RNG using chaotic tentmap seems predictable

Summary

I'm using a imperfect model (electrical) to simulate a tentmap. The little variations in my model and limited amount of decimals cause it to generate pseudo random numbers. My problem/confusions stems from the predictable nature of my model in short term which doesn't seem random. It doesn't feel right to me, but it might just be the nature of pseudo random number generators.

Tentmap has this shape:

• x_n+1 = mu * x_n for x_n < 0.5
• x_n+1 = mu * (1- x_n) for x_n > 0.5

My model is a simulation of an electrical circuit implementation of this tentmap, so it has the same general shape.This should be able to generate random numbers. The iterations with small deviations cause chaos. However the short term effect seems less random. Say you have 0.1 as your first random number and you can predict that the next number is more or less 0.2. Which also causes it being impossible to go from say 0.3 to 0.2 or back to 0.3.

Attempts

My guess was that I my system needs a few iterations to lose this predictability. So I did a test in which I take a number generated with the model and predict the next number using the ideal tentmap. I did this for multiple cases(predicting 1, 2, 8 numbers ahead). My indicator for randomness is the average difference between the ideal prediction and the values of my model. The difference between 2 random numbers between 0 and 1 is 0.3333. The graph plot the mean difference between the model and the ideal case for a particular spating. Average distance

I interpret this graph as indicating every 10th number is random. Is this a correct way of thinking ? If so only 1 in 10 values useful, which doesn't seem very efficient. Is there a way to solve this ?