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Thread: Spanish 21 EV?

  1. #66


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    If we agree on this ...
    Quote Originally Posted by All Clear View Post
    I fully agree that the best way to work out this problem is, as you wrote, using the "value" of the coupon as the amount of additional live money you can expect to have in your pocket after the process of using the coupon has been resolved
    then you cannot believe these ...
    Quote Originally Posted by All Clear View Post
    YES. Absolutely. When I bet a match play, with a regular bet, I am betting 1.5 units, so when I win, I win 1.5 units.
    Quote Originally Posted by All Clear View Post
    YES. Absolutely. When I bet a match play, with a regular bet, I am betting 1.5 units, so when I lose, I lose 1.5 units.
    They are contradictory.
    Once it has been bet, the coupon no more than a reminder to the dealer that the payout structure of the game has been changed.
    Quote Originally Posted by All Clear View Post
    While I would expect that my surrender strategy (and my forfeit strategy, and the double-down strategy that I generated, but haven't posted in this thread) would be very VERY close to what your simulation shows, I look forward to your results.
    I think that you're in for a bit of a rude surprise. I tried applying your surrender model to blackjack and got nothing close to the strategy that Grosjean and I have both independently computed.
    Quote Originally Posted by All Clear View Post
    Thanks! :-)
    My pleasure.

  2. #67


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    Quote Originally Posted by ZenMaster_Flash View Post
    Who am I to speak up if I think that the redoubtable
    James Grosjean may have published an error?

    I am Iconoclastic, so ...

    On page #5 in "Beyond Coupons" (see link in post #4)
    it delineates a Craps "Pass Line" Bet returning significantly
    more to the holder of a Match Play coupon than a "Don't Pass"
    Bet.

    I M H O this is egregiously wrong. That is simply because the
    Pass Line House Edge is higher than the Don't Pass House Edge.
    Admittedly, the difference is small, approximately 0.02%.

    I really am looking for feedback on this.
    I did the math on this and I can confirm that Grosjean is correct. I also discovered why he went to 3 decimal places for the pass bet. Three was also correct that it makes a difference whether the coupon is saved on a push. For a $10 match play coupon:

    Pass: $4.7879
    Don't Pass (coupon relinquished on push): $4.6566
    Don't Pass (coupon saved on push): $4.7896

    I will make my spreadsheet available to anyone who asks. It works for any ratio of the coupon to the live money including zero for live money, which is what most people call a free bet but which Grosjean calls a "Funny Chip".

    Once again, the normal house edge is only one factor. It's all in the way the payout structure of the game changes. Variance is a big factor because the coupon only asserts itself when you lose. If you still need convincing, consider that a single number on roulette is the king of coupons, yet it has a horrible house edge and only wins 1 out of 37 or 38 times for 0 and 00 respectively.
    Last edited by Gronbog; 11-15-2017 at 02:40 PM.

  3. #68
    Senior Member Bubbles's Avatar
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    Thank you, Gronbog for such a thorough response. I learned something. I read the comp thing from Grosjean, but didn't understand how he came to those values. Thanks for taking the time to explain it.

    Sent from my SM-G955U using Tapatalk

  4. #69


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    I now have a match play strategy for S17 Spanish 21 but, while reviewing it, I realized that the implementation used for rescuing (surrendering) a double is the same as the one for normal surrender. i.e. keep only your original live money and relinquish the coupon. So the loss is 2 units plus relinquishing the coupon. This is probably not the right implementation since, in Spanish 21, when you rescue a double you keep the doubled amount and lose the previously bet amount.

    The correct implementation, and the one more likely to apply in a real game would be to keep the doubled amount (as usual), lose the original bet (2 units) and be rebated by the value of the coupon (1 unit) for a loss of only 1 unit.

    Because you can double on any number of cards in Spanish 21, the rescue strategy affects every other decision. Now Grosjean discusses several different implementations for normal surrender, some of which are very strange and unlikely. So if anyone would like to see the strategy I have now, I will make it available. Otherwise, my apologies, but it will be a few more days to generate the new strategy.

  5. #70


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    Quote Originally Posted by Gronbog View Post
    I now have a match play strategy for S17 Spanish 21 but, while reviewing it, I realized that the implementation used for rescuing (surrendering) a double is the same as the one for normal surrender. i.e. keep only your original live money and relinquish the coupon. So the loss is 2 units plus relinquishing the coupon. This is probably not the right implementation since, in Spanish 21, when you rescue a double you keep the doubled amount and lose the previously bet amount.

    The correct implementation, and the one more likely to apply in a real game would be to keep the doubled amount (as usual), lose the original bet (2 units) and be rebated by the value of the coupon (1 unit) for a loss of only 1 unit.
    The strategy I generated assumes that when rescuing on a double down (when using a match-play), instead of losing half your total bet, you lose 3/7 of your total bet, since (if betting $25 with a $25 match play) you would rescue (and keep) $50, while only losing to the casino $25 and a $25 match play (which, at 50% of face value, would be $12.50). My rescue strategy (generated with these assumptions, using EV tables) is identical to SP21 basic strategy, other than rescuing on an 11-16, with a dealer 7, which we should now rescue (but do not rescue if no match-play is involved with the bet).

    While I did not generate exceptions for multiple cards, the only two card doubles that are changed by the ability to double down for more, are soft 15 v 6, and soft 16 v 5. Without a match play, both are (barely) hit situations, but with the ability to double down for $50, when only betting an original $25 and a $25 match-play (in essence, doubling down for more, since the original bet is valued at $37.50, aprox), they both move to the "double" category.

    This works if we value a match-play at 50% of the amount you get if you win. This all gets more complicated, if a match-play is not valued at 50% of it's face value, which brings me to attempting to prove that point.....

    Quote Originally Posted by Gronbog View Post
    If we agree on this "I fully agree that the best way to work out this problem is, as you wrote, using the "value" of the coupon as the amount of additional live money you can expect to have in your pocket after the process of using the coupon has been resolved"

    then you cannot believe this "When I bet a match play, with a regular bet, I am betting 1.5 units, so when I win, I win 1.5 units."

    They are contradictory.
    Once it has been bet, the coupon no more than a reminder to the dealer that the payout structure of the game has been changed.
    False. Once it has been bet, the coupon is still worth $12.50 (again, I am using a $25 base-bet unit), or a number within a few cents of that. That is why if you win, you have a total of $75 in front of you. You win 1.5 units, and are going from the original 1.5 units of $37.50 (a green chip and a coupon) to three green chips, totaling $75. It is also why if you lose, you now have nothing from your bet- you lost 1.5 units. This jives well with the first statement- how the match-play coupon is worth the average amount you'll have in your pocket afterward, due to playing it. If you win half the time, and lose half the time, you'll have $25 extra half the time, and $0 half the time, for an average gain of the same $12.50. :-) I am aware that you don't win 50% of hands, but even if it is 44%, the approximation is acceptable for match-play problems, I figure. Note that in Grosjean's article, he approximates the value for the match-play in blackjack as a number relatively close to 50% of the base bet, as well.

    It could be I'm not explaining it well- I'm a math guy (I used to be a certified actuary, and now work as an engineer), and people have told me that I use numerical explanations that are not clear to all. In any case, you wrote that I am "in for a bit of a rude surprise", which I look forward to getting. If it makes me a better SP21 player, I'll take all the rude awakenings I can get. Thanks, Gronbog. :-)

  6. #71


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    Quote Originally Posted by All Clear View Post
    The strategy I generated assumes that when rescuing on a double down (when using a match-play), instead of losing half your total bet, you lose 3/7 of your total bet, since (if betting $25 with a $25 match play) you would rescue (and keep) $50, while only losing to the casino $25 and a $25 match play (which, at 50% of face value, would be $12.50).
    At least we can agree on the mechanical implementation of resucing a double with the coupon. I still disagree with your mathematical model of placing a fixed and (somewhat) arbitrary "value" on the coupon for the purpose of calculating it's actual value when surrendering or rescuing.

    Quote Originally Posted by All Clear View Post
    False. Once it has been bet, the coupon is still worth $12.50 (again, I am using a $25 base-bet unit), or a number within a few cents of that. That is why if you win, you have a total of $75 in front of you. You win 1.5 units, and are going from the original 1.5 units of $37.50 (a green chip and a coupon) to three green chips, totaling $75.
    I showed above how the value of the coupon changes as the cards are dealt and each decision is presented. This contradicts your assumption that the coupon has a fixed value throughout and is one reason why applying your method to blackjack does not match the results that Grosjean and I have independently computed using different algorithms (CA and simulation respectively.)
    Quote Originally Posted by All Clear View Post
    This jives well with the first statement- how the match-play coupon is worth the average amount you'll have in your pocket afterward, due to playing it.
    No. You missed a key word. I said "additional money". You started with $25 live money and when you win you now have $75 which is $50 more or 2 units. Similarly when you lose you go from $25 in live money to zero, which is -$25 in additional money or -1 units.
    Quote Originally Posted by All Clear View Post
    the approximation is acceptable for match-play problems, I figure.
    This is one area in which most arguments fail for incorrect mathematical arguments. The introduction of an "acceptable" approximation. You really think that a 6% difference in win rate represents an acceptable approximation when computing basic strategy?
    Quote Originally Posted by All Clear View Post
    Note that in Grosjean's article, he approximates the value for the match-play in blackjack as a number relatively close to 50% of the base bet, as well.
    Actually, I see no approximations at all in his article. Some of the results can be duplicated by calculation, as I showed with roulette and craps. Others (like blackjack) require CA software which also produces exact results. My own results are approximate only because I use simulation. Also, the value of the coupon for the blackjack games he examined ranges from 0.430 to 0.519, which is why I describe your use of 0.5 as arbitrary. We actually don't know the value of the coupon for S17 Spanish 21 using basic strategy.

  7. #72


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    Gronbog: just a quick note here today.....
    So often many of us look at your and others' interesting posts and might not appreciate the time and effort (and most of all skill) that it takes to do the kind of work that you have done with this SP21 match bet issue. Without getting into details, I am a beneficiary of some of your great past work on SP21.
    In the overall scheme of things, there are only a handful of places to use these in the universe and I would guess of the 500 most serious SP21 players out there about 2 people might benefit by an increased theoretical EV of maybe $20 per year.
    Anyway, the point is I admire your efforts to get to the bottom of this mathematical mystery.
    Thanks again for all your insightful posts.

  8. #73


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    Quote Originally Posted by stringer View Post
    Gronbog: just a quick note here today.....
    So often many of us look at your and others' interesting posts and might not appreciate the time and effort (and most of all skill) that it takes to do the kind of work that you have done with this SP21 match bet issue.
    +1

    I would like to echo the sentiments of Stringer. I constantly marvel at the generosity you and some other posters exhibit. It has been my experience that many in the AP community are selfless individuals who go out of their way to help others. I will not start listing names out of fear that I will forget someone, but thanks to all of you.

  9. #74


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    Thanks to All Clear, Bubbles, stringer, SpikeBJ and BJPloppy for the kind words. I like to help, even with these obscure issues, because I enjoy doing the work, I have a genuine interest in the answer, but also because solving these problems helps to improve my software. In my mind, we all benefit.

    The sim for generating the S17 Spanish 21 match play strategy with surrender has converged to the point where the strategy decisions are stable. I may post something later today.
    Last edited by Gronbog; 11-21-2017 at 01:43 PM. Reason: Added SpikeBJ to the list of admirers ;-p As requested

  10. #75


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    Gronbog - Add me to the list of admirers.

  11. #76


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    Match Play Strategy for S17 Spanish 21

    Here is the strategy that I've been promising for the past few days:

    http://www.gronbog.org/results/spanish21/strategy/btf.com/Coupons/Match%20Play/MPR20-20-S17+split.html

    As usual, a few notes:

    • The chart is colour coded to the strategy for 2 cards. As you can see, there are some differences from the normal 2-card strategy for S17 Spanish 21.
    • The deviations for multi-card and other potential bonus hands are noted as a footnote in parentheses followed by the strategy for that exception. See the legend at the bottom of the chart for the meaning of the footnotes. I tried to make them intuitive. For example (3), (4), (5) and (6) represent 3+, 4+, 5+ and 6+ card hands respectively. (7) and (8) are suited and spaded 7,7 respectively.
    • Each footnote also applies to the more specific versions of the same class of hand. So (4) refers to any hand of 4 or more cards. (7) refers to any suited or spaded 7,7, (11) refers only to a potential spaded 6,7,8.
    • The overall value of the coupon is noted at the top of the chart as 50.160% or 0.5016 or $5.016 for a $10 coupon.
    • As before, hover your mouse over any cell to see the raw sim data and the EVs of each available action.
    • The strategy decisions have stabilized, but the EVs have not converged to the full 4 decimal places shown. I will update the chart as the EVs become more accurate.


    As an example, consider the strategy for 13 vs T. The strategy is given as (3)(9)h,rh. This means to hit any hand of 3 or more cards or any 6,7 otherwise surrender, if possible, otherwise hit.

    The strategy assumes the following:
    • The implementation of late surrender is to relinquish the coupon and keep your live money
    • The implementation of double-down rescue is to keep the doubled amount, lose your original live money and relinquish the coupon.
    • All bonuses are paid after splitting except for the super bonus. Bonuses are not paid after doubling.
    • The hand with the coupon is played according to this strategy, even after splitting. Other split hands are played according to the normal basic strategy.


    I hope that those with access to this game find the strategy useful. I hope others find it interesting.

  12. #77
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    An absolutely excellent fantastic post by
    Gronbog.

    The data applies to hardly any Spanish21 game, so

    it is of mostly "academic interest."

  13. #78


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    Apologies for posting here months later- I completed analyzing Gronbog's sheets (after pushing it off for a while), and they look good to me.

    Quote Originally Posted by Gronbog View Post
    I think that you're in for a bit of a rude surprise. I tried applying your surrender model to blackjack and got nothing close to the strategy that Grosjean and I have both independently computed.
    Hi Gronbog,

    I'm happy to see that the "rude surprise" isn't applicable, and it looks like the results that you and I obtained, match almost exactly. The slight differences may be due to one of two reasons I can think of- or perhaps they are due to something I haven't considered.
    1) The nature of a simulation- they may not be 100% correct on some of the close plays that don't come up too often.
    2) The different nature by which we valuate match plays. I had originally used a simplistic approximation of one-half of the base unit bet, while a more exact approximation would use the player's skill level, counting system, and more as inputs. It wouldn't significantly change from 50%, but even a movement to 48% or 52% can change EV calculations- and in cases where the EV of surrendering and hitting are within one percentage point of each other, can make a difference in playing decisions.

    Quote Originally Posted by All Clear View Post
    When forfeiting after doubling, the dealer takes the original bet, and gives you back the amount used to double. This means, if you forfeit when wagering the amounts I show, you are getting back $100, and accepting a loss of just $75. It should be obvious to all that we should forfeit more often, therefore, when using a matchplay. Getting back 4/7 of your bet, or $100 out of $175, means we should surrender after doubling whenever our EV is less than -.429, as opposed to a regular double, when we forfeit whenever our EV is less than -.500. Please feel free to check my math, if you like (or comment if you disagree).

    This leads to the following forfeit basic strategy:

    12-16 v 7,8,9,T,A
    17 v A

    This is identical to regular forfeit strategy, other than a stiff hand vs a 7, which is a forfeit when using a match play, but a stand when using regular chips for the entire bet. If I knew this at the start, I probably wouldn't have crunched all these numbers for this small adjustment, but I guess it takes one person to do the work, to figure it out for everyone, to make sure there aren't other changes to make in strategy.
    Gronbog- Your results in this link match what I had written perfectly for forfeit http://www.gronbog.org/results/spani...S17+split.html.

    Quote Originally Posted by All Clear View Post
    When playing S17 Spanish 21 with a match play, and if surrendering would cause you to only lose your match play, just surrender whenever the best EV decision is still worse than -0.333. I believe that includes the following cases, and (without counting) includes ONLY the following cases:

    13vT, 13vA, 14v9, 14vT, 14vA, 15v2, 15v8, 15v9, 15vT, 15vA, 16v2, 16v7, 16v8, 16v9, 16vT, 16vA, 17v8, 17v9, 17vT, 17vA (obviously, as it is a surrender for basic strategy also).

    Notice how only one hand in Spanish 21 has worse than a -0.5 EV (17vA), but exactly 20 hands, the worst starting 20 hands in the game, are worse than -0.333 EV.
    Our results (yours via the link above) match almost perfectly for surrender (the ones we differ on, 13 v 9, 14 v 2, and 15 v 7, have the surrender EV differing from the hitting EV by less than a single percentage point. They may be slightly off due to one of the two reasons mentioned earlier. For doubling, we are off on just a single hand, A7 v 3.

    In summary- for those who were following this thread at the end of last year, and know of a store that in which one can bet match-play coupons in Spanish 21, but only lose the coupon when surrendering, feel free to use Gronbog's chart above. I will be changing my plays going forward, and will use his chart, as well.

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