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Originally Posted by
Jack Jackson
For example, an index that is +6 for the 13 point system(for splitting xxs) is smaller(more efficient) than +6 would be for splitting xxs in the 12 point count system would be..So this tells i would use the 13 point count index, right?.
I was into researching this a while back for what I do. The issue is the data is stretched out across different ranges, or in other words 1 TC is not equivalent for the two systems due to having different sum of squares. After corresponding with Don I got what was called a good approximation using the sum of squares, but Don cautioned it was not totally accurate. After using the approximation a bit, it became clear Don was right (big surprise there right, LoL), the approximation wasn't accurate enough. The only way to be accurate is as Don said, sims.
While waiting for software to catch up I used a lot of ways to approximate. The trouble is you are looking at flat betting when you need to consider your ramp. Often the main count is good enough until the ace side count get pretty out of whack on plays the side count would adjust the main count tags to be better for the play. Remember the side count adjusts the tags for more than just the ace so there are times the ace isn't why you use the side count. The adjustment to other ranks could be the reason. But it is usually the ace. Also you can add practical multiples of the side count like plus or minus 1/2 times the side count. I mostly use the side count for doubles and splits, while I wait for software updates.
Anyway I found that several things showed one as stronger than the other. You can use a sum of squares ratio to project an equivalent index for the second count being considered. The count with the lower "equivalent index" for doubles or splits usually is better. Another thing I looked at was the slope of the gain after the index is exceeded. Again the sum of squares must be factored in. This produced errant results and was my first try using Don's advice that he gave with the caveat that he didn't think the approximation would be accurate enough (it would have been a lot easier if Don was wrong, but that doesn't happen much). I briefly considered using correlation coefficient of the plays EoRs to count tags but that has its flaws for practical applications because coefficients are not efficiencies.
What I had to end up doing was using sim results for index generation. I compared the total EV for the matchup, which is all you need for anything that doesn't add more money to the table. With doubles and splits I separated the index generation results into overall results, double results, and hit/stand results. You can then compare total EV for the matchup, doubling frequency, doubling win percentage, and hit/stand win percentage. You can look at risk averse indices by moving the index by one TC increment and looking at the same 4 metrics, and calculating the cost to overall EV for your system by factoring in matchup frequency. The trouble is so far all this is for flat betting. You really need to consider this when factoring in your bet ramp.
But if you can generate about the same matchup EV while doubling (or splitting) at significantly lower frequency it is obviously better to double less often to avoid the variance increase from doubles and splits that has little effect on overall EV. What happens when you double less frequently is you win a higher percentage of hit/stand decisions and a higher percentage of doubles or splits without giving up much matchup EV, or in the case of comparing playing counts you may have a higher EV when doubling less frequently. This effect is magnified by bets size if decisions near the index affects increased bet sizes. Sometimes it is a quite significant increase in both win percentages. If you have a big bet out obviously winning a significantly higher percentage of doubles and splits while also winning a significantly higher percentage of hit/stand decision helps with BR growth certainty. As long as the cost is small (a judgement call based other on the cost per incident and/or the overall cost to your system. I express cost in per $100 bet. That helps put bet size in perspective) this is what you are looking for particularly with your biggest bets out.
This last part is why you need to factor in your bet ramp. If you have small bets out you should just go for the best overall EV for the matchup. The change in win percentage for both decisions for the matchup will not affect certainty of BR growth much when you have small bets out. Often small bets correlate to a near neutral side count, in most cases the main count is a good enough measure of the play when the side count is nearly neutral. The higher the side count TC and the larger your bet the higher the benefit from using a combined count if it is the right choice. At near neutral side counts the main count is usually an accurate approximation. If you are at or near the main count index you still might want to use the combined count if it is better.
Of course if you have a huge BR and believe you should not worry about certainty of BR growth you can choose to maximize EV. I don't like that idea but it is a matter of personal preference. I like to have more certain BR growth so I don't have to play as much most of the time to make what I need to cover my life's expenses. This helps with longevity. But that is just me. I used to play like it was a full time job and didn't use lots of the ways I have learned to make BR growth be more steady. The swings were so crazy I would have to look at a long period to even tell if I was trending up. I like seeing an obvious trend up for any relatively short period of time. When I figured out how to do that I changed my approach.
When the software catches up to be able to factor in bet size I will let you know. For know I am doing the best I can with the software's capability. Hopefully the software you use can break down index generation sims to give you the really useful information to deciding which is actually better. It should until you get to doubles, and splits. The extra information I described will help with them if the software allows that kind of summary, or gives enough information for you to generate it.
Anyway, I hope you find some helpful things in there. When the software is ready to just produce the answers you need I will let you know. It doesn't look like it will be anytime soon but that is out of my hands. I don't write the software. Hopefully I will be pleasantly surprised. I am just happy to get the help whenever it happens.
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