I have been not helpful trying to get a point across so I will use data from a matchup to illustrate the point. I chose this matchup because it illustrates the point I am trying to make as the index is the highest frequency TC and the first downswing averse index is also a RA index and the second downswing averse index appears to have a steep price tag. But a closer look shows it really is a cheap way to stack your largest contributors to variance in favor of upswing variance while reducing downswing variance. The EV maximizing index is TC 0 but the best playing count from the info gathered is a combined count so so bets are not at all correlated to the count and I could have anywhere from a minimum bet out to a maximum bet when the playing TC is at the index of 0:
At the index the EV for hitting is .1536 and the EV for doubling is .1537. So the EV gain at the index is $0.01 per $100 bet if you double (note, since this bin is just for RC 0 the previous data is for RC 0 only. the following info is global info for the total matchup).
The percentage of the time you would double the matchup using that index is 60.36%.
If you use the index of TC 0 the total EV for the matchup is .1843,
For the 60.36% of the time you double the total EV is .2229,
The remaining 39.64% of the time you hit the total EV is .1254.
The first "downswing averse" index is to double for positive RC only:
At the index the EV for hitting is .1600 and the EV for doubling is .1680. So the EV gain at the index is $0.80 per $100 bet if you double.
The percentage of the time you would double the matchup using that index is 56.91%.
If you use the index of Positive RC the total EV for the matchup is unchanged at .1843,
For the 56.91% of the time you double the total EV is .2271,
The remaining 43.09% of the time you hit the total EV is .1277.
The second "downswing averse" doubling index is TC +1:
At the index the EV for hitting is .1701 and the EV for doubling is .1903. So the EV gain at the index is $2.02 per $100 bet if you double.
The percentage of the time you would double the matchup using that index is 40.84%.
If you use the index of TC +1 the total EV for the matchup is .1830,
For the 40.84% of the time you double the total EV is .2504,
The remaining 59.16% you hit the total EV is .1365.
So for the first downswing averse index there is no change in overall EV for all the times you get the matchup by getting an extra penny at RC 0. But the increased EV and frequency of hitting and the increased EV and decreased frequency of doubling clearly makes a positive RC a better index for any bet size than the EV maximizing index of TC 0 and in fact indicates that RC 0 barely has any EV gain and is played 3.45% of the time you get the matchup.
The second downswing averse index of TC +1 is even more interesting. It gains you $2.02 per $100 bet when the TC is +1. That sounds like a lot to give up but if you flat bet all the TCs it costs the total matchup $0.13 per $100 bet in EV while doubling almost exactly 1/3rd less often. The EV all your doubles went up by over 10% due to a higher success rate of doubles. The frequency of hitting goes up 37.3% and the EV for hitting increases by 6.9%. In other words you have less frequent double loses and more frequent double wins which stacks variance to be more positive if done only for your biggest bets. Your small bets the swings for doubling aren't significant enough to worry about using a downswing averse index. Plus the matchup happens 3.52% of the time so the cost to overall EV is less than a half a cent per $100 bet.
So we have established the cost to overall EV and the EV for the total index play for this downswing averse play is minimal despite costing $2.02 per $100 bet at the DSA index to change the index from TC 0 to TC +1. Let's look at the impact on BR growth. Your exposure to the large swings associated with doubling at your largest bets is 47.8% higher if you use the EV maximizing index of TC 0. So exposure swings associated with the play are increased by almost half. In that 50% increase in large swing exposure from big bets the gain in EV is small for the overall matchup at $0.13 per $100 bet and you lose a much higher percentage of those doubles as indicated by the increase in double EV of 10%. This is because you have moved 5% of the total doubles that were losers into the winners for a net increase of 10% in double EV but with a lower double frequency. This is great for certainty of BR growth. A higher percentage of big upswings and lower percentage of big downswings associated with the biggest bets for the matchup. Variance will get a little less but the causes of variance are skewed toward more positive variance and less negative variance.
Then we look at the impact of hitting for the matchup. Hitting frequency goes up by 49.2% and the EV for the total matchup for hitting increases by 8.9%. You have a much higher success rate hitting than doubling generally speaking nut you wouldn't take another card for this matchup so the success rate at the index is unchanged, but the EV for hitting when hitting the matchup increases by 8.9%.
I might still double this one even at big bets but the argument to for increased certainty of BR growth should be obvious for big bets. Using an example where the EV maximizing index is TC 0 has the largest impact on frequency of altering the index so the certainty gain and EV cost are both amplified for your overall approach. But I hope you all get the idea of using downswing averse indices to help shape variance to be your friend that is more heavily upswing variance for the biggest contributors to variance, your big bet doubles and splits.
For big bets the same principle applies for the even biggest variance reducer, surrender. EV maximizing decisions are not the best decisions for increasing certainty of BR growth. Some highly volatile surrenders like split surrenders really scream for aggressive downswing averse moves to the EV maximizing surrender index, but many other surrender plays have little EV gain for the first TC or so that you would not surrender using EV maximizing decisions.
If you have a lot of EV I feel it is worth spending some to help make variance your friend rather than your enemy by stacking the largest contributors to variance and the strongest reducers of variance for your biggest bets to be more user friendly. I often here practitioners of the simple approach say things like a 5% gain in EV is not worth the extra effort even though the gain in EV is more like 10% to 20%. I ask: Is that extra percent or two of EV worth the added downswing variance it produces to get it when you can give it up and really stack the largest swings more toward upswing variance and less toward downswing variance?
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