Late Insurance bonus in blackjack
In video blackjack all software providers that I am aware of dealt crudely with the insurance: they offer it after three cards are dealt in total (dealer's Ace and two player's cards). In a Single Deck game that's 1/49 = 2.04% house edge and since nothing else is possible that's the end of the story. If player draws a fourth card (his third) that offer is not repeated.
It's trivial to see that things are getting interestning only AFTER that premature offer. With player's 3 cards from A to 9, insurance reaches break-even (is equivalent to 2:1 fair bet) and quickly increases with each new card - 1/47 = 2.13% for (his) 4 cards, 2/46 = 4.35% for (his) 5 cards, 3/45 = 6.67% for (his) six cards and so on. This is a hidden bonus begging to be claimed, sitting on top of composition-based exceptions! The less frequent the better. What's not to like? From the player's perspective this "late insurance bonus" is optional from his third card and recommended from the fourth. That's the only choice and that's easy to implement in the settings. In the extremely unlikely case of player's 6-card with 10 value card the insurance reaches 100% RTP again, hence theoretically may be taken into account. In practice it's a waste of time and efforts. It's enough (and simpler) to calculate with three caveats:
1) for all 16 T-value cards left in the deck (no 10-value card is on the table)
2) for player's 4+ cards only (skip break-even cases with 4 cards on the table)
3) player always uses basic strategy with exceptions worth 0.04% (insurance is not offered if player deviates)
What is the value of this bonus?
In summary, I would say that automatic late insurance is far better as a bonus than automatic winner (Charlie) because it unlocks advantage that really exist, whereas Charlie is purely artificial rule - a crime against simplicity.
On a side note, insurance in AAA vs. A can be used as a gambling feature with 2:1 payout. Effectively free Buy 4 and 10 without push.
PS: In a refined variant, if player has 3 cards, late insurance is only offered if the expected value of the main bet is negative, eg. with 676 against dealer's Ace, but not 677. What is the value of that subset alone?
Quote: MattUKI may have accidentally invented a new type of bonus in Blackjack, strangely not seen anywhere. This bonus is especially fitting in Single Deck video blackjack and adds some small value to the basic strategy without any additional rules (like 678, 777, Blackjack pays 2:1 etc.). I started to think if it's enough to reach 100% RTP in Microgaming / Switch Studios Classic Blackjack. I made calculations using pen and paper, but not more than that and would like to confirm its value. Ideally by Wizard for a new article with the findings.
In video blackjack all software providers that I am aware of dealt crudely with the insurance: they offer it after three cards are dealt in total (dealer's Ace and two player's cards). In a Single Deck game that's 1/49 = 2.04% house edge and since nothing else is possible that's the end of the story. If player draws a fourth card (his third) that offer is not repeated.
It's trivial to see that things are getting interestning only AFTER that premature offer. With player's 3 cards from A to 9, insurance reaches break-even (is equivalent to 2:1 fair bet) and quickly increases with each new card - 1/47 = 2.13% for (his) 4 cards, 2/46 = 4.35% for (his) 5 cards, 3/45 = 6.67% for (his) six cards and so on. This is a hidden bonus begging to be claimed, sitting on top of composition-based exceptions! The less frequent the better. What's not to like? From the player's perspective this "late insurance bonus" is optional from his third card and recommended from the fourth. That's the only choice and that's easy to implement in the settings. In the extremely unlikely case of player's 6-card with 10 value card the insurance reaches 100% RTP again, hence theoretically may be taken into account. In practice it's a waste of time and efforts. It's enough (and simpler) to calculate with three caveats:
1) for all 16 T-value cards left in the deck (no 10-value card is on the table)
2) for player's 4+ cards only (skip break-even cases with 4 cards on the table)
3) player always uses basic strategy with exceptions worth 0.04% (insurance is not offered if player deviates)
What is the value of this bonus?
In summary, I would say that automatic late insurance is far better as a bonus than automatic winner (Charlie) because it unlocks advantage that really exist, whereas Charlie is purely artificial rule - a crime against simplicity.
On a side note, insurance in AAA vs. A can be used as a gambling feature with 2:1 payout. Effectively free Buy 4 and 10 without push.
PS: In a refined variant, if player has 3 cards, late insurance is only offered if the expected value of the main bet is negative, eg. with 676 against dealer's Ace, but not 677. What is the value of that subset alone?
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Have rule #3 that "player always uses basic strategy" is counter to the concept of the game of BJ and would be almost unworkable. A wager on a side-bet should not limit the way that the main game is played. Also, places a burden on dealer to know what the BS should always be.
> Also, places a burden on dealer to know what the BS should always be.
There is no dealer. We're talking video game here with a known BS.
