Insuring good hand at TC+2 for less variance?

Hi guys! I am trying to improve my play and was reading about insurance bets, shockingly that it accounts for about 30% of a counter's profits, so I wanna improve that.
I'm looking for a chart or reference on insurance EV vs TC. I'm trying to assess if it's a good idea to ensure a good hand at TC+2 to lower variance ( I know your hand doesn't matter in the insurance "side bet" but it does matter in terms of variance).
I am already over-betting my bankroll so this could be helpful. I'm not that worried about bets placed at TC+2, but when the TC was +6 or more and I place 8 min bets in 2 hand (1-16 spread) then all the faces dealt make the TC around +2 for example, then it's a pretty important case!

Sounds like you've already identified a way to lower your variance without having to "hedge" your bets to try to do the same... Stop over betting your bankroll =). What you're saying is you want to bet a known house edge bet to try to lower the variance of another bet... That's the same as getting a 4 on the Don't Pass line, max odds, then throwing $10 on "hard 4" in craps... Goodbye money. "Thou shalt not hedge bets" - Wizard

When you go to make your insurance decision it doesn't matter that the TC was +6 at the beginning of the round. What matters is what is it RIGHT NOW? TC +2, okay then no insurance, simple as that.

Quote: Romes

What you're saying is you want to bet a known house edge bet to try to lower the variance of another bet... That's the same as getting a 4 on the Don't Pass line, max odds, then throwing $10 on "hard 4" in craps... Goodbye money. "Thou shalt not hedge bets" - Wizard

I have to disagree on that one. I don't have the numbers which is what I'm asking about, but it's definitely not the same as just playing a known house edge bet.

If you think about it we are always making a compromise between advantage and variance, otherwise, why not bet table max when you have a small advantage? Because the variance is not worth the gain! That's why my question is what is the house edge on insurance at TC+2, I think it would be veeeery small. And what effect does that have on the variance of a good hand. It's probably a better compromise than say not betting table max but only 1% of your bankroll only on a very high count.
Now this is all just intuition of course, and I couldn't find ins HE at TC+2 and Var to compare.

But it's not really that simple. To quote James Grosjean in 42.08 "Contrary to what numerous authors have argued, insurance is not a side-bet independent of your main hand. Though usually negative-expectation, the insurance wager will indeed reduce overall variance on the player's \good" hands." It can make sense to insure good hands below the index as a measure to reduce risk. In some countries you can purchase insurance after you have resolved your hand but before the dealer has resolved theirs. So in these countries you can actually insure a hit to 21. So insuring 20 and 21 does make sense because you are maximizing your chance of being ahead at the end of the round. You might also abstain from insuring a sixteen right at the index to avoid the possibility of losing both the insurance wager and the hand. Keep in mind that right at the index the insurance wager is presumably break even or close to it so you are basically agnostic over whether you should make the play or not. It is the same principle as abstaining from doubling 9 v 7 at TC 3.2 because despite the fact that this play has marginally higher expected value it's really not worth the additional risk especially if you making a full kelly wager. So it's a little facile to say that expectation is the be all and end all of making decisions at the blackjack table. There are other considerations as well.


By taking measures to reduce variance, such as abstaining from excessively risky doubles where the gain in expectation is marginal (until of course the count is so high that the gain in ev is not marginal) and insuring good hands close to the index you can then bet more aggressively with less risk and end up making more money.

The ops questions was since he was over betting his bankroll is this something else he could do to try to lessen the variance. The real lesson here is that you should not be over betting your bankroll and looking for a way to hedge down variance. Over betting your bankroll leads to ruin, not more EV.

Quote: BlackjackGuy123

But it's not really that simple. To quote James Grosjean in 42.08 "Contrary to what numerous authors have argued, insurance is not a side-bet independent of your main hand. Though usually negative-expectation, the insurance wager will indeed reduce overall variance on the player's \good" hands." It can make sense to insure good hands below the index as a measure to reduce risk. In some countries you can purchase insurance after you have resolved your hand but before the dealer has resolved theirs. So in these countries you can actually insure a hit to 21. So insuring 20 and 21 does make sense because you are maximizing your chance of being ahead at the end of the round. You might also abstain from insuring a sixteen right at the index to avoid the possibility of losing both the insurance wager and the hand. Keep in mind that right at the index the insurance wager is presumably break even or close to it so you are basically agnostic over whether you should make the play or not. It is the same principle as abstaining from doubling 9 v 7 at TC 3.2 because despite the fact that this play has marginally higher expected value it's really not worth the additional risk especially if you making a full kelly wager. So it's a little facile to say that expectation is the be all and end all of making decisions at the blackjack table. There are other considerations as well.


By taking measures to reduce variance, such as abstaining from excessively risky doubles where the gain in expectation is marginal (until of course the count is so high that the gain in ev is not marginal) and insuring good hands close to the index you can then bet more aggressively with less risk and end up making more money.

Thank you! That is exactly what I mean. But I couldn't find the numbers ... like just as an example what is the EV and VAR of betting more than kelly and insuring at TC+2(Only good hands, as ins on bad hands increases the variance) compared to Kelly and TC+3 insurance.

Actually over betting your bankroll clearly does lead to more EV, at least until you go broke, because the formula for EV is action * edge. So if edge remains constant and action is increased then you are going to generate more expected value. But the problem is, as you say, that ruin is increased. You are going to hit a downswing and then you don't have a bankroll any more and you cannot generate any more expected value. So in the long run over betting will lead to less EV, which is the reason why bankroll management exists in the first place. Betting more than kelly is counter productive for the purposes of bankroll growth. Even kelly itself is a wild enough ride and if taken to it's full and logical conclusion means a 50 max bet bankroll.

I'm trying yo follow this and get confused about "good hand". You're betting whether there's a 10 under the dealer's Ace. The "goodness" of your hand shouldn't matter, except that if it has one or two tens in it, it influences the odds of that undercard also being a 10. Otherwise, as May West noted... "goodness has nothing to do with it."

In fact, when discussing insurance with someone who DOES insure a "good hand" with no awareness of the count, I try to tell the guy that it's a side bet on the presence of an undercard 10, and that a "good hand" of twenty REDUCES that chance because it's used up two more of them.

OK - let the value of your hand go towards determining the true count, and take insurance when the math dictates it, but "goodness"? Absent bringing attention to my professional expertise, I'd insure my 16, or my 6, or... my 20... when the TC is +3 or greater. If I feel compelled to explain it on a "not good" hand, it's because at +3 I have 6 units out there, and "I get scared when I have a lot on the line,"

Do we sometimes over-think this business? The ancients analyzed this game for us, for years and years, and there have been no new numbers invented since someone thought up the "zero". The difficulty in the game is not having competing theories. It's being unemotional enough and focused enough to apply the elementary and simple ones we've been given in a hectic, sometimes hostile environment. That's where I screw up.

Quote: racquet

I'm trying yo follow this and get confused about "good hand". You're betting whether there's a 10 under the dealer's Ace. The "goodness" of your hand shouldn't matter, except that if it has one or two tens in it, it influences the odds of that undercard also being a 10. Otherwise, as May West noted... "goodness has nothing to do with it."

In fact, when discussing insurance with someone who DOES insure a "good hand" with no awareness of the count, I try to tell the guy that it's a side bet on the presence of an undercard 10, and that a "good hand" of twenty REDUCES that chance because it's used up two more of them.

OK - let the value of your hand go towards determining the true count, and take insurance when the math dictates it, but "goodness"? Absent bringing attention to my professional expertise, I'd insure my 16, or my 6, or... my 20... when the TC is +3 or greater. If I feel compelled to explain it on a "not good" hand, it's because at +3 I have 6 units out there, and "I get scared when I have a lot on the line,"

Do we sometimes over-think this business? The ancients analyzed this game for us, for years and years, and there have been no new numbers invented since someone thought up the "zero". The difficulty in the game is not having competing theories. It's being unemotional enough and focused enough to apply the elementary and simple ones we've been given in a hectic, sometimes hostile environment. That's where I screw up.

The OP raises a good question that many overlook. In a nutshell hes basically talking about risk averse play and certainty equivalent. Just like index plays, there is the EV maximizing index of lets say when to split tens or doubling A9v6 and then there are the risk averse index plays. If the EV maximizing index for example is TC +4 for A9v6, the risk averse index might instead be around TC+7. Keep in mind risk averse indicies have shown to have a higher SCORE and reduced variance.

Of course, with that being said, the main drawback of risk averse indices is that of a lower short term win rate compared to that of the EV maximizing plays, but 'IF' you have a small bankroll and want the most optimal bankroll growth, it is in your best interest to use risk averse indices for plays such as splitting 10s or doubling A9v6 as well as the aformentioned insurance at +2 with a good hand out. The short term loss in win rate will pay big dividends for someone with a small bankroll as they will make it back on the back-end due to being able to last longer and win more in the long run.

Norm's CVCX and CVDATA can simulate all the risk averse indices that you need.

Thanks Zenking, I will look up risk averse indices, it's the first time I hear the term and it definitely sounds like something I should know.
Thanks as well Racquet. I do understand it's a side bet and that's what I tell people too, I know the EV of insurance is independent of your hand, but the VAR is not! Insurance on a bad hand increases the VAR while insurance on a good hand reduces it (Compared to the initial VAR of the hand) and that's what I'm trying to figure out, when is the reduction in VAR worth the small -EV.

The theory with risk averse plays is that you can bet more each round, because your over all game has less variance, and therefore have an immediately higher win rate, despite making some choices which have slightly lower expected value. And there really isn't much difference in EV anyway in choosing to hit 9 v 7 @ TC 3.5 as opposed to choosing to double. A9 and TT v 6 are good examples because not only are you doubling / splitting, but you are also giving up a nearly unbeatable hand in the process, so you are incurring a ton of variance. Which isn't to say these plays don't have merit but just that it is wiser to abstain from making them until a slightly higher index, especially if you taking an aggressive stance and wagering full kelly. There is less of a case for using risk averse indexes if you are taking a very conservative position and wagering 1/4 kelly or an even smaller fraction thereof.

Are you talking about a situation where there is no risk of drawing heat? All of the subtle sub-rules and angels-on-the-head-of-a-pin theological discussions.

I WON'T double A-9 or split 10s under any circumstance, The only player at the table who would grant me even the slightest leniency is a fellow counter. The hue and cry from the non-counters as I make the play would rouse the dead. The positive count that justifies the play is the same count that has my maximum bet out there. What more would they need to call upstairs or come over to watch the rest of the shoe, which I assume is going to be strongly in my favor for a while longer?

I guess I don't mind getting down in the weeds about this from a theoretical or abstract point of view, but my point is the same: there is too much going on around me in the real world where I play to have the focus to see these once-in-a-session situations when they happen, and not enough bandwidth to recognize them when they do.

I still have a day job. I've won more than I've lost. I eat and drink for free. I've never thought I have any kind of luck, but that I do have a hard-earned skill that allows me to beat them at this game over the long term. And, so far, THEY HAVE NO IDEA.

I'll stick with basic strategy, I18, and a shallow ramp. And for anyone who frequents this forum and is NOT a professional, I think that's all you need.

I enjoy reading all of this. I pay all due respect to those of you who can understand, and most importantly, APPLY this to your work. But it flies right over my head. I'd love to see it all being applied as I stand in the background. Good for you if you can.