encountered new bj rule

[DSchles]

Found a game that pays 5-1 on the insurance bet on condition of dealer having a suited blackjack. Care to take a stab at the EV? I expect it to be tiny.

So far, no answer you have received seems correct to me. I can answer once you specify number of decks and whether it is a standard 52-card pack.

Don

[Meistro123]

Assuming six deck game


probability of suited blackjack = 24 / 311 or 7.71%


returns 6 units 7.71% of the time for a total return of .4626


probability of non suited blackjack
72/311 or 23.15%
3 units 23.15% of the time

returns .6945
in total insurance returns 1.1571 off the top so 15.7% edge and going up rapidly

[DSchles]

Assuming six deck game


probability of suited blackjack = 24 / 311 or 7.71%


returns 6 units 7.71% of the time for a total return of .4626


probability of non suited blackjack
72/311 or 23.15%
3 units 23.15% of the time

returns .6945
in total insurance returns 1.1571 off the top so 15.7% edge and going up rapidly

Hmm. Perhaps you'd like to subtract the times the insurance bets loses? Then, perhaps you'd like to factor in the probability that the dealer ever shows an ace in the first place? Finally, consider that the insurance wager is HALF of an original wager. Hmm.

Don

[Jabberwocky]

[quot

[SpikeBJ]

Sounds like rain in DonS forecast.

[DSchles]

In a six-deck game, I make this worth 0.606%. If anyone would like to see the math, let me know.


Don

[Jabberwocky]

With all the ten spots, I presume.

[Banker]

In a six-deck game, I make this worth 0.606%. If anyone would like to see the math, let me know.

Don

Thanks Don
I would like to see the math, for learning purposes.

[DSchles]

Thanks Don
I would like to see the math, for learning purposes.

It's sometimes easier to just find a least common multiple that makes all the numbers even. So, suppose you play 4,043 hands, betting $2 on each hand. The total outlay in dollars is $8,086. The dealer will show an ace 4,043/13 = 311 times. Well, that's how many cards are left for his hole card, so he has a suited ten 24 times, a non-suited ten 72 times and a non-ten the remaining 215 times. Our total outlay for insurance, which is only half a bet each time, is $1 x 311 = $311. We pick up $3 72 times, for $216, and we pick up $6 24 times for another $144, for a grand total of $360. But our outlay for insurance was $311, so we have profited to the tune of $49. Since the total original bets were $8,086, in order to make $49, the edge is 49/8,086 = 0.606%.

Don

[ZenMaster_Flash]

Thanx muchly D.S., for an elegantly uncomplicated solution!

Simplicity reigns supreme .

[Banker]

Don
Thanks for taking the time to explain this. Much appreciated.

[Bubbles]

Thank you Don :-) you rock.

Sent from my SM-G955U using Tapatalk

[Dog Hand]

It's sometimes easier to just find a least common multiple that makes all the numbers even. So, suppose you play 4,043 hands, betting $2 on each hand. The total outlay in dollars is $8,086. The dealer will show an ace 4,043/13 = 311 times. Well, that's how many cards are left for his hole card, so he has a suited ten 24 times, a non-suited ten 72 times and a non-ten the remaining 215 times. Our total outlay for insurance, which is only half a bet each time, is $1 x 311 = $311. We pick up $3 72 times, for $216, and we pick up $6 24 times for another $144, for a grand total of $360. But our outlay for insurance was $311, so we have profited to the tune of $49. Since the total original bets were $8,086, in order to make $49, the edge is 49/8,086 = 0.606%.

Don

As others have indicated in this thread, one-fourth of the dealer's BJ's will be suited, so three-fourths will be unsuited. Therefore, the average payout on a successful insurance wager will be 2x¾ + 5x¼ = 11/4. Therefore, the break-even X density is 4/(4+11) = 4/15 = 0.266666...

If we consult an earlier post of mine:

https://www.blackjacktheforum.com/sh...ht=dealer+bust

we can see from the "Up Rate" graph that the X density falls to about 4/15 at about -5 (for a 6D game).

This means that the insurance wager in this thread is +EV for all TC's of -5 and up for a 6D game.

Hope this helps!

Dog Hand