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19h

comment 
Analysis of NimLike Game?
bof: I wouldn't say that. First, some Nimtype games are equivalent to Nim with one pile of size up to $n$. Second, there are infinitely many moves possible when you have a heap of size greater than $1$, so a priori there could be infinite ordinal nimbers necessary to describe the game. 
20h

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Analysis of NimLike Game?
Again, the analysis of this game is an exercise. The only way this might be ontopic is as a reference request. Perhaps people have looked at families of games on partitions generalizing this one. 
20h

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Analysis of NimLike Game?
@bof: That looks like a mistake, but you can move from $[1,2,3]$ to $[1,2,2,2]$ which is equivalent to $[1,2]$. 
20h

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Analysis of NimLike Game?
By the way, this is equivalent to Nim with one pile, though it takes a little effort to see the correspondence. The winning positions for the second player have an even number of heaps of each size. It's easy to find the nimber of a position base $2$. 
23h

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Analysis of NimLike Game?
I don't think the analysis is researchlevel, but it might be ok as a reference request. 
1d

awarded  co.combinatorics 
2d

comment 
Regarding lefttoright minima
Second, I used the union bound. For the max of $l_1, ..., l_n$ to be at least $x$, at least one of them must be, so the probability that the max is at least $x$ is at most the sum of the probabilities that each $l_i$ is at least $x$. 
2d

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Regarding lefttoright minima
I used two steps there. First, there is a standard trick that comes from rewriting a nonnegative integervalued random variable $M$ as a sum of indicators of whether the random variable is at least n. $M = Z_1 + Z_2 + ...$ so $E[M] = E[Z_1 + Z_2 + ...] = E[Z_1] + E[Z_2] + ... = P(Z_1=1) + P(Z_2=1) + ...$. Let $h= \lfloor 1+\epsilon H_n \rfloor, M = \max(h,\max(l_1,...,l_n)).$ Then $M = h + 1_{\{M \ge h+1\}} + 1_{\{M \ge h+2\}} + ...$ so $E[\max(l_1,...,l_n)] \le E[M] = h + P(M \ge h+1) + P(M \ge h+2) + ...$. 
2d

revised 
Regarding lefttoright minima
Corrected misplaced epsilon^2 in one formula. Made trivial changes. 
2d

answered  Regarding lefttoright minima 
2d

comment 
Regarding lefttoright minima
By $\rho_{i...n}$, you mean the suffix of the permutation, $j \mapsto \rho(j)$ for $i \le j \le n$? 
Apr 23 
comment 
Size of smallest multiple $\sum \epsilon_i p^i$ of $n$ with digits $\epsilon_i\in \{0,1\}$ for $p$ a prime
Which part doesn't make sense for nonprime $p$? 
Apr 23 
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Size of smallest multiple $\sum \epsilon_i p^i$ of $n$ with digits $\epsilon_i\in \{0,1\}$ for $p$ a prime
Coincidentally, I just answered a different but related question here: programmers.stackexchange.com/questions/272517/… 
Apr 22 
comment 
Trapped Billiard trajectories on nonconvex billiard tables
The paper you cite has the assumption that the curvature doesn't vanish anywhere. If the curvature at a point doesn't vanish, and the third derivative is bounded in a neighborhood of the point, then no trajectory can get stuck at the point. Global failure of convexity isn't important. So, what remains is to consider the cases where the curvature vanishes. 
Apr 21 
comment 
First collision time of $n$ random walkers on a cycle
That definition of collision isn't a function of the resulting position, though. 
Apr 21 
comment 
Determinant of a checkerboard Hankel matrix with Catalan numbers
What are the first few values? Anything in the Online Encyclopedia of Integer Sequences? 
Apr 21 
revised 
Maximum occupancy balls in bins with limited independence
Used convex substitute for binomial. 
Apr 19 
comment 
Raising coefficients of a power series to some power
David Handelman pointed out that this is the Hadamard product of P with itself. Hadamard proved some results that might be useful, perhaps in J. Hadamard, Th´eor eme sur les s´eries enti eres, Acta. Math. 22 (1899) 55–63. I haven't tracked down that reference yet, though papers that cite it mention some theorems that might be useful.

Apr 18 
answered  Maximum occupancy balls in bins with limited independence 
Apr 18 
answered  Decomposition of a crosspolytope into simplices 