Hi everyone, I'm looking to validate some index charts I've generated with my own simulation. My indices are similar to Don Schlesinger's in The Hi-Lo Counting System book, but many are off by 1. I understand that Don's indices are risk-averse and optimize SCORE, but is there a similar reference for EV-maximizing indices? Or would I have to generate this through CVData or something?
Thanks, that's good to know. I'm flooring too, and the errors are both positive and negative. I suspect it is just a precision issue since the EV difference for all of the erroneous indices is smaller than the standard error for each value.
Don, Can I ask how many rounds you simulated? I'm currently able to simulate ~30mil per minute
I simulated 200 billion rounds for each rule set we generated indices for. Dr Stewart Ethier provided us with a methodology for estimating certainty when it came to extremely close decisions. For the stubborn cases for which the certainty was still low, we made the more risk averse choice. This may explain some of the differences.
Ok, currently running a 20 billion round sim to see if it gets better. Do you happen to remember the threshold for certainty you used before making the risk-averse choice? And was your simulation somehow weighted to get a better distribution across counts or hands?
I appreciate the help! I want to make sure I'm doing this 100% correctly for blackjack before running simulations on other variants and sidebets.
The differences are probably due to how you're calculating the TC. Not only should the indices be floored, but dividing the RC by the remaining decks also has its nuances. For example: How do you estimate the remaining decks?Originally Posted by Chuckles!
Sincerely,
Cac
Luck is what happens when preparation meets opportunity.
Yes, but consider the strength of the remainder for an increase of your simulated betting ramp. Example, your true 2 bet is 2 units, your true 3 bet is 4 units - consider 3 units for your true 2.5 bet.. Is flooring standard for deck estimation?
The bet does not appear to be optimal, but is utilizing half true counts. Has the further benefit of making you look weak.
In the book, the estimate of remaining decks is rounded to the nearest half deck. That is, the RC can be divided by 6, 5.5, 5, 4.5, 4, 3.5, 3, 2.5, 2, 1.5, 1.
Then the division is rounded down (floored).
Hope this helps.
Sincerely,
Cac
Luck is what happens when preparation meets opportunity.
There was no attempt made to change the distribution of the cards in order to speed up the process. As such, some plays at some counts resolve much more slowly than others. That's why, even after 200 billion rounds, there were still some stubborn cases.
Dr Ethier's formula essentially gave us the standard error of the difference of the EVs for two given actions, given their individual EVs, standard deviations and sample size. A difference in EV of 3 or more of these standard errors was considered resolved.
Ok, I implemented this and ran another 20 billion. It's closer now, but there are still a few areas where the numbers are uniformly fuzzy. I think I just need to spend time tinkering with parameters to see their effect on the results. I'll post my latest run for anyone curious.
Thanks for everyone's input, you've all been super helpful! I'll post back once I have an update.
Index_Results.jpg
Agreed, I do plan to run it for 200 billion at some point. But since I'm still seeing repeated patterns of errors (13/14/15/s16/s17/s18/s19 vs 2/3/4 is consistently high by 1), I'm almost certain that there's a problem with my ruleset. (I might also optimize my code a bit since 200 billion rounds will take me 5 days, haha)
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