Expected Return: player hitting
May 31st, 2010 at 7:27:50 AM
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If someone could help with my logic here? I am assuming infinite deck, dealer stands on soft 17 and want to calculate the player's expected return from hitting.
Example: Player has hard 15 & Dealer has 7.
Wizard shows expected return of -0.3698. However, based on my table listed above I get -0.3744.
Where am I going wrong? Am I doing something wrong around assuming only one card is drawn?
Many thanks in advance
Wardos
Example: Player has hard 15 & Dealer has 7.
| Next Card | P(x) | Total | Win | Push | Lose | E(R) |
|---|---|---|---|---|---|---|
| A | 7.69% | 16 | 26.23% | 0.00% | 73.77% | -0.0366 |
| 2 | 7.69% | 17 | 26.23% | 36.86% | 36.91% | -0.0082 |
| 3 | 7.69% | 18 | 63.09% | 13.78% | 23.13% | 0.0307 |
| 4 | 7.69% | 19 | 76.87% | 7.86% | 15.27% | 0.0474 |
| 5 | 7.69% | 20 | 84.73% | 7.86% | 7.41% | 0.0595 |
| 6 | 7.69% | 21 | 92.59% | 7.41% | 0.00% | 0.0712 |
| 7 | 7.69% | bust | 0.00% | 0.00% | 100.00% | -0.0769 |
| 8 | 7.69% | bust | 0.00% | 0.00% | 100.00% | -0.0769 |
| 9 | 7.69% | bust | 0.00% | 0.00% | 100.00% | -0.0769 |
| T | 30.77% | bust | 0.00% | 0.00% | 100.00% | -0.3077 |
| Total | -0.3744 |
Wizard shows expected return of -0.3698. However, based on my table listed above I get -0.3744.
Where am I going wrong? Am I doing something wrong around assuming only one card is drawn?
Many thanks in advance
Wardos
May 31st, 2010 at 7:40:33 AM
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Quote: wardos
Wizard shows expected return of -0.3698. However, based on my table listed above I get -0.3744.
Where am I going wrong? Am I doing something wrong around assuming only one card is drawn?
Many thanks in advance
Wardos
The numbers are very close, so my guess is that it is the times you receive an Ace, because the hand will be hit 1 more time in that situation (16 vs. 7) unless it's ANOTHER Ace (Soft 17 vs. 7), then there could be a few more hits possible.
May 31st, 2010 at 2:29:06 PM
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CCLUB79 - you're right, I need to draw another card where an Ace is drawn as the third card e.g. 6&9, then Ace, then draw again so that the lowest total the player gets is 17. The test is that drawing again lowers the expected loss for the player so it is in their interest to draw again when the third card is an Ace.
What I don't understand is why you can't assume just one card is drawn when determing player hitting expected returns and then look at the next total after that one card is drawn. E.g. 6&9 initial two cards, versus dealer 7, hitting is optimal play with expected return of -0.3744 by drawing one card, then third card is a 3, then you look up the expected return for hard 18 where standing has the higher expected return so you stand.
So why can't I assume just one card is drawn then you move to next total to assess optimal play?
What I don't understand is why you can't assume just one card is drawn when determing player hitting expected returns and then look at the next total after that one card is drawn. E.g. 6&9 initial two cards, versus dealer 7, hitting is optimal play with expected return of -0.3744 by drawing one card, then third card is a 3, then you look up the expected return for hard 18 where standing has the higher expected return so you stand.
So why can't I assume just one card is drawn then you move to next total to assess optimal play?
