it's recommended to apply e.g. the game genie codes APEGLEPV and APEGGEPV, which bypasses the RNG's dependence on player inputs. Entering the Singe fight on the same frame will therefore lock Singe into the same pattern. The following save states (for FCEUX and Powerpak) start from right before Singe, [[File: Dragon's_Lair_(USA)_Singe_RNG_manip.zip]]. They require a modified ROM, either by having applied the mentioned game genie codes (or patch a ROM by changing instructions $C003 and $C004 to 0x18). Save state 1 is for method 1 (L, L, L, H, L, L) and save state 2 for method 2 (H, L, L, H, L, L). For the patterns to work, you need to move right without delay and make a small jump into the fight.<br /><br />
+A pre-requisite for attempting a 6-puff fight in a speedrun is to practice the execution. For this purpose, it's recommended to apply e.g. the game genie codes APEGLEPV and APEGGEPV, which bypasses the RNG's dependence on player inputs. Entering the Singe fight on the same frame will therefore lock Singe into the same pattern. The following save states (for FCEUX and Powerpak) start from right before Singe, [[File: Dragon's_Lair_(USA)_Singe_RNG_manip.zip]]. They require a modified ROM, either by having applied the mentioned game genie codes (or patch a ROM by changing instructions $C003 and $C004 to 0x18). Save state 1 is for method 1 (L, L, L, H, L, L) and save state 2 for method 2 (H, L, L, H, L, L). For the patterns to work, you need to move right without delay and enter the fight by making a small jump.<br /><br />
-===RNG-analysis of Singe's TAS puff pattern for method 2===
+===RNG-analysis of 6-puff fights===
-As has been mentioned above, the game uses an [[Dragon%27s_Lair_(NES)/Game_Mechanics(ntscu)#RNG|RNG-algorithm]] that results in bias. If the RNG-calculation had been ideal, one would have expected the TAS pattern to occur with a probability of 1/64 (= 1/2^6). As will be shown in this section, that is however not the case and there are considerations on how to improve the chances of getting the correct puff pattern.<br /><br />
+As has been mentioned above, the game uses an [[Dragon%27s_Lair_(NES)/Game_Mechanics(ntscu)#RNG|RNG-algorithm]] that results in bias. If the RNG-calculation had been ideal, one would have expected every 6-puff pattern to occur with a probability of 1/64 (= 1/2^6). As will be shown in this section, that is however not the case and there are considerations on how to improve the chances of getting the correct puff pattern.<br /><br />
 After having taken care of the last baby dragon, there is enough time before the Singe fight begins for the RNG-values to enter CL1, 2 or 3 (see the RNG-section for an explanation). And before the first smoke puff is blown, the RNG will change to NCL1, 2 or 3. As can be seen in the "CL to NCL" chart in the RNG-section, there isn't a big difference in the probabilities whether one starts from CL1, 2 or 3. For the sake of simplicity, let's therefore assume the following average probabilities:
@@ Line 373: / Line 373: @@
 * CL to NCL3 - 17%
-One cannot reasonably know in real-time the RNG-values, or even which RNG-loop the game is in. However, by simulating the smoke pattern for all possible seeds (so each element in the three possible NCLs (1-3)), combined with how likely it is for the game to be in each NCL, it's possible to calculate the probability of a specific pattern.<br /><br />
+One cannot reasonably know in real-time the RNG-values, or even which RNG-loop the game is in. However, by simulating the smoke pattern for all possible seeds (so each element in the three possible NCLs (1-3)), combined with how likely it is for the game to be in each NCL, it's possible to calculate the probability of a specific pattern. ''Note: it has been assumed that each RNG-pair in a loop has equal chance of being the "entrance" to the loop. This assumption does not seem to be entirely correct, but has not been investigated further.''<br /><br />
 <u>Method 1</u><br />
@@ Line 381: / Line 381: @@
 A few observations:
-* To jump over the 6th puff as shown for this method, you need to start pressing right before the high/low check for the 6th puff has been done. The simulation result for the 6th puff will therefore not be accurate in a real-time attempt (unless when having to mitigate and go for a 7-puff fight).
+* To jump over the 6th puff as shown for this method, you need to start pressing right before the high/low check for the 6th puff has been done. The simulation result for the 6th puff will therefore not be accurate in a real-time attempt (unless when having to mitigate and go for a 7-puff fight). The area for the 6th puff has therefore been colored differently.
 * There is a positive bias for the first puff, where a bit over half of them will be low.
 * Except for puff 4, there is significant negative bias for the remaining puffs.
-* Based on the above two observations, in attempts getting past puff 1, it should be beneficial to introduce R-presses mid-jump as often as possible to "scramble" the RNG and force it to temporarily leave whichever NCL it was in. It's not evident to simulate the probabilities after "scrambling" the RNG like this, but it should be in the whereabouts of 50% (at least better than by not "scrambling").
+* Based on the above two observations, in attempts getting past puff 1, it should be beneficial to introduce R-presses mid-jump to "scramble" the RNG and force it to temporarily leave whichever NCL it was in. It's not evident to simulate the probabilities after "scrambling" the RNG like this, but it should be in the whereabouts of 50% (at least better than by not "scrambling").
 <br />
@@ Line 393: / Line 393: @@
 A few observations:
-* There is a negative bias already for the first puff, where a bit over half of the Singe fights will end. A possible way to increase the percentage up to the expected 50% would be to introduce R-presses all the way up to when Singe is about to  blow the first puff to avoid the RNG being stuck in one of the NCLs. However, the remainder of the fight will then be difficult to predict (and this hasn't been attempted to be simulated).
+* The bias for the first puff is inverse from method 1 and a bit over half of the Singe fights will end here
-* Similar to the point above, there is significant negative bias for the 3rd puff. Only about a third of the attempts reaching this far will result in a low puff here. One could again argue for introducing R-presses (during the jump over the 2nd puff) to scramble the pattern and get out of the NCLs. This should reasonably improve the chances significantly for the 3rd puff, at the expense of randomizing the rest of the puffs.
+* Similar to the point above, there is significant negative bias for the 3rd puff. Only about a third of the attempts reaching this far will result in a low puff here.
-* Of the patterns getting past puff 3, puffs 4 and 5 have a very high probability of being high and low, respectively. The probabilities are so high that the aggregated probability even gets in front of the expected value after puff 5 (4.9% iso 3.1%)! This effect is pretty clearly not by game design, but just "how it ended up to be". NCL1-3 only consist of 201 elements. The number of possible start seeds is then greatly reduced when we get to puff 4 and 5, so a few "lucky" outcomes are all that's needed for the probabilities to be greatly off, which appears to be the case here. This would not be expected to be seen if any manipulations had been done at puff 1 and 3.
+* Of the patterns getting past puff 3, puff 4 and 5 have a very high probability of being high and low, respectively. The probabilities are so high that the aggregated probability even gets in front of the expected value after puff 5 (4.9% iso 3.1%)! This effect is pretty clearly not by game design, but just "how it ended up to be". NCL1-3 only consist of 201 elements. The number of possible start seeds is then greatly reduced when we get to puff 4 (17 possible seeds) and 5 (12 possible seeds), so a few "lucky" outcomes are all that's needed for the probabilities to be greatly off, which appears to be the case here.
-* The effect reverses for puff 6, which has a much lower probability of being low than expected.
+* The effect reverses for puff 6, which has a much lower probability of being low than expected
-* Based on the above, one can maximize the probability of getting the TAS pattern by accepting the probabilities up to puff 5. During the jump before puff 6, one should however press R to scramble the RNG-values. This should lead to a probability closer to 50% for the 6th puff, instead of the 27% that will result from not pressing R. If this is done, the chance of getting the TAS pattern increases from around 1/75 to 1/41, so well worth doing!
+* Based on the above, one can maximize the probability of getting the TAS pattern by accepting the probabilities up to puff 5. During the jump before puff 6, one should however press R to scramble the RNG-values. This should lead to a probability closer to 50% for the 6th puff, instead of the 27% that will result from not pressing R. If this is done, the chance of getting the necessary pattern should increase considerably, so well worth doing!