1. Is the math right here?
2. Why does standard deviation get smaller as the count gets higher?
Thanks.
SCORE by Count jpeg.jpg
1. Is the math right here?
2. Why does standard deviation get smaller as the count gets higher?
Thanks.
SCORE by Count jpeg.jpg
To MercySakesAlive: Twice now you've talked about a SCORE for each count, and I already explained to you that there is no such thing. The term is meaningless. A game has a SCORE; a true count has no SCORE. Why do you insist upon making simple ideas complicated??
Don
Thanks, Don. I understand a count doesn't have a SCORE. I put "SCORE" in quotes to try to communicate that. Then I tried calling it Count SCORE for the same reason.
A particular count has an EV and an SD, and those two values have a ratio. I'm interested in knowing if (1,000 * win loss / SD)^2 would be a good way to compare those ratios between different counts.
The purpose is just to understand EV and SD a little more deeply.
I'm sorry, but the purpose is a poor one. You won't understand either e.v. or s.d. any more or less for simply observing that, with each positive TC, e.v. gets higher and s.d. gets a little lower. Now that you know that, what will you do with the information? Best answer: not much of anything at all.
Don
OP, your second question about the trend in s.d. versus true count is a good one, that I don't think we have a clear answer to-- or at least I don't. That is, s.d. does not *always* decrease with increasing TC, as shown here (in the second group of plots). Very roughly, basic strategy and simple counting-based modifications of basic strategy such as I18 exhibit the decreasing s.d. vs. TC trend you're observing... but strategies "nearer to optimal" seem to have the opposite behavior, with negative true counts having lower s.d. I don't know of a clear explanation for this effect, let alone quantitative analysis to support it.
Hi Eric. Glad to see you interest is peeked on something. Here is my thoughts on full indices reversing the general trend for SD vs TC. With full indices you are doubling and splitting more at high counts than with the I18 only. More extra splits than doubling on your initial hand, but splits often become extra doubles.
MercySakesAlive,
I'll show how to calculate the overall IBA (or what CVCX calls the "%W/L") using the numbers you posted at the start of this thread.
At each TC, multiply the Freq. (expressed as a decimal) by the Exact Bet, then sum all these to find the Average Bet: that is the average number of units in initial bets per round. With your example, the first few products are 0.4527, 0.2428, etc., and the Average Bet is 2.4113 Units. If your unit is $10, then this result will be shown in CVCX as an Average Bet of $24.11.
Next at each TC calculate the Freq. times the Exact Bet times the W/L: once again, be sure to use decimals rather than percents. Sum these values to find the Overall W/L in Units. Using your values, the first few numbers are -0.00779, -0.00073, 0.00040, etc., and the Overall W/L is 0.03174 units per round. If your unit is $10, then this result will be shown in CVCX as a Win/Rnd of $0.32.
Finally, the IBA is the ratio of the Overall W/L in Units to the Average Bet in Units:
IBA = 100%*0.03714/2.4113 = 1.32%.
This is called %W/L in CVCX.
Hope this helps!
Dog Hand
Regarding question 2 in this thread, "Why does standard deviation get smaller as the count gets higher?", thats not actually correct. I use KO and I observed that SD increases with deck depth at lower counts and DECREASES with deck depth at higher counts. The count at which the SD begins to decrease instead of increase is the "pivot" count (which is 4 for an IRC of -20).
I suppose the with deeper pen's that the SD begins to drop in the higher counts because of the increase in pushes as Three said. And then the SD increases in the lower counts because there are more possible outcomes by having more cards in play as is the case in deeper penetrations. Does that sound like my reasoning is correct?
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