No. It affects overall EV and SD, and therefore the main bets if you are betting optimally. Read the OP's question. The overall result of a strategy is what matters.
You are right. The original question is vague. It’s not a question a mathematician would ask.
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A few references might prove useful. Start with Grosjean, Beyond Counting, pages 11-12.
But, the definitive work on everything having to do with insurance, risk aversion, variance, etc., is Michael Canjar's (MathProf) 32-page authoritative study on the subject:
https://www.bjrnet.com/archive/AdvancedInsurancePlay_MichaelCanjar.pdf
There's little point in discussing seat-of-the-pants stuff when such a compelling work exists.
Don
This is an interesting result. If the SD would have been much smaller, it would imply that for players on a small bankroll that for survival purposes it would be correct to also take insurance in situations where the bet was still slightly negative. This result says no to that idea.
Best wishes,
Mason
Small bankroll is always a problem and other rules, penetration, and decks will obviously affect this. Insurance is a valuable index for funded players. But these days, positive EV on an Insurance bet for a typical game available with a small bankroll is something like 1 in 200 hands. So the value to a small bankroll player who may be playing at a high risk of ruin may not be that valuable.
Now we get to what kind of player. If the player with a small bankroll is attempting to build a bankroll (good luck), risk aversion is important and session sims would probably suggest Insurance, possibly even at a slightly lower index. If the small bankroll is replenishable, perhaps not. If the player just wants to enjoy himself for a time and has budgeted his bankroll, up to him. Devil is in the details.
Of course, you can also look at which hands you insure. But, if it is a small bankroll player, probably better to not add any additional rules.
Just had a bottle of wine with my trout and will look over my response in the morn.
Last edited by Norm; 01-20-2022 at 06:03 PM.
"I don't think outside the box; I think of what I can do with the box." - Henri Matisse
Whatever the spread, it's the same for both players in Norm's sim, whereas, if the insurance player were betting optimally, he'd be betting more than the non-insurance player, because he has a greater overall advantage by virtue of insuring when it's correct to do so. Those larger bets would, in turn, lead to a greater s.d. than the one for the non-insurance player, provided both bet optimally.
Don
Basically, if your playing strategy is improved with the same betting levels (i.e. it has a higher SCORE or balance between EV and SD), then your risk of ruin drops. So, you can increase your betting, and consequently EV, while bringing your risk back to the level of the inferior playing strategy. More money, same risk.
Now, you mentioned buying Insurance at a different index than one that maximizes EV. That's where risk-averse indices come in. These maximize the balance between EV and SD. With Insurance, the index could vary by the hand as that could reduce SD as you've pointed out. Canjar's paper, linked to by Don, covers all this. Academically valuable as someone had to delve into the subject. But, I've never thought it mattered enough to warrant the increase in complexity.
As for the small bankroll player. I suppose his aversion to risk matters. Gamblers generally like risk. Smaller bankrolls also mean less betting flexibility. It's more difficult to bet optimally with a smaller bankroll, and rules are commonly less favorable.
Last edited by Norm; 01-21-2022 at 04:29 AM.
"I don't think outside the box; I think of what I can do with the box." - Henri Matisse
Not considering other factors which affect strike point, is there an available graph that displays % EV captured by True Count. I would be especially interested in either Hi Lo or Halves.Now, you mentioned buying Insurance at a different index than one that maximizes EV.
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