inconsistent shrink parameter(lambda) distribution in ridge regression

Question

This is an extension of the question on Variablity in cv.glmnet results. I've recently been running cross validation to find the best shrinkage parameter($\lambda$).

I was aware of the variability in cv.glmnet because it shuffles the training and validation data every time it gets called. So I called cv.glmnet multiple times in a for loop and created a histogram of frequencies of lambdas. The results were baffling:

On most iterations, this is the distribution I get. So the distribution of best lambdas is bimodal. But then after couple more iterations i get this:

Despite the variability in cv.glmnet, I was at least hoping for a consistent distribution of lambdas. Am I doing something wrong in my code? Here is the code I wrote:

library(glmnet)
library(ISLR)
fix(Hitters)
Hitters = na.omit(Hitters)

x =model.matrix(Salary~., Hitters)[,-1]
y = Hitters$Salary

# Before Cross Validation, split data into train and test data
train=sample(1:nrow(x), nrow(x) * 0.8, replace=FALSE)
test=(-train)
y.test = y[test]

grid=10^seq(5, 2, length=200)
ridge.mod=glmnet(x[train,], y[train], alpha=0, lambda=grid, thresh=1e-12)

# Number of iteration of cross validation
n = 1000
mses = NULL
bestlams = NULL
minmses = NULL
for (i in 1:n)
{
  cv.out = cv.glmnet(x[train,], y[train], alpha=0, nfolds=10)
  mses = cv.out$cvm
  index = which.min(mses)
  minmses = cbind(minmses, cv.out$cvm[index])
  bestlams = cbind(bestlams, cv.out$lambda.min)
}

par(mfrow=c(2,2))
hist(log(minmses), 
     breaks=20,
     main="Min MSE Histogram",
     xlab="Log(Min MSE)",
     border="blue",
     col="green")
hist(bestlams, 
     breaks=20,
     main="Best lambda Histogram",
     xlab="Lambda",
     border="blue",
     col="green")

Here are some stuff I am thinking/thought about to fix this:

1. change the number of iteration : changed it to n=1000, same results

2. get rid of the intercept: this was an error on my end. I got rid of the intercepts in my feature matrix. But results were the same.

3. specifying lambda parameter for cv.glmnet