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Aaron White
Australia Bathurst New South Wales
Bennett from Brawl
Slow and Thoughtful

Hi,
Based on my other posts you can see I enjoy Shift. I have owned it for a while now and realised that some characters are harder to enjoy than others. This is because it is harder for some characters to do their things due to the probability of success on their attacks. To explain, every attack has a modifier and a critical effect. The modifier depends on if you get a combination of heads and tails over a number of coin flips (HT needs a HT or TH to succeed on two coin flips). The critical depends on if you got the combination in the exact order (HT needs H and then T to succeed on the two coin flips, T then H is not successful). It is possible to get a modifier but not the critical, but you always get the modifier if you get the critical. The requirements on each attack is different, some are easy with a single H while others are hard with combinations like THT.
This sounds fine, but when you look at the probabilities it can be really hard to get the critical effects or sometimes the modifiers  see below. H is Heads, T is Tails, W is Wild which can be H or T. I have only listed combinations that are currently on the cards.
H or T 50% chance of modifier and critical 50% chance of failure
HH or TT: 25% chance of modifier and critical 75% chance of failure
TW or HW: 50% chance of modifier and critical 25% chance of modifier only 75% overall chance of modifier 25% chance of failure
HT or TH: 25% chance of critical and modifier 25% chance of modifier only 50% overall chance of modifier 50% chance of failure
HTW: 25% chance of critical and modifier 37.5% chance of modifier only 62.5% overall chance of modifier 37.5% chance of failure
THT, HTH, TTH, THH: 12.5% chance of critical and modifier 25% chance of modifier only 37.5% overall chance of modifier 62.5% chance of failure
If you are unfamiliar with Shift the above probabilities appear reasonable. Critical hits should not happen all the time and more powerful effects should be infrequent. However each attack may be used only a few times each game due to shifting and different attacks on different gears. So low probabilities can mean you never use a modifier or critical on some attacks. This is important because each character is defined by their core ability, their modifiers and their critical effects (there is also attack and defense but these are not relevant to this article). If you play a game of Shift and have terrible luck then it feels like playing a noncharacter with no abilities. This takes away from the fun and reduces the decision making because you cannot play the odds if the odds are extremely low.
Having said the above there are some critical effects or modifiers you do not want to happen all the time because it makes certain characters overpowered. Take BoomerRanger Dingo as an example. His ability allows him to flip a coin if he critical hits. On H he can shift to a higher gear for free. Dingo also has a Duo Crit available on all three gears (allows him to skip his opponents turn). If you combine the two effects and get good flips you can attack your opponent several times from a higher gear and they can do nothing in return (except spirit guard or active guard). This is crazy powerful and lots of fun when you pull it off.
But the problem is he can rarely do it at all. On his THT gear 1 attack, there is only 12.5% chance of a critical and then he has to get a H on another flip for his ability, meaning the chance of getting both is only 6.25%. On his TH or HT gear 2 attacks there is a 25% chance of a critical and again he has to get H on another flip. His Omega gear 3 attack is an automatic critical, this is the most consistent chance to use his ability but still only works 50% of the time. Because you might use his most powerful Omega attack once or twice per game it is likely you will never use his ability at all during a game. This makes Dingo not much fun because he fails to get his effects so often.
After much thought I decided I want to improve the probabilities in this game to improve the fun. But if I improve them too much then characters like Dingo go from being very weak to crazy good. I played with dice and other things but did not like them as they required too many changes to the game. I wanted the change to be minimal so we did not have a separate sheet of house rules or variations. After much thought and a few calculations I came up with the reflip method.
In the current game you flip the coin one at a time. If you flip the requirement in the exact correct order, you get the modifier and critical effect.
Quote: Need HT, flip two coins getting H then T, which means both critical and modifier effects are successful. If you flip the requirement but in a different order, you only get the modifier
Quote: Need HT, flip two coins getting T then H, which means I get the modifier effect only. I changed this to instead be flip all coins at once. If you get the requirement you get the critical and modifier regardless of the order you flipped them.
Quote: Need HT so flip 2 coins, got H then T so I get both the critical and modifier effects. Order did not matter. However, if you do not get the requirement then you can reflip 1 coin to try and succeed. If you succeed with a reflip then you get the modifier only.
Quote: Need HT, flip two coins and get T and T. Reflip one of the T to get H, so I get the modifier only. To see what this method does please see below revised probabilities based on using the reflip method.
H or T: 50% chance of modifier and critical 25% chance of modifier 75% overall chance of modifier 25% chance of failure
HH or TT: 20% chance of modifier and critical 20% chance of modifier only 40% overall chance of modifier 60% chance of failure
TW or HW: 60% chance of modifier and critical 20% chance of modifier only 80% overall chance of modifier 20% chance of failure
HT or TH: 33.33% chance of critical and modifier 33.3% chance of modifier only 66.66% overall chance of modifier 33.33% chance of failure
HTW: 60% chance of critical and modifier 20% chance of modifier only 80% overall chance of modifier 20% chance of failure
THT, HTH, TTH, THH: 25% chance of critical and modifier 33.33% chance of modifier only 58.33% overall chance of modifier 41.66% chance of failure
The reflip method improves the probabilities but not drastically. The critical chance on HH or TT drops to 20%, but the modifier chance is increased from 50% to 75%. HT and TH change to a nice 1/3 chance for critical and 2/3 chance for modifier effects. Most importantly the THT/HTH/TTH/THH probabilities are higher, with a 1/4 chance of critical or roughly 1/2 chance of modifier. Playing this way allows characters to "do stuff" more often than before, which is important because the fun factor is higher when you can do more stuff.
The big problem I did have is the requirements that have W or wild in them such as HW, TW or HTW. 80% chance of modifier and 60% chance of critical is pretty massive. Looking at the characters that have a wild there are several that this would make insane good, including Kuma (multiple Duo Crits), Reginald (lots of Shift Crit), Mark II (lots of Shift Crit), Melpome (lots of Shift Crit, plus spirit regenation via ability) and Berry (worst one, refresh spirit and chance to heal off crit). Based on this, if you use the reflip method then change the W symbol for H or T. Choose the opposite to the previous symbol on the requirement. For example Berry has HTW on his alpha gear 2 attack. Change this to HTH. For Kuma's alpha gear 2 attack change it from TW to TH. This will bring these attacks in line with everything else.
For ease of reference, see below summary of the reflip method.
1. Flip a number of coins at the same time equal to the number of coins shown in the requirement (2 coins for HT, 3 coins for TTH etc). 2. If you flip the required results in any order then you get the critical effect and the modifier. 3. If you did not flip the required results, you can reflip one coin. If after the reflip you have the required result, you get the modifier only. 4. If after reflipping one coin you do not have the required results, you do not get the critical effect or the modifier. X. If the requirement has a wild requirement, change this to H or T, whichever is opposite to the previous symbol in the requirement (HW becomes HT etc).
A quick disclaimer  I am not a professional mathematician. If I made any mistakes with probabilities at all please let me know, will happily admit if I am wrong. Also if you had any other alternative ideas for tweaking the probability in Shift that is easy to implement then please share.
If you play any games with Shift using the above I would love yo hear your thoughts and if it improves your games.
Thank you for taking the time to read.


Brian
United States California

I wish this game got revisited. There's some neat concepts and idea but the whole idea of the coin flip really turned me off (same thing happened with me and the Pokemon TCG). I really should go try to find my cards again, the changes below might make it more fun rather than a probability nightmare.



