Eggroll: House advantage??

[Eggroll]

A local casino has the following game. 6 deck, Hit soft 17, DAS. Every time a player receives a blackjack consisting of Ace and King of Clubs you will receive a bonus which be the amount of your bet multiplied by the value of the next card out. Ten value cards receive 10 times and aces receive 20 times the bet. Is there any way of figuring the house advantage? Thanks for the help.

[Geoff Hall]

> A local casino has the following game. 6
> deck, Hit soft 17, DAS. Every time a player
> receives a blackjack consisting of Ace and
> King of Clubs you will receive a bonus which
> be the amount of your bet multiplied by the
> value of the next card out. Ten value cards
> receive 10 times and aces receive 20 times
> the bet. Is there any way of figuring the
> house advantage? Thanks for the help.

I'm assuming that the 'bonus' is paid on top of the 3/2 already received from the Blackjack ?

OK, the game, under normal conditions, would have a house edge of around 0.64%, so what difference does this bonus make ?

Firstly, there are 64 different 'Blackjacks', if you look at the denomination and suit. Therefore, Ace Clubs, King Clubs will appear once in every 64 Blackjacks that you get.

The bonus payouts range from 2/1 to 20/1, depending on the next card, and this will average out at :-

(2+3+4+5+6+7+8+9+10+10+10+10+20)/13 = 8/1

This is ignoring the very slight difference that an Ace or 10 is (very) slightly less likely to follow assuming that you have a Blackjack.

So, in every 64 Blackjacks you will get an 8/1 bonus, on average.

Therefore, overall, each Blackjack will be worth 8/64 = 1/8 extra unit to you.

So, instead of Blackjacks paying 3/2 you can say that Blackjacks pay 3/2 + 1/8 = 13/8.

If Blackjacks were to pay 2/1 (i.e. an extra 1/2 or 4/8) then this would add approximately 2.3% edge to the player.

So, 4/8 = + 2.3% therefore 1/8 extra = + 2.3% / 4

= approximately + 0.56%

So, if all the other rules are as in regular Blackjack, then the game would appear to have a casino edge of about 0.1%.

It's nice to see a casino promoting Blackjacks with a bonus instead of the more commonly found method of paying them at 6/5.

Best regards

Geoff

http://www.blackjackswitch.com

[Eggroll]

> I'm assuming that the 'bonus' is paid on top
> of the 3/2 already received from the
> Blackjack ?

> OK, the game, under normal conditions, would
> have a house edge of around 0.64%, so what
> difference does this bonus make ?

> Firstly, there are 64 different
> 'Blackjacks', if you look at the
> denomination and suit. Therefore, Ace Clubs,
> King Clubs will appear once in every 64
> Blackjacks that you get.

> The bonus payouts range from 2/1 to 20/1,
> depending on the next card, and this will
> average out at :-

> (2+3+4+5+6+7+8+9+10+10+10+10+20)/13 = 8/1

> This is ignoring the very slight difference
> that an Ace or 10 is (very) slightly less
> likely to follow assuming that you have a
> Blackjack.

> So, in every 64 Blackjacks you will get an
> 8/1 bonus, on average.

> Therefore, overall, each Blackjack will be
> worth 8/64 = 1/8 extra unit to you.

> So, instead of Blackjacks paying 3/2 you can
> say that Blackjacks pay 3/2 + 1/8 = 13/8.

> If Blackjacks were to pay 2/1 (i.e. an extra
> 1/2 or 4/8) then this would add
> approximately 2.3% edge to the player.

> So, 4/8 = + 2.3% therefore 1/8 extra = +
> 2.3% / 4

> = approximately + 0.56%

> So, if all the other rules are as in regular
> Blackjack, then the game would appear to
> have a casino edge of about 0.1%.

> It's nice to see a casino promoting
> Blackjacks with a bonus instead of the more
> commonly found method of paying them at 6/5.

> Best regards

> Geoff
Thanks for the info. I just found outthey are having the same bonus on their single and double deck games. Based on your info the player will have a slight advantanage especially in the single deck game. Thanks again!!

[mondo21]

> A local casino has the following game. 6
> deck, Hit soft 17, DAS. Every time a player
> receives a blackjack consisting of Ace and
> King of Clubs you will receive a bonus which
> be the amount of your bet multiplied by the
> value of the next card out. Ten value cards
> receive 10 times and aces receive 20 times
> the bet. Is there any way of figuring the
> house advantage? Thanks for the help.

Based on my calculation using the probability of an Ac Kc occuring, I estimate the value to the player to be +.07%. Therefore if the house advantage is .63 going in the house advantage with this promotion is .56. Hope this helps!

[mondo21]

> A local casino has the following game. 6
> deck, Hit soft 17, DAS. Every time a player
> receives a blackjack consisting of Ace and
> King of Clubs you will receive a bonus which
> be the amount of your bet multiplied by the
> value of the next card out. Ten value cards
> receive 10 times and aces receive 20 times
> the bet. Is there any way of figuring the
> house advantage? Thanks for the help.

Oops! After I posted, I realized I made a mistake on the value of the payout. The actual advantage to the player of the promotion is about .29% assuming:

1) You are playing "heads up" against the dealer.

2) You do not vary your bet.

The number of players and varying the amount bet change things a bit!

[Geoff Hall]

> Oops! After I posted, I realized I made a
> mistake on the value of the payout. The
> actual advantage to the player of the
> promotion is about .29% assuming:

This is roughly 1/2 of the value that I got - I think that you have miscalculated the value of the 'bonus Blackjack' by 50%.

The game will have a house edge of just under 0.1%, all other rules being the same.

Best regards

Geoff

http://www.blackjackswitch.com

[mondo21]

> This is roughly 1/2 of the value that I got
> - I think that you have miscalculated the
> value of the 'bonus Blackjack' by 50%.

> The game will have a house edge of just
> under 0.1%, all other rules being the same.

> Best regards

> Geoff

I factored into my calculation the fact that the dealer is just as likely to get the Ac, Kc (or Kc, Ac) blackjack as the player. When the dealer get this "bonus" blackjack the payout is zero, but that blackjack is removed from the future probability until reshuffle. I don't belive your calculation takes the "dealer" factor into account. Also, my analysis of this promotion was based soley on the calculated probability of the frequency of occurance of the bonus blackjack. I readily admit that my method of calculation was based soley on basic probability mathematics and not simulation. I think only running a SIM would give totally accurate results.

If you are interested in how I did the calculation just post the question and I will gladly give the gorey details!

Another factor one might want to consider in evaluating wheteher this promotion is playable is the fequency of actually getting this particular bonus blackjack. After all, the payout does not matter at all if the player never gets the hand!

I estimate that this hand will occur only once in about 1350 hands. So, to see this particular blackjack, a player is going to have to play 100 hands per hour for about 13.5 hours! Also, when this hand does occur the probability that the dealer will get it instead of the player is .5! I am assuming "heads up" play, hence the .5 probability.

I do not in any way fault your calculation, nor do I claim that I am right and you are wrong, but I do believe in my approach.

I have played advantage blackjack since 1974. I have analyzed many such promotional variations and have consulted many people on how such calculations should be done. In the 70's an average player, like me, did not have the ability to run SIMs. Therefore all of my analysis has always been based on probability and statistics. I quit playing in the mid 80's and have just started playing again recently.

I have never run a SIM and do not have the software to do one. I rely soley on logic and probability. I am just a "recreational" player and have no designs to ever be a pro. I do enjoy the game and I do definately play with an advantage. I am also very confident in my ability to analyze any promotional variation and the expected value to the player.

In regards to the "value" of geting this bonus blackjack, it is about 7.6 times the amount bet. I think you and I do agree, almost to the dollar, on that calculation.

Thanks,

mondo21

[Geoff Hall]

> I factored into my calculation the fact that
> the dealer is just as likely to get the Ac,
> Kc (or Kc, Ac) blackjack as the player. When
> the dealer get this "bonus"
> blackjack the payout is zero, but that
> blackjack is removed from the future
> probability until reshuffle. I don't belive
> your calculation takes the
> "dealer" factor into account.
> Also, my analysis of this promotion was
> based soley on the calculated probability of
> the frequency of occurance of the bonus
> blackjack. I readily admit that my method of
> calculation was based soley on basic
> probability mathematics and not simulation.
> I think only running a SIM would give
> totally accurate results.

> Thanks,

> mondo21

The dealer factor may be where the discrepancy comes in as both of us seem to agree with the mathematics i.e. number of times it will occur and the average payout.

My assumption was that if the player gets Ac,Kc then he will get the bonus, even if the dealer has a 'Blackjack', but he will 'push' his Blackjack bet.

If both the dealer and player get Ac, Kc then I assume that this may be an overall 'push' but the odds on this happening are very extreme and are unlikely to affect the overall EV by a significant amount.

I don't quite follow the reasoning about if the player gets Ac, Kc in roughly 1,350 hands (agree) then the dealer will also have a 0.5 chance of getting the Ac, Kc. Although this is true, the player does not have to pay a 'bonus' to the dealer so, for example, if, after 13,500 hands both the player and dealer have received 10 lots of Ac,Kc, then the player will have gained 10 lots of bonuses (unless the extreme event of them both getting it at the same time).

I totally agree with you that the frequency of the Ac, Kc turning up makes a difference. Taking your point further then imagine a casino that offers a 'bonus' on a player losing with four suited 5's to a dealer '21', made up of 3 suited 7's. Not sure what the odds are but, for the purpose of this exercise, imagine that the casino are paying out such a 'bonus' that it adds 1% to the player's overall EV.

Now the casino could quite rightly advertise the game at 0.5% player advantage. In fact, they could stop a rule like allowing players to 'split' and still claim that the game had an edge off the top for the player.

So, which game do you play ? The one without 'splits' that has this extreme 'bonus' and, therefore, a player edge of, say 0.1% or the table next to it that has splits but has a player edge of - 0.5% ?

I suppose the Ac, Kc is not that extreme, it just won't come up very often.

Finally, I felt intrigued enough to program the rules into a simulator. Unfortunately, SBA does not allow you to pay 8/1 on a 'bonus' Blackjack so, to get around this, I have incorporated a 'bonus' of 2/1 for ANY suited Blackjack i.e. AK, AQ, AJ & A 10 (so, 4 times as many but 1/4 the 'bonus' payout).

After 500 million hands (I'm not as patient as Norm with his 2 Billion hand simulations :-) ), SBA is coming out at a house edge of 0.073% St.Err 0.004%.

Maybe the difference we have in our results has come from the way that we have both interpreted the question and, in fact, we are both right.

I hope that this helps and I wish you every success on your recent reintroduction to the Blackjack world. Have you noticed a lot of changes from when you played back in the 70's ?

Best regards

Geoff

http://www.blackjackswitch.com

[Don Schlesinger]

Considering the dealer's getting the hand instead of the player shouldn't enter into the calculation, as you made your assumptions based solely on the player's hand. If we throw in the dealer's hand, we're getting two hands every round, instead of one, so, by symmetry, the odds don't change for simply considering the player's one hand and calculating the odds as you did.

In other words, your approach was correct, Geoff.

Don

[mondo21]

> Considering the dealer's getting the hand
> instead of the player shouldn't enter into
> the calculation, as you made your
> assumptions based solely on the player's
> hand. If we throw in the dealer's hand,
> we're getting two hands every round, instead
> of one, so, by symmetry, the odds don't
> change for simply considering the player's
> one hand and calculating the odds as you
> did.

Well of course you are correct! I can't believe I made such an elementry mistake. I haven't thought about this stuff in close to twenty years and I guess I'm a little rusty. In the past I was always content to let folks like you do the math. I guess now I rember why!!

[mondo21]

> I don't quite follow the reasoning about if
> the player gets Ac, Kc in roughly 1,350
> hands (agree) then the dealer will also have
> a 0.5 chance of getting the Ac, Kc. Although
> this is true, the player does not have to
> pay a 'bonus' to the dealer so, for example,
> if, after 13,500 hands both the player and
> dealer have received 10 lots of Ac,Kc, then
> the player will have gained 10 lots of
> bonuses (unless the extreme event of them
> both getting it at the same time).

You are correct, my first calculation is off by exactally 50%. My calculation should have resulted in +.58 rather than the +.29.

> I hope that this helps and I wish you every
> success on your recent reintroduction to the
> Blackjack world. Have you noticed a lot of
> changes from when you played back in the
> 70's ?

It is difficult for me to compare the mid 70's/80's to today because in those days I played in Las Vegas and I now play mostly in Mississippi. However, by the early 80's there was plenty of very negative heat in Las Vegas and I believe counters were even more despised by casino personnel than now.

Good Cards!

M.

[Geoff Hall]

> Well of course you are correct! I can't
> believe I made such an elementry mistake. I
> haven't thought about this stuff in close to
> twenty years and I guess I'm a little rusty.
> In the past I was always content to let
> folks like you do the math. I guess now I
> rember why!!

I was beginning to think that I had misinterpreted the original question in some way. It was only after the 'seal of approval' from Don that I started to feel more comfortable about my analysis.

Anyway, you were actively aiming to help a player who had a question about a particular set of rules, which is an honorable cause. Anyone can make a mistake ( as the Dalek said climbing off the garbage/trash can :-) ). I hope that your contribution to this thread has, at least, benifitted you by oiling some of the rust spots over the last 20 years.

It's the old adage - if you don't make any mistakes then you are not doing anything :-)

Best regards

Geoff

http://www.blackjackswitch.com