Giving a little back

acercher

acercher

Member
It feels a little awkward for me to request advice from the members here without providing anything in return. However, as a novice with less than a year of mini-tournament experience (I took last winter off), it would be presumptuous of me to think that anything I came up with could help the experts on here. But perhaps some of the people on here have even less experience than I do, so for what it's worth, here's a thought about insurance....

I think that basic strategy pretty universally regards taking insurance as a negative expectancy bet. But the casino I play at pays off a blackjack at 2:1 for tournaments. This anomaly suggests that taking insurance if you have a natural be re-examined under this specific scenario.

For instance, assume you bet 200 and are dealt a natural...and the dealer shows an ace. If you buy 100 of insurance, and the dealer does not have a blackjack, you lose 100 and are paid 400, for a net gain of 300. If the dealer does have a blackjack, you are paid 200 on the insurance and push on your bet, for a net gain of 200. The chances of the dealer having a blackjack after showing an ace are 4/13, or 30.7% So about 70% of the time you'll make 300, and about 30% of the time you'll make 200; your average payout will equal about 270 if you take insurance when the dealer shows an ace. (The chances of the dealer having a blackjack after showing a 10 card are 1/13, or 7.7%, so taking insurance will be a losing bet 92% of the time--I don't see how that could ever be worthwhile. Same story with insuring anything other than a natural--a win only pays 1:1, so that could never be worthwhile).

If you don't take insurance on a dealer ace in a BJ pays 2:1 scenario, then about 70% of the time you'll get paid 400 on your 200 bet, and about 30% of the time there will be a push and you get nothing; your average payout will equal about 280. So at 280 versus 270, taking insurance against an ace if you have a natural still seems like a negative expectancy bet, albeit much less than if naturals were paid at the standard 3:2 rate.

Here's why I think it may nevertheless make sense to take the insurance on a natural against an ace in a BJ pays 2:1 scenario: although the payoffs favor not buying insurance by a small amount on average, it is a certainty that you will win either 200 or 300 if you buy the insurance, whereas if you don't buy insurance, 30% of the time you will win nothing on your hand. I think the great majority of the time (but not always), we would prefer to win our bet (or more likely 150% of our bet) versus a 70% chance of doubling our bet, but a 30% chance of pushing with the dealer.

OK, that's my thinking about a very small corner of the field. If I've made a mistake (always a significant possibility given my lack of facility with numbers), please correct it so that I don't lead anyone astray.

Thanks--Acercher
 
I don't know of a place that offers insurance with a dealer ten showing, but for the case of a dealer Ace, your approximated math checks out. The correct decision is clearly to never take insurance at 2:1 if your goal is to maximize EV (unless you know something -- e.g. you are counting and know the correct index for 2:1 insurance for your count). But you are correct that there other considerations.

In tournament play, the decision of whether to take insurance is, like all other playing decisions, usually a strategic one. It all depends on what your goal is for that hand and whether taking insurance increases the probability of achieving that goal. For that reason, you will see that the decision is usually offered in order to each player, beginning with the puck. In the early hands of a round, with small bets out, that goal may very well be to maximize the EV of your hand. Later in the round, our bet sizes are more likely to be for a specific purpose. If the guaranteed payout of the 2:1 insurance meets your goal, then you would be wise to take it for guaranteed success. Taking insurance, or not, may also be a correlation play, where mimicking the decision of a player to your right has value. The bottom line is that, like any other playing decision, you should take insurance if it improves the probability that you will achieve your goal for the hand.

As another tid-bit -- like doubling for less, taking insurance for less can sometimes be the best play.
 
Tournament play aside, if you are playing 2:1 BJ (e.g. as a promotion) you should never take even money but take insurance for the reasons you outlined. Nevertheless, the index for taking insurance is not affected by 2:1 BJ promotion. The insurance bet is an independent side bet on the dealer's hand and has nothing to do with the pay on your own hand.
 
Thanks for the input. Sorry for referencing insurance offer with 10 showing--ugh! I do like the idea of insurance for less; I can definitely see how that might be a better bet than full insurance depending on the bankrolls of your competitors.
 
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