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Wizard
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Wizard
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August 14th, 2016 at 7:33:07 AM permalink
Quote: Paradigm

If an Ace is in the mix, the cards would have to come 5/6/Ace in some order (assuming H17 rules) and then could only bust if the 4 came next followed by the 7, correct?



That would seem correct. The rack card didn't answer the question. I'm still trying to get an answer anywhere.
It's not whether you win or lose; it's whether or not you had a good bet.
Wizard
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Wizard
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June 11th, 2017 at 6:08:20 PM permalink
Quote: someone

OK after seeing the detailed rules I redid the sim. This time 6 deck,H17 I get HA of approx 6.35%. The strategy is raise 1x against dealer 2 or 3, raise 5x against dealer 4, 5, or 6, don't raise against A, 7, 8, 9, or 10 card.



This side bet has come to my front burner. Based on these rules and the pay table provided earlier, assuming the 4-5-6-7 can be in any order (as long as it ends in a 6 or 7), and no extra cards allowed for the 4-5-6-7 pays, then I get a house edge of 6.26%. My strategy is the same as yours except I show to make a 1x raise with a 7.

With a 7 here is my EV each way:

Small raise: -0.430645
No raise: -0.476128
It's not whether you win or lose; it's whether or not you had a good bet.
rdw4potus
rdw4potus
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June 11th, 2017 at 9:03:01 PM permalink
What is the player advantage if the raise isn't necessary to trigger the graduated paytable? I know a dealer who does this & wouldn't let me correct him.. .
"So as the clock ticked and the day passed, opportunity met preparation, and luck happened." - Maurice Clarett
Wizard
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Wizard
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June 11th, 2017 at 9:36:00 PM permalink
Quote: rdw4potus

What is the player advantage if the raise isn't necessary to trigger the graduated paytable? I know a dealer who does this & wouldn't let me correct him.. .



Player advantage of 7.87%.

The correct strategy under such a rule twist would be to make the small raise on 4-6 and not raise at all on everything else.
It's not whether you win or lose; it's whether or not you had a good bet.
Ace
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June 12th, 2017 at 6:49:03 PM permalink
I just calculated this using a Markov chain (actually 10 of them, one for each dealer upcard) assuming infinite deck and S17. I calculate proper strategy as small raise on dealer 2-3 and full raise on 4-6.

My final number is very close - 6.11 %, but this is the element of risk. The house advantage as we define it - on initial bet only - is 14.1%. The difference is a factor of 30/13 which is (total units bet / ante units bet) assuming above strategy.
Wizard
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Wizard
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June 13th, 2017 at 6:04:26 PM permalink
Okay, I hope you're happy, I spent all day on this. Here is my new page on Raise the Roof.

Although my page is based on my own math, I have a GLI report on the game too, kindly provided by Score Gaming, which does not agree with my numbers. However, they muddy the waters by talking about the blackjack game itself, but even considering that, we still don't agree.

The 1-1-2-5-10-30-300 pay table is supposed to be for two decks and the dealer hits a soft 17. All the previous work on this page seems to be based on this pay table but six decks. Maybe this is selfish, but I hate to try to find out who is correct based on a set of rules that doesn't exist. Can I trouble those who have analyzed this to change the number of decks to two. Then please post your results. Thank you.
It's not whether you win or lose; it's whether or not you had a good bet.
Boz
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June 13th, 2017 at 7:25:10 PM permalink
Just looking over the rules on #7 if the player busts, the wager stays active. I am assuming if you are playing heads up, the game would be over. Assuming heads up would change the odds or does the dealer still play the hand out looking for a pat hand or bust?
Wizard
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Wizard
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June 13th, 2017 at 8:39:26 PM permalink
Quote: Boz

Just looking over the rules on #7 if the player busts, the wager stays active. I am assuming if you are playing heads up, the game would be over. Assuming heads up would change the odds or does the dealer still play the hand out looking for a pat hand or bust?



I assumed the side bet would still be active and the dealer would draw against a dead hand. Bad game design, in my opinion, but that is how I read the rules.
It's not whether you win or lose; it's whether or not you had a good bet.
Ace
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June 14th, 2017 at 10:18:34 AM permalink
Hi Wizard,

I compared my calculation for infinte deck to your simulation for 6 deck, S17, pay table 4. The difference between 6 deck and infinite deck is miniscule while the calculation is orders of magnitude easier for infinite.

I get element of risk of 4.93% vs your 4.01%.

The difference is in the 4-5-6-7 bonus calculation. For instance, with dealer showing 7 I calculate the total probability of hitting the bonus (suited or not) as 2 / 2197. With 13^3 = 2197 permutations of the next 3 cards coming only 2 of them - 456 and 546 - will win the bonus. Your table shows the bonus about 3 times more probable than my calculation. This also causes your strategy to raise 1x on a dealer 7 (mine doesn't).

I believe your simulation assumes that with dealer showing 7, the 6 can come as any of the next three cards. To win the 4567 bonus the dealer must bust, and for that to happen 6 can only come as the last card.

Ace
Last edited by: Ace on Jun 14, 2017
Wizard
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Wizard
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June 14th, 2017 at 2:43:17 PM permalink
Quote: Ace

I compared my calculation for infinte deck to your simulation for 6 deck, S17, pay table 4. The difference between 6 deck and infinite deck is miniscule while the calculation is orders of magnitude easier for infinite.

I get element of risk of 4.93% vs your 4.01%.

The difference is in the 4-5-6-7 bonus calculation. For instance, with dealer showing 7 I calculate the total probability of hitting the bonus (suited or not) as 2 / 2197. With 13^3 = 2197 permutations of the next 3 cards coming only 2 of them - 456 and 546 - will win the bonus. Your table shows the bonus about 3 times more probable than my calculation. This also causes your strategy to raise 1x on a dealer 7 (mine doesn't).

I believe your simulation assumes that with dealer showing 7, the 6 can come as any of the next three cards. To win the 4567 bonus the dealer must bust, and for that to happen 6 can only come as the last card.



You're absolutely right. I over-counted the ways to get the 4-5-6-7 wins. After correcting for that, my house edge for pay table 4 (six decks S17) is 11.17% with an element of risk of 3.96%. The math report by GLI says the house edge for that pay table is 10.05% and the element of risk is 4.36%.
It's not whether you win or lose; it's whether or not you had a good bet.

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