https://www.blackjackincolor.com/cardcountingcover6.htm
Of course, this is SCORE, not EV.
Or is this what you're looking for: https://www.card-counting.com/cvcxonlineviewer3.htm
Change the drop down to Insurance, the bottom selection.
https://www.blackjackincolor.com/cardcountingcover6.htm
Of course, this is SCORE, not EV.
Or is this what you're looking for: https://www.card-counting.com/cvcxonlineviewer3.htm
Change the drop down to Insurance, the bottom selection.
Last edited by Norm; 01-21-2022 at 05:09 AM.
"I don't think outside the box; I think of what I can do with the box." - Henri Matisse
I jumped into this discussion because I noticed you published books on gambling theories. I posted these numbers above but haven’t received anybody’s confirmation. I am an amateur mathematician, so my questions and conclusions are specific. Consider the following two cases:Originally Posted by MMalmuth
1. Suppose we have a natural against a dealer ace in a 1-deck blackjack game. If we don't count cards, the insurance EV=-8.2%; SD=1.383.
2. Suppose we have a nature against a dealer ace in a modified deck with 52 original cards and 3 extra 10s. If we count cards and find the true count (TC) to be +2.8 (before dealt) and 0 (after dealt), the insurance EV=+3.8%; SD=1.427.
The SD number when counting cards is definitely greater. I also constructed other TC>+3 deck compositions and found their SD numbers are greater, mostly but not all.
can you or anybody verify these numbers?
Email: [email protected]
I have no idea how I could have missed that. Not just insurance, but the whole range of comparisons. Extremely valuable. The study of same could easily lead to strategy changes on some of my plays (cover related)Or is this what you're looking for: https://www.card-counting.com/cvcxonlineviewer3.htm
Change the drop down to Insurance, the bottom selection.
Two comments
1. Would be nice to see my typicals - ES10 H17 LS - have to extrapolate
2. I’ll study more fully, looks like I essentially operate as per the graphs
Targeting Insurance, I was recently backed off a hi limit game utilizing halves with an unknown add on factor, apparently regaled system. The game featured deep pen with reasonable rules. My max bet in this game was a paltry 7 units - a spread considered by many as not suitable to beat a shoe game. Notwithstanding some purposeful errors under GM supervision, my play was perfect (has to be at that low spread) though deck estimation was “poor”.
I made various decisions on insurance at strike point utilizing the unknown regaled system, as well as by considering quality of hand. My insurance success on the higher TC’s was excellent, winning all of the big ones, except one where I did win the hand. This, coupled with hit, stand, surrender decisions 14, 15, 16 v 10 were likely also a factor.
Despite the modest spread, I was politely told any game but…….Hourlies at this facility higher than you might think.
Hi Norm:
I'm coming back to this since I now understand better what exactly is happening.
Having a standard deviation of $193.91 per hand (I think) for the non-insurance player and a standard deviation of $193.29 for the player who is taking insurance is an amazing result, and for practical purposes I think we can say that these two standard deviations are essentially the same. Yet, the player who is taking insurance is putting more money in action, so wouldn't you expect his standard deviation to go up?
What I think is happening is that some of his bets are not independent of each other and, in fact, are inversely correlated. Specifically when the dealer has a blackjack, unless the player also has a blackjack (which should happen only rarely) he must then lose the standard bet. This produces a result of $0 which probably has the effect of lowering the standard deviation. Next, which we can call the second case, when he losses the insurance bet but wins the standard bet he may also be lowering his standard deviation since his result is now half of what it would be if he hadn't taken insurance (and I'm ignoring things like doubling down and splitting to keep this explanation simple). It's only when, the third case, the player losses both bets that he drives his standard deviation up since he's actually losing 1-and-a-half bets instead of 1 bet. My guess is, based on the numbers that Norm has provided, that all of this approximately washes out.
But based on the way I understand things, which comes from mostly poker (see my Gambling Theory book), if taking insurance increases your win rate (which is sometimes different from advantage) but you keep your standard deviation the same, your bankroll requirements go down. So, here is an example that will appear counterintuitive to many people.
Following up on this a little more, if you play with the equations in my Gambling Theory book you'll end up with this equation (which appears in my book Poker Essays):
BR = [(9)(SD)^2]/[(4)WR] where BR is bankroll, (SD)^2 is the standard deviation squared (or the variance), and WR is the win rate. Now, this equation is not perfect, but in my experience it does a very good job of estimating the required bankroll at three standard deviations. And in this problem which we're discussing, since according to Norm's simulation the standard deviation is essentially the same, but the win rate will obviously go up for the player taking insurance, the required bankroll for the player taking insurance will be less even though he's putting more money into action.
To finish, DSchles points out that the player taking insurance should be using a more aggressive betting scheme than the one not taking insurance. I think it would be interesting to see what this does to the standard deviation. Perhaps Norm can run another simulation.
Best wishes,
Mason
Good stuff. The point of using more aggressive betting with higher EV is to keep the same risk of ruin with a better win rate (assuming that is one's goal). SD may very well go up as well -- but at a rate that still ends up with the same RoR with a better win rate. A higher SD is not necessarily bad if the EV increases at a rate to keep the same RoR. We always need to look at both at once.
Happy to run sims as I am now up to 110 million rounds a second with a standard desktop chip. Just need detailed specs.
BTW, I'll send you my Poker software if I ever get around to finishing it.
Last edited by Norm; 01-21-2022 at 05:22 PM.
"I don't think outside the box; I think of what I can do with the box." - Henri Matisse
I'm really trying to understand this statement. My understanding is that insurance is probably the easiest of all actions to understand. Very very simple at its core. If (X's remaining > 1/3 of the deck) insuring is profitable.
How is it even vaguely possible the comment above rings true?
At its (I had to manually fix that) core, it is incredibly simple. An (extreme) example I like to give to give and have done so on this board, is 26 cards remaining on a 6 deck shoe, RC 5 or TC 10 - prepare a list of all the combinations of high middle and low cards capable of pricing of TC 10. There’s @ couple def8nitely not worth insuring. Try it.My understanding is that insurance is probably the easiest of all actions to understand. Very very simple at its core.
If you have a side count that improves the insurance decision compared to the main count. A count I developed with a good insurance improvement would sometimes (correctly) tell you to take insurance even in negative counts, or to (correctly) not take insurance even with the main count in large excess of the index.
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