Double Exposure simulator?
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BLACKJACK SWITCH -rules,edge,strategy *PIC*
BLACKJACK SWITCH
By Michael Shackleford
Michael Shackleford is known to the gambling world as the "Wizard of Odds." His book, Gambling 102, is scheduled to be published this summer. In the meantime you can visit his popular web site at www.wizardofodds.com.
One way to win at blackjack is to play two hands and try to change two bad hands into two good ones by surreptitiously switching the cards. That's not allowed; it's cheating. Unless, that is, you're playing a new game at the Four Queens called Blackjack Switch, in which case you can switch cards right out in the open. In this game, the player must play two hands and may switch only the second cards dealt to each hand. Of course, nothing ever comes for free. In exchange for being allowed to switch cards, blackjacks pay even money and if the dealer gets a total of 22, all non-busted player hands push (a player bust always loses). Following optimal strategy, the house edge is a low 0.2%.
The complete switching strategy is very lengthy, but fortunately, most of the important switches are obvious (see www.wizardofodds.com for the complete switching strategy). Less obvious is the amended basic strategy that you should play, which requires many changes from conventional basic strategy-primarily more hitting and less doubling and splitting.
Presently Blackjack Switch is offered at the Four Queens in Las Vegas (although additional casinos in Las Vegas are considering installing Blackjack Switch) and at Internet casinos powered by Playtech software
Playtech Rules
The following rules apply to the Playtech version.
All rules are based on conventional blackjack unless otherwise noted.
The player must make two bets of equal size.
Cards will be dealt face up.
The player may switch the 2nd card dealt to each hand. For example if one hand has 5,10 and the other has 10,6 the player may switch the 10 and 6 to have two hands of 11 and 20.
Six decks are used.
Dealer hits a soft 17.
Player may double on any 2 cards.
Player may double after a split.
Player may not resplit.
Winning player blackjacks pay even money.
Full European no-peek rule. Player loses total amount bet against a dealer blackjack. A benefit of this rule is that the player can switch to a blackjack, even if the dealer has a blackjack.
A dealer total of 22 will push against any player total of 21 or less. A player blackjack will still beat a dealer 22.
Four Queens Rules
The Four Queens offers the same rules as Playtech with these changes:
Dealer peeks for blackjack and will turn over a blackjack immediately. Unlike conventional blackjack peeking for blackjack favors the casino by 0.11% because the player does not have the chance to switch to a blackjack if the dealer has one.
Eight decks instead of six.
Player can resplit to four hands instead of two.
The following table shows the basic strategy under Playtech rules after the switch decision has been made. The reason for the differences compared to conventional blackjack strategy is the push on 22 rule. This table is based on the 6-deck Playtech rules and was developed by Bill Kirkpatrick. The Four Queens strategy is the same except the player should split aces against an ace.
S = stand
H = Hit
D=Double if allowed, otherwise hit (except stand on soft 18)
P=Split
Ignoring the above changes and playing regular basic strategy increases the house edge by about 0.22%.
At Internet casinos powered by Playtech software, the dealer does not peek for blackjack, which works in the player's favor, because you can switch to a blackjack all the time. At the Four Queens, if the dealer has a blackjack, the player is stuck with what he was dealt.
Following optimal strategy, the house edge at Playtech casinos is just 0.05%, and Playtech offers 0.1% cashback and bonuses for new players.
BLACKJACK SWITCH
By Michael Shackleford
Michael Shackleford is known to the gambling world as the "Wizard of Odds." His book, Gambling 102, is scheduled to be published this summer. In the meantime you can visit his popular web site at www.wizardofodds.com.
One way to win at blackjack is to play two hands and try to change two bad hands into two good ones by surreptitiously switching the cards. That's not allowed; it's cheating. Unless, that is, you're playing a new game at the Four Queens called Blackjack Switch, in which case you can switch cards right out in the open. In this game, the player must play two hands and may switch only the second cards dealt to each hand. Of course, nothing ever comes for free. In exchange for being allowed to switch cards, blackjacks pay even money and if the dealer gets a total of 22, all non-busted player hands push (a player bust always loses). Following optimal strategy, the house edge is a low 0.2%.
The complete switching strategy is very lengthy, but fortunately, most of the important switches are obvious (see www.wizardofodds.com for the complete switching strategy). Less obvious is the amended basic strategy that you should play, which requires many changes from conventional basic strategy-primarily more hitting and less doubling and splitting.
Presently Blackjack Switch is offered at the Four Queens in Las Vegas (although additional casinos in Las Vegas are considering installing Blackjack Switch) and at Internet casinos powered by Playtech software
Playtech Rules
The following rules apply to the Playtech version.
All rules are based on conventional blackjack unless otherwise noted.
The player must make two bets of equal size.
Cards will be dealt face up.
The player may switch the 2nd card dealt to each hand. For example if one hand has 5,10 and the other has 10,6 the player may switch the 10 and 6 to have two hands of 11 and 20.
Six decks are used.
Dealer hits a soft 17.
Player may double on any 2 cards.
Player may double after a split.
Player may not resplit.
Winning player blackjacks pay even money.
Full European no-peek rule. Player loses total amount bet against a dealer blackjack. A benefit of this rule is that the player can switch to a blackjack, even if the dealer has a blackjack.
A dealer total of 22 will push against any player total of 21 or less. A player blackjack will still beat a dealer 22.
Four Queens Rules
The Four Queens offers the same rules as Playtech with these changes:
Dealer peeks for blackjack and will turn over a blackjack immediately. Unlike conventional blackjack peeking for blackjack favors the casino by 0.11% because the player does not have the chance to switch to a blackjack if the dealer has one.
Eight decks instead of six.
Player can resplit to four hands instead of two.
The following table shows the basic strategy under Playtech rules after the switch decision has been made. The reason for the differences compared to conventional blackjack strategy is the push on 22 rule. This table is based on the 6-deck Playtech rules and was developed by Bill Kirkpatrick. The Four Queens strategy is the same except the player should split aces against an ace.
S = stand
H = Hit
D=Double if allowed, otherwise hit (except stand on soft 18)
P=Split
Ignoring the above changes and playing regular basic strategy increases the house edge by about 0.22%.
At Internet casinos powered by Playtech software, the dealer does not peek for blackjack, which works in the player's favor, because you can switch to a blackjack all the time. At the Four Queens, if the dealer has a blackjack, the player is stuck with what he was dealt.
Following optimal strategy, the house edge at Playtech casinos is just 0.05%, and Playtech offers 0.1% cashback and bonuses for new players.
Do you buy that basic strategy for BJS?
I see it is different from standard BJ BS, drawing on 14 vs. 2, etc., and I understand that the reasoning is to compensate for the push-on-dealer-22 rule. But I don't see how that would work- if the dealer is going to get a 22 you push and there is nothing you can do about it, and it won't help to bust more stiffs. Mayor, any opinion on this?
I see it is different from standard BJ BS, drawing on 14 vs. 2, etc., and I understand that the reasoning is to compensate for the push-on-dealer-22 rule. But I don't see how that would work- if the dealer is going to get a 22 you push and there is nothing you can do about it, and it won't help to bust more stiffs. Mayor, any opinion on this?
14 vs 2
AM,
The reason for standing on 14 verses a dealer 2, in regular BJ, is that you are better off going for a dealer 'Bust' rather than taking the chance of improving your hand.
With BJ Switch you do not get the full payback as you do not get paid on a dealer 22. This slight change means that you are actually better off trying to improve with a 14 rather than standing and hoping for a 'Bust'.
Incidentally, 14 vs 2 is a very marginal decision (bit like 16 vs 10 in regular).
Best regards
Geoff
AM,
The reason for standing on 14 verses a dealer 2, in regular BJ, is that you are better off going for a dealer 'Bust' rather than taking the chance of improving your hand.
With BJ Switch you do not get the full payback as you do not get paid on a dealer 22. This slight change means that you are actually better off trying to improve with a 14 rather than standing and hoping for a 'Bust'.
Incidentally, 14 vs 2 is a very marginal decision (bit like 16 vs 10 in regular).
Best regards
Geoff
My opinion on BJSwitch's vulnerability
>Mayor, any opinion on this?
A bit of math first. You are playing two hands. Each hand must be considered an "ordered" pair, since you can only switch the top cards. Therefore there are 10x10 = 100 possible first hands. To have a potential for a switch, the top cards cannot match, so a switch will be considered if the second hand has any differnt first card from the other pair (9 choices) and a different top card (9 choices). That gives 9x9 = 81 second hands, for a total of 100x81 = 8,100 switchable situations. By symmetry, (reverse left and right hands), there are only 4,050 actual different starting positions. Any of these faces one of ten dealer up cards. This makes 4,050 x 10 = 40,500 starting configurations. My math may not be quite right, it is early in the day, but you get the idea.
Yes, this game is vulnerable, but the basic strategy for which cards to switch in each of the possible 40,500 initial situations is enormous (and getting count based indices for switching is even more daunting). Mostly it is played from an 8 deck shoe, so finding a game with decent penetration may also be problematic. A computer (or someone who was willing to devote A LOT of time) could easily beat this game. For the rest of us, there are so many more lucartive opportunities, I think Geoff has, by the sheer complexity of the games BS, made the game off limits to the AP community.
Of course if you learn a simplified basic strategy and basic switching strategy, and spread heavily, and the game is deeply dealt, I am certain you have the edge. I'll leave it to Geoff to tell us how much of an edge and which strategy!
Good work Geoff!
--Mayor
>Mayor, any opinion on this?
A bit of math first. You are playing two hands. Each hand must be considered an "ordered" pair, since you can only switch the top cards. Therefore there are 10x10 = 100 possible first hands. To have a potential for a switch, the top cards cannot match, so a switch will be considered if the second hand has any differnt first card from the other pair (9 choices) and a different top card (9 choices). That gives 9x9 = 81 second hands, for a total of 100x81 = 8,100 switchable situations. By symmetry, (reverse left and right hands), there are only 4,050 actual different starting positions. Any of these faces one of ten dealer up cards. This makes 4,050 x 10 = 40,500 starting configurations. My math may not be quite right, it is early in the day, but you get the idea.
Yes, this game is vulnerable, but the basic strategy for which cards to switch in each of the possible 40,500 initial situations is enormous (and getting count based indices for switching is even more daunting). Mostly it is played from an 8 deck shoe, so finding a game with decent penetration may also be problematic. A computer (or someone who was willing to devote A LOT of time) could easily beat this game. For the rest of us, there are so many more lucartive opportunities, I think Geoff has, by the sheer complexity of the games BS, made the game off limits to the AP community.
Of course if you learn a simplified basic strategy and basic switching strategy, and spread heavily, and the game is deeply dealt, I am certain you have the edge. I'll leave it to Geoff to tell us how much of an edge and which strategy!
Good work Geoff!
--Mayor
BJ Switch - Vulnerable ?
Thank's for your reply Mayor - nice to know that BJ Switch is a very challenging game even for the experts
I think that there are 10,350 'switching' decisions and roughly 80% of these are either obvious or are able to be performed by reasonably competent players. The other 2,000 are tricky and quite a few of them contain 'switches' involving an Ace. However, the really nasty decisions generally have a low penalty ev for making the incorrect decision.
Remembering back I think that 8,8 & 2,6 verses a dealer 6 is one of the very tricky decisions which players will play either way.
I have also seen that Arnold Snyder's new book has a chapter devoted on 'Blackjack Switch' and I will be interested to read that as he has performed the analysis using his own methods.
As far as the Basic Strategy for 'switching' goes then you can apply some 'rule of thumb' generalisations. I also produced a 'cheat sheet' which seemed to cover a lot of the possible 'switches'. I don't want to produce it here as it wouldn't give the experts anything to do
I have run a few counting simulations and haven't found a count system, as yet, that works particularly well with BJ Switch. It goes without saying that the game can be beaten with card counting as it is 95% regular Blackjack.
So what about 'switching' errors ?
I have run simulations using different standards of 'switching' ability - Computer (perfect), expert, good, average & mediocre.
On the plus side I found that mediocre players would not get too burnt by incorrect 'switches'. A relatively poor player would expect to lose about 0.7% in ev from 'switches' which is a lot less than they will lose by applying incorrect Basic Strategy, even in the regular game.
On the other hand, an 'expert' will expect to lose 0.1% - 0.3% (depending on how good). At a starting edge of 0.2% this means that an expert will start at around 0.3%-0.5%, which I think is acceptable in today's multi-deck game. If a player uses regular Basic Strategy then this will hurt him by 0.23%.
The problem with the edge is that a lot of casino managers are scared off by the relatively low edge and don't realise that 'switch' errors add considerably to the house edge. I even had one manager who told me, after watching the game for 3 months, that this was the only game that had a player edge. This came from someone with 30 years in the casino industry (and the game was holding slightly higher than their regular game at the time). When the game is running well for the players it is difficult to see how the 'push 22' can compensate for the 'switch'.
Casino Royale now have 6 Blackjack Switch tables and you cannot play regular multi-deck Blackjac there anymore. Casinos do not install games like this unless the bottom line is achieving acceptable targets. However, one thing I have noticed, is that the hold% has dropped since it's initial appearance last year and that managers have told me that players are returning to the game and seem to be wiser to the 'switch' decisions. (I blame these helpful Blackjack forums ).
The game was removed from Harrahs because they did not win at the game despite taking more than expected on the game. I still don't know why they didn't hold as well as they should have although I suspect dealer error formed a large part of the negative deviation. As a result 'Strip' properties are more reluctant to house the game due to the apparently unattractive house edge and the failure to be profit-making at Harrahs. The removal from Harrahs cost me a lot of installation in Las Vegas.
However, there is a new version approved in Nevada and this version is likely to be installed into the major 'Strip' properties. I've had to bow to pressure and although I want as fair a game as possible I also want to see Blackjack Switch in as many locations as I can get. The newer version will have 'switched Blackjacks' = 21 (not 'Blackjack') - this means that they will push against a dealer 21 & 22. I'll leave it to you to see what effect this has on the house edge. Needless to say it adds a substantial amount to the starting ev (although is acceptable for 'Hit S17' versions).
As far as expansion of the game.
I have 2 large casinos, towards the East coast, that wish to install the game and numerous casino in Washington that want the game (problem there is getting the approval due to their 7-box rule).
Without saying too much I would expect the game to expand very quickly before the end of the year. I'll post something as soon as anything concrete has been formed.
If you get this far in the message then 'thankyou' for spending the time reading this post and I hope that you get the chance to try out the game sometime.
Best regards
Geoff
Thank's for your reply Mayor - nice to know that BJ Switch is a very challenging game even for the experts
I think that there are 10,350 'switching' decisions and roughly 80% of these are either obvious or are able to be performed by reasonably competent players. The other 2,000 are tricky and quite a few of them contain 'switches' involving an Ace. However, the really nasty decisions generally have a low penalty ev for making the incorrect decision.
Remembering back I think that 8,8 & 2,6 verses a dealer 6 is one of the very tricky decisions which players will play either way.
I have also seen that Arnold Snyder's new book has a chapter devoted on 'Blackjack Switch' and I will be interested to read that as he has performed the analysis using his own methods.
As far as the Basic Strategy for 'switching' goes then you can apply some 'rule of thumb' generalisations. I also produced a 'cheat sheet' which seemed to cover a lot of the possible 'switches'. I don't want to produce it here as it wouldn't give the experts anything to do
I have run a few counting simulations and haven't found a count system, as yet, that works particularly well with BJ Switch. It goes without saying that the game can be beaten with card counting as it is 95% regular Blackjack.
So what about 'switching' errors ?
I have run simulations using different standards of 'switching' ability - Computer (perfect), expert, good, average & mediocre.
On the plus side I found that mediocre players would not get too burnt by incorrect 'switches'. A relatively poor player would expect to lose about 0.7% in ev from 'switches' which is a lot less than they will lose by applying incorrect Basic Strategy, even in the regular game.
On the other hand, an 'expert' will expect to lose 0.1% - 0.3% (depending on how good). At a starting edge of 0.2% this means that an expert will start at around 0.3%-0.5%, which I think is acceptable in today's multi-deck game. If a player uses regular Basic Strategy then this will hurt him by 0.23%.
The problem with the edge is that a lot of casino managers are scared off by the relatively low edge and don't realise that 'switch' errors add considerably to the house edge. I even had one manager who told me, after watching the game for 3 months, that this was the only game that had a player edge. This came from someone with 30 years in the casino industry (and the game was holding slightly higher than their regular game at the time). When the game is running well for the players it is difficult to see how the 'push 22' can compensate for the 'switch'.
Casino Royale now have 6 Blackjack Switch tables and you cannot play regular multi-deck Blackjac there anymore. Casinos do not install games like this unless the bottom line is achieving acceptable targets. However, one thing I have noticed, is that the hold% has dropped since it's initial appearance last year and that managers have told me that players are returning to the game and seem to be wiser to the 'switch' decisions. (I blame these helpful Blackjack forums
).The game was removed from Harrahs because they did not win at the game despite taking more than expected on the game. I still don't know why they didn't hold as well as they should have although I suspect dealer error formed a large part of the negative deviation. As a result 'Strip' properties are more reluctant to house the game due to the apparently unattractive house edge and the failure to be profit-making at Harrahs. The removal from Harrahs cost me a lot of installation in Las Vegas.
However, there is a new version approved in Nevada and this version is likely to be installed into the major 'Strip' properties. I've had to bow to pressure and although I want as fair a game as possible I also want to see Blackjack Switch in as many locations as I can get. The newer version will have 'switched Blackjacks' = 21 (not 'Blackjack') - this means that they will push against a dealer 21 & 22. I'll leave it to you to see what effect this has on the house edge. Needless to say it adds a substantial amount to the starting ev (although is acceptable for 'Hit S17' versions).
As far as expansion of the game.
I have 2 large casinos, towards the East coast, that wish to install the game and numerous casino in Washington that want the game (problem there is getting the approval due to their 7-box rule).
Without saying too much I would expect the game to expand very quickly before the end of the year. I'll post something as soon as anything concrete has been formed.
If you get this far in the message then 'thankyou' for spending the time reading this post and I hope that you get the chance to try out the game sometime.
Best regards
Geoff
Thanks for the update!
You said:
>If you get this far in the message then 'thankyou' for spending the time reading this post and I hope that you get the chance to try out the game sometime.
It is very rare for a game developer to be this candid, about the game, its vulnerabilities, its successes (Casino Royale) and failures (Harrahs). It is not at all unexpected about the BJ -> 21 variation -- that sort of thing is happening all over, but it does take a big chunk of the thrill out of the game. There are much easier fixes to add house edge that don't hurt the game's excitement (e.g. restrict doubling to hard hands, or nDAS).
As for the number of starting configurations being (approx) 10,000, I would be interested in how you arrived at that, if it's not too much trouble. We are talking about the two player's hands vs. the dealer's up card -- that's 5 cards in play (not just the 4 player's cards).
Thanks,
--Mayor
You said:
>If you get this far in the message then 'thankyou' for spending the time reading this post and I hope that you get the chance to try out the game sometime.
It is very rare for a game developer to be this candid, about the game, its vulnerabilities, its successes (Casino Royale) and failures (Harrahs). It is not at all unexpected about the BJ -> 21 variation -- that sort of thing is happening all over, but it does take a big chunk of the thrill out of the game. There are much easier fixes to add house edge that don't hurt the game's excitement (e.g. restrict doubling to hard hands, or nDAS).
As for the number of starting configurations being (approx) 10,000, I would be interested in how you arrived at that, if it's not too much trouble. We are talking about the two player's hands vs. the dealer's up card -- that's 5 cards in play (not just the 4 player's cards).
Thanks,
--Mayor
Number of Switches
Mayor : "As for the number of starting configurations being (approx) 10,000, I would be interested in how you arrived at that, if it's not too much trouble."
I am having difficulty coming up with the 10,350 figure, I keep getting 10,250 which I suppose is near to it although I am overlooking something. Karel Janecek did the original calculations and I have emailed him but have not received a reply as yet.
I think that it's too early in the morning for me now (6am) Getting ready for my flight to Las Vegas tomorrow - I hate that 9 hours on the 'plane.
My calculations are based on a player receiving 2 hands a/b & c/d ('a' and 'c' being the top, or second, cards) which are 'switchable' provided 'a' does not match 'c' or 'b' does not match 'd'.
So, number of ways the 4 cards can be dealt out is :-
No. of ways 'a' = 10 X no. of ways 'b' = 10 X no. of ways 'c' = 9 X no. of ways 'd' = 9 = 8,100.
However, there are various combinations of a/b & c/d which give identical 'switches :-
a/b & c/d = b/a & d/c = c/d & a/b = d/c & b/a = a/d & c/b = d/a & b/c
= b/c & d/a = c/b & a/d
So, there are 8 combinations.
8,100/8 = 1,012.5 (this is where I am overlooking something)
There are 10 possible dealer upcards so :-
1,012.5 X 10 = 10,125 individual 'switches'.
Hope this helps and doesn't confuse the issue further. If anything it may help you to calculate the figure and spot my (deliberate ) error.
Best regards
Geoff
Mayor : "As for the number of starting configurations being (approx) 10,000, I would be interested in how you arrived at that, if it's not too much trouble."
I am having difficulty coming up with the 10,350 figure, I keep getting 10,250 which I suppose is near to it although I am overlooking something. Karel Janecek did the original calculations and I have emailed him but have not received a reply as yet.
I think that it's too early in the morning for me now
(6am) Getting ready for my flight to Las Vegas tomorrow - I hate that 9 hours on the 'plane.My calculations are based on a player receiving 2 hands a/b & c/d ('a' and 'c' being the top, or second, cards) which are 'switchable' provided 'a' does not match 'c' or 'b' does not match 'd'.
So, number of ways the 4 cards can be dealt out is :-
No. of ways 'a' = 10 X no. of ways 'b' = 10 X no. of ways 'c' = 9 X no. of ways 'd' = 9 = 8,100.
However, there are various combinations of a/b & c/d which give identical 'switches :-
a/b & c/d = b/a & d/c = c/d & a/b = d/c & b/a = a/d & c/b = d/a & b/c
= b/c & d/a = c/b & a/d
So, there are 8 combinations.
8,100/8 = 1,012.5 (this is where I am overlooking something)
There are 10 possible dealer upcards so :-
1,012.5 X 10 = 10,125 individual 'switches'.
Hope this helps and doesn't confuse the issue further. If anything it may help you to calculate the figure and spot my (deliberate
) error.Best regards
Geoff
Interaction
"Geoff has enjoyed interaction with APs since he first formulated this game." zg
Hi Zen,
Yes, you are correct that I enjoy and admire players who use their intellectual ability to take advantage of a situation.
Probably the main reason though is that I used to be an AP too and travelled the UK earning good money, particularly when the 'over/under' was predominant here.
The game has probably suffered (installation wise) because I was insistent on providing a game that was fair to the players. I would think that the stubborness to fairness attitude comes from my days of being a player.
Best regards
Geoff
"Geoff has enjoyed interaction with APs since he first formulated this game." zg
Hi Zen,
Yes, you are correct that I enjoy and admire players who use their intellectual ability to take advantage of a situation.
Probably the main reason though is that I used to be an AP too and travelled the UK earning good money, particularly when the 'over/under' was predominant here.
The game has probably suffered (installation wise) because I was insistent on providing a game that was fair to the players. I would think that the stubborness to fairness attitude comes from my days of being a player.
Best regards
Geoff
Thanks!
I only accounted for one symmetry (a/b & c/d = c/d & a/b), that pretty much answers my question.
>a/b & c/d = b/a & d/c = c/d & a/b = d/c & b/a = a/d & c/b = d/a & b/c
= b/c & d/a = c/b & a/d
Note that if both of the hands is paired (e.g. 8,8 vs. T,T) then you don't get all 8 symmetries, you only get 4 symmetries.
8,8 vs. T,T
T,T vs. 8,8
T,8 vs. 8,T
8,T vs. T,8
There are 10 choices for the first pair, and 9 choices for the second pair. THis gives 90 possible pair/pair hands with 4 symmetries.
Thus, out of the 8,100 you have:
(8010/8) + (90/4) = 1012.5 + 22.5 = 1035 possibilities. Against 10 dealer up cards, this gives 10,350 possible switches.
But, I'm glad it created a question for you!
--Mayor
I only accounted for one symmetry (a/b & c/d = c/d & a/b), that pretty much answers my question.
>a/b & c/d = b/a & d/c = c/d & a/b = d/c & b/a = a/d & c/b = d/a & b/c
= b/c & d/a = c/b & a/d
Note that if both of the hands is paired (e.g. 8,8 vs. T,T) then you don't get all 8 symmetries, you only get 4 symmetries.
8,8 vs. T,T
T,T vs. 8,8
T,8 vs. 8,T
8,T vs. T,8
There are 10 choices for the first pair, and 9 choices for the second pair. THis gives 90 possible pair/pair hands with 4 symmetries.
Thus, out of the 8,100 you have:
(8010/8) + (90/4) = 1012.5 + 22.5 = 1035 possibilities. Against 10 dealer up cards, this gives 10,350 possible switches.
But, I'm glad it created a question for you!
--Mayor