VNI gives 5 % to drone tracking and velocity while the Ishtar gets 7 . 5 % per Gallente cruiser level , so it in theory applies damage better against smaller targets . <| sep |> The nips demand more attention , lets show some light on it . <| sep |> Not in Damascus . It ' s actually pretty cool there . I miss it <| sep |> THeir freaking log shows THEY HAD THE CR ' S to do the fight normally . THey could ' ve saced the tank on each p 3 breath . They said it themselves '' we had the CR ' s to dodge every single breath ''<| sep |> Of course they can do it . Any website can . The libcucks running this website are ~~ just stupid enough to admit to doing it ~~ beautiful flowers <| sep |> After discussing with my colleague , we find that the problem is actually deceptively difficult . Below is some of our discussion for the optimal strategy . The degenerate caseTo begin with what strategy to use , we know that the payoff of any strategy is between 0 and 1 inclusive . In other word , whenever the strategy achieve a payoff of 1 , then we stop the betting and get the win . Hence , if the first flip is a head , then you always quit because you are not getting any better . Similarly , if the first flip is a tail , then you always play because it cannot get worse and you can certainly terminate the game at any time by having a fixed stopping time or what not . S 0 If the first flip is a head , we always quit the game . Otherwise we will play at least one more round . The expected payoff of S 0 is at least 0 . 5 . In fact you can achieve an expected payoff of 0 . 625 using the following variant S 0 a If the first flip is a head , we quit the game . Otherwise we flip another round then quit the game . and a strategy that is at least as good as S 0 a with halting probability 1 . S 0 b If the first flip is a head , we quit the game , otherwise we play until the first head appears . For the sake of simplicity , assume that the rest of the following strategies also include the degenerate case that we quit on the first flip if it is a head . The intuitionSince we know that flipping a fair coin will have equal chance of head and tail , we also know that any sequence of headtail is equally likely . If we only put our attention to only one step , then we know that every step will have an expected proportion of 0 . 5 not total proportion . Intuitively speaking , one may consider the following strategy as the stopping time rule . In fact it is the most natural one to consider S 1 We continue to play the game until we have a proportion p of at least 0 . 5 . We quit whenever the proportion is at or above 0 . 5 . The strategy does hold merit in a lot of sense It has a halting probability of 1 . And if we are at a losing position p 0 . 5 , then we have nothing to lose by just playing the long game law of large number . However , if we are at a winning position p 0 . 5 , then there is no reason for us to play one more round only because the expected proportion is always going to drop . The strategy , while intuitive , has one big caveat We are not looking one step ahead only . It is possible for us to get a long win streak some time in the future . So why should we use the expected proportion of next step as our consideration of winning strategy ? Why not wait until we get a long string of head ? We should eventually get a streak that is lucky enough that can gain even better ? Remember we as the player get to decide when to quit . So why not just play it out ? The stopping time involves the maximum of proportion , not just the average . This , my friend , is what I call an optimist strategy . The optimistIf we go beyond the fair game p 0 . 5 , then consider the following deterministic strategy S 2 We play the game until the proportion p is larger than a cutoff s , s 0 . 5 . We quit whenever ps . So for this line of strategy , we may want to optimize s to obtain an optimal strategy . We know s is at least 0 . 5 , but how large it should be ? The optimist will find that s is a number arbitrarily close to 1 , which may sound crazy at the first glance , but ultimately make sense in a nonrigorous way . Suppose that you are at a certain proposition s ' 1 , then our payoff if we quit is s '. However , we can continue to play the game . Given infinite number of time , we should theoretically have a chance of a proportion of larger than s '. In other word , we will be lucky enough to get a long streak to do even better . This stands for any value of s ' because we should theoretically have a chance of always getting something better say for example , getting a head on next flip . What if after the next flip our position is worse ? It does not matter , we just wait until the proportion eventually gets to the level s ' or above . This argument seems to suggest that we can choose an arbitrary cutoff but can always do better , no matter what cutoff we choose . But is S 2 a valid strategy for any value of s ? Well , there is one huge caveat . The concept of eventually is not as intuitive as our brain thinks , similar to many nonintuitive cases when we deal with infinity . The nuisanceThe optimist strategy ultimately fails on one end There is no guarantee that the game will halt eventually . It can very well happen that the game will never end if we set the cutoff at say 0 . 8 . But hey , isn ' t there always exists a sequence that can improve our proportion eventually ? Say a sufficiently long streak of head towards the end ? This comes to the concept of almost sure . While such sequence exists , the probability of such sequence may go to zero . In other word , if the only sequence that can satisfy our cutoff requirement has a probability goes to zero , then the probability of the game never ending goes to 1 in other word , the game will continue forever almost surely . To imagine the picture , consider that you have played a very long time , then each individual flip at that point hardly matters . The bulk of the 10 billion flips you have done so far far outweigh the impact of you next flip . In fact , we know that the proportion will go to 0 . 5 almost surely as guaranteed by strong law of large number . The proportion is likely to be fluctuating at a very thin interval around 0 . 5 after many flips , making it virtually impossible probability goes to zero that you can ever achieve a cutoff that is higher than 0 . 5 . ConclusionFrom the above argument we can see why the game is deceptively difficult . This is because while the sample mean i . e . the payoff you get at any given time goes to 0 . 5 , it is also possible for you to get a streak long enough to gain more than 0 . 5 . However we need to keep in mind that being too optimistic mean we may land on a strategy that does not end in the long run . To further complicate thing , we have not yet discussed other type of strategies , such as a dynamic cutoff strategy e . g . we quit the game whenever the proportion is larger than sn , a random stopping strategy we quit the game whenever the proportion is larger than some other random variable . See secretary problem for example or other cutoff metric number of head or tail .