Mission146
Mission146
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June 7th, 2012 at 5:03:58 AM permalink
Two Off the Top Side Bet

This is a new side bet that I thought of, but my casino Blackjack experience is a bit limited, in terms of number of casinos, so please let me know if this side bet already exists.

The side bet amount may not exceed the amount of the base bet under any circumstances.

The way the, "Two Off the Top," bet would work is that, after every player is dealt their cards, the side bet would be based off of the first two cards hit for by any player, including the dealer.

In the event that any player Splits, then one or both of the cards (in the event of no previous hits) would count towards the bet. If a player doubles, then that, of course, also constitutes a hit.

In the event that either zero hits or only one hit is taken during the course of a betting round, then the bet will be resolved with the next one or two cards (if applicable) off of the top after the betting has concluded.

Simply put, the first, "Two Off the Top," resulting in a Natural would pay the player at 15:1 and the first, "Two Off the Top," resulting in a value of 20 would pay the player off at 1:1.

The Math Behind the Bet is as Follows:

(16/52 * 4/51) + (4/52 * 16/51)

(.3076923 * .0784314) + (.0769231 * .3137255)

.02413273785 + .02413278

.04826547585 or 4.826547585% (Probability of 21)

150 * .04826547585 = $7.24 (EV of 21)

(16/52 * 15/51)

.3076923 * .294117647

.09049773527 (Probability of 10 + 10)

$10 * .09049773527 = $0.905 (EV of 10 + 10)

(4/52 * 4/51)

.0769231 * .07843137254

.00603318431 or .603318431% (Probability of A + 9)

$10 * .00603318431 = $0.06 (EV of A + 9)

Total EV of Wins $0.06 + $0.905 + $7.24 = $8.205

Total EV of Losses -$10 * (1 - .04826547585 - .09049773527 - .00603318431)

-$10 * .85520360457 = $8.55...$8.55 - $8.205 = $0.345

Advantage: House $0.345 per $10.00 bet or 3.45%


CONCLUSION

I think this could be a popular Side Bet, imagine glittering lights with the words, "Natural Blackjack Pays 15:1," that's going to draw some attention!

This is actually not a horrible side bet, as far as side bets go, for the player in a perfect deck. The HA, as you can see, is actually less than the HA in a game of Roulette, but it still gets the player's money on the table and into the casino's checking account.
https://wizardofvegas.com/forum/off-topic/gripes/11182-pet-peeves/120/#post815219
Mission146
Mission146
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June 9th, 2012 at 8:15:29 PM permalink
I have been informed that we are going to need a few more specifics about this side bet, particularly with respect to the influence of card counting. For the sake of simplicity, we're going to go with an Eight-Deck shoe, but with 75% penetration, leaving essentially two decks in the shoe for the final hand.

First of all, there are going to be 104 cards left in the shoe. For the first calculation, we're going to say that Aces are even, with eight remaining, but we're in the good with +10 ten value cards.

Therefore, there would normally be eight aces and thirty-two tens in the two decks. In this case, there are eight aces and forty-two tens.

In order to achieve the 15:1 payout, we need hits of an Ace and a Ten. The probability of picking up the Ace on the first hit is 8/104 or 7.6923%. We would need a Ten at this point which would be 42/103 or 40.7767%. The probability of picking up the Ten on the first hit is 42/104 or 40.3846% and the probability of drawing the Ace on the second hit would be 8/103 or 7.767%.

In other words, our overall probability of winning the bet can be expressed as such:

[(8/104) * (42/103)] + [(42/104) * (8/103)]

[.076923 * .407767] + [.40385 * .07767]

.0313667 + .031367

= 6.273373% Probability of success.

If we bet 10 units, we profit 150 units, so:

150 * .06273373 = $9.41 EV of 15:1 Payout

_______________________________________

We now have to look at the fact that 20 pays 2:1 for 10 + 10 or A + 9.

[42/104 * 41/103]

.40385 * .39806

= 16.076%

20 * .16076 = $3.22 EV of 2:1 payout on 10 + 10

(A + 9)

[8/104 + 8/103]

.076923 * .07767

= .0059746

20 * .0059746 = $0.12 EV on A + 9

Total EV= $9.41 + $3.22 + $0.12 = $12.75

Ouch.

The probability of any loss is simply 100% - 6.273373% (Probability of 21) - 16.076% (Probability of 10 + 10) - .0059746% (probability of A + 9) or 77.053167%.
The expected value of a loss is -$10.00 * .77053167 or -$7.71.

The total EV is a positive $5.04 for the player.

GAME CORRECTION

The first thing that we are going to do is change the payout for 20 to 1:1 instead of 2:1. In the +10 ten-cards scenario, that would then reduce the expected value of the bet in half for all 20's down to $1.67 for an overall of $3.37.

That will improve the House Edge off a game with perfect deck composition to 17% of all bets:

$7.25 + $2.10 = or $9.35

Becomes

$7.25 + $1.05 = $8.30 ($1.70 per $10.00 bet or 17%)

***

Unfortunately, that still leaves us with the problem of a Positive Expected Value during a really bad count leaving susceptibility to card counters.

I might suggest that this problem is somewhat mitigated the same way that the problem of a card counter in the Base game is mitigated. If you have a player that has no interest in the side bet until late in the shoe, at which point he suddenly starts matching his base bet on the side bet, then you run it through surveillance, check the count, and it may just be time for him to go.

However, I think it will still be important to figure out the negative EV point for the casino, which is essentially to determine at what point in a positive count that the casino loses its edge.

PLUS FIVE TENS (37 TENS)

[(8/104) * (37/103)] + [(37/104) * (8/103)]

[.076923 * .3592233] + [.355769 * .07767]

.0276325 + .0276326

.0552651 or 5.52651%

$150 * .0552651 = $8.29


[37/104 * 36/103]

.355769 * .349515

.1243466 or 12.43466%

$20 * .1243466 = $2.49

(A + 9)

[8/104 + 8/103]

.076923 * .07767

= .0059746

20 * .0059746 = $0.12 EV on A + 9

Total EV of Win: $8.29 + $2.49 + $.012 = $10.90

The expected value of a loss is $10.00 * .8144137 or $8.14

The player has the best of it by $2.76.

If we reduce the payout to 1:1 for any twenty, the player still has the best of it by $2.76 - $1.31 = $1.45

PLUS THREE TENS (34 TENS)

[(8/104) * (35/103)] + [(35/104) * (8/103)]

[.076923 * .339806] + [.336538 * .07767]

.0261389 + .026139

.052278 or 5.2278%

150 * .052278 = $7.84

[35/104 * 34/103]

.336538 * .337097

.113446 or 11.3446%

$20 * .113446 = $2.27

(A + 9)

[8/104 + 8/103]

.076923 * .07767

= .0059746

20 * .0059746 = $0.12 EV on A + 9

The total expected value of a win is $7.84 + $2.27 + $0.12 = $10.23

The expected value of any loss is -$10.00 * .8283014 = -$8.28

The total expected value favors the player $1.95. If we reduce the 20 pays to 1:1, then the EV drops by $1.20 to $0.75 in the player’s favor.

PLUS TWO TENS

[(8/104) * (34/103)] + [(34/104) * (8/103)]

.076923 * .330097 + .326923 * .07767

.025392 + .0253921

.0507841 or 5.07841%

$150 * .0507841 = $7.62

[34/104 * 33/103]

.326923 * .320388

.1047422 or 10.47422%

$20 * .1047422 = $2.09
(A + 9)

[8/104 + 8/103]

.076923 * .07767

= .0059746

20 * .0059746 = $0.12 EV on A + 9

The EV of all wins is $0.12 + $2.09 + $7.62 = $9.83

The EV of a loss is -$10 * .8384991 or -$8.38

The total EV favors the player $1.45 or $0.34 if 20 pays 1:1.

PLEASE SEE NEXT POST
https://wizardofvegas.com/forum/off-topic/gripes/11182-pet-peeves/120/#post815219
Mission146
Mission146
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June 9th, 2012 at 8:29:19 PM permalink
It appears that this game is, unfortunately, highly susceptible to card counting. However, it should be kept in mind that we are assuming that the deck penetration is 75% on an Eight-Deck Shoe.

It appears that the player starts playing with an advantage at +2 Tens at this point in the shoe.

I do not have time for the Math at the moment, but there are any number of ways this problem can be overcome:

1.) PAYOUT REDUCTION

In the post above, I provided the numbers for a 20 paying 2:1 and a 20 paying 1:1. I would say that, for this game to have any chance against an AP, the payout for 20 is going to have to be reduced to 1:1. The payout for a Natural could also be reduced, but that defeats the entire draw of the game being that a Natural pays 15:1.

The simplest thing for the Dealer, if we are to reduce the payout for a Natural, is to reduce it to 10:1, but that will result in an intolerably low EV even for the average player. I would venture to say that, without doing any Math, the average player would know that is a terrible bet.

2.) NORMAL CASINO PRACTICE

If you have an AP who doesn't play this side bet until the penetration is deep, and then he suddenly starts piling money on the Side Bet, that's going to give a pretty good indication that he is a counter, so normal surveillance, skills check, and other practices could be followed.

3.) LESS DECK PENETRATION

I'm going to run some numbers, hopefully tomorrow, for 50% penetration in an eight-deck shoe for the Natural paying 15:1 and 20 paying 1:1 to see where in the count the casino loses the advantage on this bet.

4.) 20=PUSH

This is possible, but then the player only has one way to actually win. The casino getting 17% of all bets with 20 paying 1:1 is probably more than sufficient in a perfect deck, anyway. It would be very difficult to make the odds against the player any worse and still have an attractive game.
https://wizardofvegas.com/forum/off-topic/gripes/11182-pet-peeves/120/#post815219
SOOPOO
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June 9th, 2012 at 8:34:35 PM permalink
This bet can never happen. If the one card already hit is a 'good' card, then there will be pressure on the last player to hit, regardless of his hand. Imagine if the last player has an 18 and the dealers has a 6, but 4 players before this player bet big money on the side bet.....
I think you wasted a lot of time and effort....
Mission146
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June 9th, 2012 at 8:40:17 PM permalink
Quote: SOOPOO

This bet can never happen. If the one card already hit is a 'good' card, then there will be pressure on the last player to hit, regardless of his hand. Imagine if the last player has an 18 and the dealers has a 6, but 4 players before this player bet big money on the side bet.....
I think you wasted a lot of time and effort....



1.) You make the bet before you know what the first card is going to be, so that really doesn't affect the odds in any way.

2.) I've also suggested that the two can come off the top, regardless of the amount of hits. In other words, if there has only been one hit, then the dealer will pull one from the top (only for the purposes of the SB) after the normal round has completed. If there are no hits taken, then the dealer simply pulls two from the top after the conclusion of the normal bets/payouts.

In that event, there would be no incentive to play other than the best possible strategy for any player in any circumstances, as the cards will come off the top regardless of the number of hits taken.
https://wizardofvegas.com/forum/off-topic/gripes/11182-pet-peeves/120/#post815219
Mission146
Mission146
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June 9th, 2012 at 9:30:56 PM permalink
SooPoo,

Also, thank you for your response.

The other thing I should mention is, given that the Odds of the Side Bet are no better or worse prior to the making of the bet (even if the two-off-the-top is not guaranteed to resolve) the casino would certainly benefit from having a player make a -EV hand on a base bet, such as hitting on 18.

I think that the bet will have to resolve one way or another, though. It'll be far easier that way.
https://wizardofvegas.com/forum/off-topic/gripes/11182-pet-peeves/120/#post815219
Mission146
Mission146
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June 10th, 2012 at 8:51:07 PM permalink
8 DECKS-50% PENETRATION

We have seen that this game, even with a 1:1 payout on 20, will not work very well with 75% penetration on an eight-deck shoe. The player will actually gain the Edge at +2, so that's, unfortunately, not acceptable.

It is for this reason that we must reduce the deck penetration and determine the effects of counting. Therefore, the deck penetration will be reduced to 50%, which would theoretically be a full four decks (208 cards) on the final hand.

There would normally be 64 Tens and 16 Aces in a perfect four decks, so we will calculate this at +5 Tens first, with 69 Tens.

(69/208 * 16/207) + (16/208 * 69/207)

(.331731 * .0772947) + (.0769231 * .3333333)

.025641 + .025641 = .051282 or 5.1282%

$150 * .051282 = $7.69 EV on 21

10 + 10 = 20

(69/208) * (68/207)

.3317308 * .3285024

.1089744 or 10.89744%

$10 * .1089744 = $1.09 EV on 20

A + 9

(16/208 * 16/207)

.076923 * .0772947

.0059457 or .59457%

$10 * .0059457 = $0.06 EV on A + 9 = 20

Total EV of All Wins = $7.69 + 1.09 + $0.06 = $8.84

Total EV of all Loses = -$10 * (1 -.0059457 - .1089744 - .051282)

-$10 * .8337979 = $8.34

Expected Value in favor of Player = $0.50 on $10.00 bet or 5%

+3 Tens

(67/208 * 16/207) + (16/208 * 67/207)

(.322115 * .0772947) + (.076923 * .3236715)

.0248978 + .0248978

.0497956 or 4.97956%

$150 * .0497956 = $7.47


(67/208) * (66/207)

.322115 * .318841

.1027035 or 10.27035%

$10 * .1027035 = $1.03


A + 9

(16/208 * 16/207)

.076923 * .0772947

.0059457 or .59457%

$10 * .0059457 = $0.06 EV on A + 9 = 20

Total EV of Win = $0.06 + $1.03 + $7.47 = $8.56

Total EV of Loss = -10 * (1 - .0059457 - .1027035 - .0497956)

-10 * .8415552 = -$8.42

Total EV = +$0.14 for the player

[+2 Ten Count]

(66/208 * 16/208) + (16/208 * 66/207)

(.31731 * .076923) + (.0769231 * .318841)

.0244084 + .02452624

.04893464 or 4.893464%

$150 * .04893464 = $7.34


(66/208) * (65/207)

.317308 * .31401

.099638 or 9.9638%

$10 * .099638 = $1.00


A + 9

(16/208 * 16/207)

.076923 * .0772947

.0059457 or .59457%

$10 * .0059457 = $0.06 EV on A + 9 = 20


EV of All Wins = $7.34 + $0.06 + $1.00 = $8.40

EV of All Losses = -$10 * (1 - .0059457 - .099638 - .04893464)

-$10 * .84548166 = -$8.45

The total expected value of the game is +$0.05 or .5% for the house with a +2 count.

See Next Post
https://wizardofvegas.com/forum/off-topic/gripes/11182-pet-peeves/120/#post815219
Mission146
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June 10th, 2012 at 9:01:32 PM permalink
CONCLUSION OF ABOVE:

1.) The Two will come Off The Top regardless of the amount of in-round hits, but in-round hits will, of course, count.

2.) Twenty must pay 1:1. We could also consider having A + 9 be a loss, in which event two Ten Cards would be the only other payout. The impact of doing such a thing is literally pennies, though, and could be seen by the player as a rip-off.

3.) We have determined with an eight-deck shoe at 50% penetration, +3 Tens is the cutoff where the player starts to experience an advantage, namely of 1.4% for this bet. This leads me to a couple of questions:

A.) Is such an advantage, given the count and penetration needed, acceptable to the casino given the advantage the casino gets off of a perfect deck?

and

B.) Would it be worth it for an AP, who customarily lays off side bets, to risk exposure by backing his bet in full by playing the side bet?

finally

C.) Would this fact actually be an advantage to the casino in being able to more easily identify counters by the fact that they are playing the side bet towards the end of the shoe suddenly?

Two Choices:

1.) Keep the game in its current form and determine at what point in an eight-card shoe (in terms of number of cards) the House loses its advantage on this side bet with a count of +3 Tens.

2.) Eliminate the payout for twenty and make it a push.

What do you guys think?
https://wizardofvegas.com/forum/off-topic/gripes/11182-pet-peeves/120/#post815219
Mission146
Mission146
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June 10th, 2012 at 9:38:10 PM permalink
OOPS!!!

I thought that there was too much disparity for a +2, +3 and +5 count with only 50% Deck Penetration in an Eight-Deck shoe. My mistake was not readily apparent to me because my initial computations of the house's expected take were entirely incorrect.

The problem was that I was just looking at all wins and subtracting them from $10.00, but $10.00 is NOT the expected value of a loss because you will not lose 100% of the time.

Fortunately, it turns out that this side bet, with 20 paying 1:1 still favors the casino, but not as much as thought initially.

Behold, the new numbers below:

(16/52 * 4/51) + (4/52 * 16/51)

(.3076923 * .0784314) + (.0769231 * .3137255)

.02413273785 + .02413278

.04826547585 or 4.826547585%

150 * .04826547585 = $7.24

(16/52 * 15/51)

.3076923 * .294117647

.09049773527

$10 * .09049773527 = $0.905

(4/52 * 4/51)

.0769231 * .07843137254

.00603318431 or .603318431%

$10 * .00603318431 = $0.06
Total EV of Wins $0.06 + $0.905 + $7.24 = $8.205

Total EV of Losses -$10 * (1 - .04826547585 - .09049773527 - .00603318431)

-$10 * .85520360457 = $8.55...$8.55 - $8.205 = $0.345

Advantage: House $0.345 or 3.45%

Conclusion

This is actually not a horrible side bet, as far as side bets go, for the player in a perfect deck. The HA, as you can see, is actually less than the HA in a game of Roulette, but it still gets the player's money on the table and into the casino's checking account.

Please be assured that the rest of the calculations are correct, as I only failed to determine the expected value of a loss properly in my OP.

The game is quite susceptible to card-counting however, so it remains to either:

1.) Turn 20 into a Push

or

2.) Determine at what point +3 with 50% deck penetration gives the player an advantage.

Thoughts?

I'm also interested in:

3.) We have determined with an eight-deck shoe at 50% penetration, +3 Tens is the cutoff where the player starts to experience an advantage, namely of 1.4% for this bet. This leads me to a couple of questions:

A.) Is such an advantage, given the count and penetration needed, acceptable to the casino given the advantage the casino gets off of a perfect deck?

and

B.) Would it be worth it for an AP, who customarily lays off side bets, to risk exposure by backing his bet in full by playing the side bet?

finally

C.) Would this fact actually be an advantage to the casino in being able to more easily identify counters by the fact that they are playing the side bet towards the end of the shoe suddenly?
https://wizardofvegas.com/forum/off-topic/gripes/11182-pet-peeves/120/#post815219
Mission146
Mission146
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June 10th, 2012 at 9:43:07 PM permalink
I will now correct the OP.
https://wizardofvegas.com/forum/off-topic/gripes/11182-pet-peeves/120/#post815219
Mission146
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June 11th, 2012 at 3:34:42 PM permalink
We will now see the effects of +3 Tens on Eight Decks that have been penetrated 40%. We know that +3 is the cutoff where the player gets an advantage for 50%, so we will see if the advantage is with the player for 40%. If not, then we will see if +4 Tens presents an advantage.

52 Cards/Deck * 8 Decks = 416 Cards

416 - 40% = 249.6 Cards in the Deck

There would normally be 16 * 8 - 40% = 76.8 Tens left in the Deck

There would normally be 4 * 8 - 40% = 19.2 Aces left in the Deck

There would normally be 4 * 8 - 40% = 19.2 Nines left in the Deck

We're adding Three Tens, so even though you can't have a fraction of a ten, the Math needs to be right, so 79.8 Tens.

A + 10 = 21

(79.8/249.6 * 19.2/248.6) + (19.2/249.6 * 79.8/248.6)

(.31971153846 * .07723250201) + (.07692307692 * .32099758648)

.02469212203 + .02469212203

.0493842206 or 4.93842206%

$150 * .0493842206 = $7.41 EV on Natural

10 + 10

(79.8/249.6 * 78.8/248.6)

.31971153846 * .31697506033

.10134058419 or 10.134058419%

$10 * .10134058419 = $1.01

A + 9

(19.2/249.6 * 19.2/248.6)

.07692307692 * .07723250201

.00594096169 or .584096169%

$10 * .00594096169 = $0.06

EV of All Wins = $0.06 + $1.01 + $7.41 = $8.48

EV of All Losses = -10 * (1 - .00594096169 - .10134058419 - .0493842206)

-10 * .84333423353 or 84.333423353%

-$8.43.

CONCLUSION

It seems that a counter will experience an advantage of $0.05 per $10 hand, or 0.5% for each hand played with 40% penetration in an eight-deck shoe at a count of +3.
https://wizardofvegas.com/forum/off-topic/gripes/11182-pet-peeves/120/#post815219
Mission146
Mission146
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June 11th, 2012 at 6:47:58 PM permalink
The game is still highly susceptible to card counting if 40% penetration on an eight deck shoe at +3 Tens still swings an advantage of 0.5% to the player.

If we were to change the Twenty Payout to 1:2 on the base game, then we would change the casino's expected take to $0.825 on a $10 bet or 8.25% on the base game with a perfect deck. I'm not sure if this side bet would be favorable enough to the player to sustain, and 1:2 also seems like a strange payout.

1.) From a player's standpoint, does the fact that twenty pays something matter more, or would a Push almost seem to make more sense to the player on 20?

2.) It still remains to be seen at what % deck penetration the player gains an advantage at +3. We have already learned that +2 does not offer an advantage to the player on 50% penetration, and that's as deep as we will intend to cut them for this game.

3.) When we determine exactly where the player gains an advantage with a +3 count, how many potential bets does that expose the house to as far as the side bet is concerned?

***For example, we know that the casino is exposed to a 1.4% player advantage at +3 Tens with 50% penetration on an eight-card deck based on 1:1 payout for any twenty, (and that's as deep as the penetration will go) and a .5% advantage at +3 Tens with 40% penetration.

The mean advantage for the player, between 40-50% deck penetration is then about (1.4% + .5%) /2 = 0.95%

There are 416 cards in an eight-deck shoe, so the casino is exposed to this mean .95% player edge at +3 10 cards for 41.6 cards. (10% of the cards)

If there are only two players (including the dealer) then there will be a maximum of 6.93 (round it to 7) hands that the casino plays at this disadvantage. This is assuming that neither the casino nor the player takes any hits during those hands. (2 Cards for Casino, 2 Cards for Player, 2 Off the Top)

If there is $100 bet on the side bet during this period, the casino is expected to have the worst of it by $0.95.

However, it remains to be determined exactly at what count the player's advantage begins at +3 Tens, so that will have to be completed. The same will have to be done for +4 Tens, and so on.

I'm also not exactly sure what we should call the point of ridiculousness and stop making determinations. For example, with 50% penetration on Eight Decks, zero Tens could theoretically show up which would result in a count of +64 Tens. All 128 tens could theoretically remain out of 208 cards left in the deck!

(128/208) * (127/207)

.61538461538 * .61352657004

.37755481232 or 37.755481232

$10 * .37755481232 = $3.78

(128/208 * 16/207) + (16/208 * 128/207)

(.61538461538 .07729468599) + (.07692307692 * .61835748792)

.0475659606 + .0475659606

.0951319212 or 9.51319212%

$150 * .0951319212 = $14.27

A + 9

(16/208 * 16/207)

.076923 * .0772947

.0059457 or .59457%

$10 * .0059457 = $0.06 EV on A + 9 = 20

TOTAL EV OF ALL WINS = $14.27 + $0.06 + $3.78 = $18.11

Total EV OF ALL LOSES= -$10 * (1 - .0951319212 - .0059457 - .37755481232)

-$10 * .52136756648 = -$5.21

TOTAL EV = $12.90 on $10.00 Bet in favor of the player. 129% returned on all bets. 29% Player Edge!

***Of course, it's ridiculous to even consider a count of +64!!! I suppose the question is, where do you stop?
https://wizardofvegas.com/forum/off-topic/gripes/11182-pet-peeves/120/#post815219
SOOPOO
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June 11th, 2012 at 9:10:00 PM permalink
Hey mission, have you noticed with the exception of my pithy comment you are basically just talking to yourself? But I do like your persistence.....
Mission146
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June 11th, 2012 at 10:07:56 PM permalink
Quote: SOOPOO

Hey mission, have you noticed with the exception of my pithy comment you are basically just talking to yourself? But I do like your persistence.....



I appreciate the semi-compliment.

My reasoning is that I have to put it down somewhere, so it might as well be here. I think one of the problems was the OP wasn't very good, and I made a pretty simple error to correct, so I have done so. The OP is much better now, and I am still analyzing the effects of card counting.

The problem is that the player has an advantage of .5% at 40% deck penetration in an eight-deck shoe with a count of +3 tens or better. I wish I knew whether or not the casino would tolerate this risk as concerns AP's. I know that they would try to catch them, but would the side bet be too risky?

Obviously, as with the base game of BJ, the casino cannot avoid situations in which the player is occasionally at an advantage if the hand is played correctly, but how much of an advantage would they be willing to tolerate?

You could have an eight-deck shoe at 75% penetration without there ever being an Ace, theoretically. That would leave 32 Aces, if we assume that tens are where they should be (also 32, two decks left) then the player has a:

(32/104 * 32/103)

(.30769230769 * .31067961165)

.09559372666 or 9.56% chance of being dealt a BJ.

The casino has the same chance, but it's not getting paid 3:2 if the player doesn't have it.

The chance of both being dealt BJ:

.09559372666 (Player) * (31/102 * 31/101)-Dealer

.09559372666 * (.30392156862 * .30693069306)

.09559372666 * .09328285769

.008917256 (Of both Player/Dealer getting BJ on the same hand)

If you subtract .09559372666 - .008917256 = .08667647066 or 8.667647066% (The liklihood of one getting BJ and not the other)

***This actually depends on the cards the player gets. If the player fails to draw an Ace or Ten, then the dealer's chances of a BJ improve to (32/102 * 32/101).

The point is that the player's expectations, on BJ alone are:

$15 * .08667647066 = $1.30

vs.

-$10 * .08667647066 = -$0.87

This gives the player an Edge of $0.43 per $10.00 bet, or 4.3%.

The point is that, in a finite deck, it is nearly impossible to make rules for this sort of thing where the casino will never be at a disadvantage given a limited sample.

The question is, what is the biggest disadvantage they would tolerate against AP's?
https://wizardofvegas.com/forum/off-topic/gripes/11182-pet-peeves/120/#post815219
MonkeyMonkey
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June 12th, 2012 at 3:02:35 AM permalink
The biggest problem I see with this sidebet is that it potentially effects players that don't want to participate. For example, I deal 19's or 20's to 3 players. My up card is a 6. (this sort of thing happens all the time, btw...). No one wants a hit, but one player placed a sidebet wager, so I have to resolve it by drawing 2 cards. Without running through every possible scenario, I have to tell you there are a lot of card combos that are going to piss off 2 of the players (3 if we don't have a winning sidebet). In the other sidebets I'm familiar with non-participation carries no penalty, but this one very potentially does.

Another issue is stopping all the action after the 2nd card has been drawn to pay/take the sidebet wagers. This is procedurally awkward and would screw up some dealers every time it happened.
Mission146
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June 12th, 2012 at 1:36:25 PM permalink
Quote: MonkeyMonkey

The biggest problem I see with this sidebet is that it potentially effects players that don't want to participate. For example, I deal 19's or 20's to 3 players. My up card is a 6. (this sort of thing happens all the time, btw...). No one wants a hit, but one player placed a sidebet wager, so I have to resolve it by drawing 2 cards. Without running through every possible scenario, I have to tell you there are a lot of card combos that are going to piss off 2 of the players (3 if we don't have a winning sidebet). In the other sidebets I'm familiar with non-participation carries no penalty, but this one very potentially does.

Another issue is stopping all the action after the 2nd card has been drawn to pay/take the sidebet wagers. This is procedurally awkward and would screw up some dealers every time it happened.



1.) I have revised the Rules on the sidebet. The two will come off the top regardless, but they will be comprised of the first two cards hit, the first hit (if only one is taken) and an extra card at the end of the regular round, or two cards at the end of the regular round if no hits are taken.

The only thing a SB will affect is how many cards ultimately come out of the deck, but in this scenario, the SB has no effect on actual hand distributions prior to the cards being drawn.

It's really no different than another player sitting at the table, or someone leaving. It chances the distribution, but nobody really knows how it changes it ahead of time.

2.) You would not have to stop it immediately after. You could have an electronic outlay that lights up for a Ten-Value Card, Nine, Ace or X for losing card.

If the first card is a 2-8, then it would just be an X because the bet can't win. If the second card is a 9-A, then the outlay would light up 9, 10, J, Q, K or A.

The second hit could come out and would light either an X, 9, 10, J, Q, K or A and then the SB is finished, but the results remain until the dealer clears them. Thus, it could be paid at the end of a hand.

GAME VALUE

I think this adds to the value of the game. Imagine if you are playing the SB and are dealt 14 against a dealer showing Ten. If you hit and bust, you still have a horse in the race...a big horse at that...and reason to remain interested in the rest of the Round!
https://wizardofvegas.com/forum/off-topic/gripes/11182-pet-peeves/120/#post815219
MonkeyMonkey
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June 14th, 2012 at 11:47:03 AM permalink
Quote: Mission146

1.) I have revised the Rules on the sidebet. The two will come off the top regardless, but they will be comprised of the first two cards hit, the first hit (if only one is taken) and an extra card at the end of the regular round, or two cards at the end of the regular round if no hits are taken.



I understand that, and from my experience "burning" those cards will cause player dissatisfaction. In the event no extra cards are drawn there's no problem, but drawing 1 or 2 more cards WILL piss some people off. And I would go as far as to suggest that even players with the sidebet that lose will be as upset as players that are just there for blackjack.

Quote: Mission146


It's really no different than another player sitting at the table, or someone leaving. It chances the distribution, but nobody really knows how it changes it ahead of time.



I think I recall you said in the past that you're more of a slots player. I would suggest you spend some time at a blackjack table just observing if nothing else to see how players react to others joining or leaving mid-shoe. You and I may know that it has no mathematical effect on the outcome but many, many players believe otherwise.

Quote: Mission146


2.) You would not have to stop it immediately after. You could have an electronic outlay that lights up for a Ten-Value Card, Nine, Ace or X for losing card.

If the first card is a 2-8, then it would just be an X because the bet can't win. If the second card is a 9-A, then the outlay would light up 9, 10, J, Q, K or A.

The second hit could come out and would light either an X, 9, 10, J, Q, K or A and then the SB is finished, but the results remain until the dealer clears them. Thus, it could be paid at the end of a hand.



I'm not sure I follow what you're talking about with the electronic stuff. Sounds expensive. I know where I work that sort of thing wouldn't be adopted.

Quote: Mission146


GAME VALUE

I think this adds to the value of the game. Imagine if you are playing the SB and are dealt 14 against a dealer showing Ten. If you hit and bust, you still have a horse in the race...a big horse at that...and reason to remain interested in the rest of the Round!



I understand that part, I have a sidebet I've been working on that would also give the busting player another chance to win, but I think the other issues I outlined would keep your sidebet from being widely adopted.

Above where I suggest you spend some time at the table isn't intended as a jab, I think it would be valuable research for you. I would talk to the players that play sidebets and find out why they like them. I would also talk to non-sidebet players and ask what they would think of the additional draws.
buzzpaff
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June 14th, 2012 at 11:53:48 AM permalink
I would not be exactly thrilled when you burn 1 or2 Aces ! Forget about third base. Now players can scream about a stupid side bet
screwing them !
MonkeyMonkey
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June 14th, 2012 at 11:57:22 AM permalink
Quote: buzzpaff

I would not be exactly thrilled when you burn 1 or2 Aces ! Forget about third base. Now players can scream about a stupid side bet
screwing them !



It wouldn't even have to be aces, players can think of a reason for any known value card that was burned to be a calamity.
buzzpaff
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June 14th, 2012 at 12:13:39 PM permalink
Full table, only one chump plating asinine side bet. Dealer has 6 up, s17. Nobody takes hit. Dealer turns over an A.
I am playing two hands at first base. Dealers burn AK, or KQ. Gee, I surely would love that !
Mission146
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June 14th, 2012 at 2:21:46 PM permalink
Quote: MonkeyMonkey

I understand that, and from my experience "burning" those cards will cause player dissatisfaction. In the event no extra cards are drawn there's no problem, but drawing 1 or 2 more cards WILL piss some people off. And I would go as far as to suggest that even players with the sidebet that lose will be as upset as players that are just there for blackjack.



I agree with you, to a certain extent, because some people are fundamentally irrational.

For counters, just as many favorable as unfavorable cards should be burnt off in the long run. Furthermore, when another player makes a side bet, particularly early in the shoe, counters get to count some cards that they don't have to pay for by gambling more money against the HE. "Free looks," if you will.

Quote:

I think I recall you said in the past that you're more of a slots player. I would suggest you spend some time at a blackjack table just observing if nothing else to see how players react to others joining or leaving mid-shoe. You and I may know that it has no mathematical effect on the outcome but many, many players believe otherwise.



I have said that, and it is true, but I have spent substantial time at the BJ Table, as well. I think that you are still right because some people are irrational, but people who are losing will find something to whine about, regardless.

I can actually understand a counter having problems with people joining mid-shoe during a favorable count because they are losing hands at the positive EV. I can also understand a counter having problems with people leaving early in a shoe because that is more cards they have to pay to see at a negative EV.

With exception to those two things, such feelings are irrational.

Quote:

I'm not sure I follow what you're talking about with the electronic stuff. Sounds expensive. I know where I work that sort of thing wouldn't be adopted.



No more expensive than a Roulette Spins tracker, probably cheaper.


Quote:

I understand that part, I have a sidebet I've been working on that would also give the busting player another chance to win, but I think the other issues I outlined would keep your sidebet from being widely adopted.

Above where I suggest you spend some time at the table isn't intended as a jab, I think it would be valuable research for you. I would talk to the players that play sidebets and find out why they like them. I would also talk to non-sidebet players and ask what they would think of the additional draws.



I take no offense, and I have never asked anyone such questions, so I will. I have, however, spent significant time at the BJ Table. I've spent significant time playing Craps, and some playing Roulette, but there's not much to understand with either. My favorite game is Let It Ride. The games that I would not claim to know anything about and have only played in passing are probably Three-Card and Pai Gow, and I like neither.
https://wizardofvegas.com/forum/off-topic/gripes/11182-pet-peeves/120/#post815219
Mission146
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June 14th, 2012 at 2:25:05 PM permalink
Quote: buzzpaff

Full table, only one chump plating asinine side bet. Dealer has 6 up, s17. Nobody takes hit. Dealer turns over an A.
I am playing two hands at first base. Dealers burn AK, or KQ. Gee, I surely would love that !



You're counting. You're playing at a place with a six-deck shoe. You're nearing 75% penetration, which is the cut-off. The count is +4 ten cards, someone is playing the asinine side bet and nobody takes a hit. The dealer burns a deuce and a four. I'd surely love that, now I'm +6 near the end of the shoe!
https://wizardofvegas.com/forum/off-topic/gripes/11182-pet-peeves/120/#post815219
buzzpaff
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June 14th, 2012 at 2:32:43 PM permalink
Oh Yes Of course how silly of me. Gee whiz the count went from +4 to +6

How wonderful I will feel when my first cards on my 2 hands are now a 5 and a 6 instead of an Ace and a King.
MonkeyMonkey
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June 14th, 2012 at 2:45:35 PM permalink
Quote: Mission146

I agree with you, to a certain extent, because some people are fundamentally irrational.

For counters, just as many favorable as unfavorable cards should be burnt off in the long run. Furthermore, when another player makes a side bet, particularly early in the shoe, counters get to count some cards that they don't have to pay for by gambling more money against the HE. "Free looks," if you will.



Hanging around here you could easily get the idea that most players count, but they don't. In fact, even many that try to count don't do it very successfully.

However, the irrationality is present in nearly every player. As Buzz is illustrating (not to say he's being irrational), many players will not like extra cards being drawn.


Quote: Mission146


I have said that, and it is true, but I have spent substantial time at the BJ Table, as well. I think that you are still right because some people are irrational, but people who are losing will find something to whine about, regardless.



That is certainly true. When people lose they look for anything to blame it on.

Quote: Mission146


I can actually understand a counter having problems with people joining mid-shoe during a favorable count because they are losing hands at the positive EV. I can also understand a counter having problems with people leaving early in a shoe because that is more cards they have to pay to see at a negative EV.

With exception to those two things, such feelings are irrational.



The thing is, it doesn't matter if it's irrational or not, if it pisses people off they won't play.


Quote: Mission146


No more expensive than a Roulette Spins tracker, probably cheaper.



I'm not sure how to explain this except to say that any "unneeded" expense is too expensive. With many sidebets available that don't require extra equipment, yours would be a long shot to adopt.
Mission146
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June 14th, 2012 at 2:51:08 PM permalink
Quote: buzzpaff

Oh Yes Of course how silly of me. Gee whiz the count went from +4 to +6

How wonderful I will feel when my first cards on my 2 hands are now a 5 and a 6 instead of an Ace and a King.



It's the same argument. It works both ways, as does everything else in BJ.
https://wizardofvegas.com/forum/off-topic/gripes/11182-pet-peeves/120/#post815219
Mission146
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June 14th, 2012 at 2:55:52 PM permalink
Quote: MonkeyMonkey

Hanging around here you could easily get the idea that most players count, but they don't. In fact, even many that try to count don't do it very successfully.

However, the irrationality is present in nearly every player. As Buzz is illustrating (not to say he's being irrational), many players will not like extra cards being drawn.



That's true. I guess you want to keep the players as happy as possible, and there will be certainly more players who avoid the side bet than those who make it...because they know that much.


Quote:

The thing is, it doesn't matter if it's irrational or not, if it pisses people off they won't play.



I'll concede that. It could well irritate more players than players who get enjoyment out of it.


Quote:

I'm not sure how to explain this except to say that any "unneeded" expense is too expensive. With many sidebets available that don't require extra equipment, yours would be a long shot to adopt.



I'll also concede that. Do you really think the sidebets simply being paid (or raked) during the round would be that much of a distraction?
https://wizardofvegas.com/forum/off-topic/gripes/11182-pet-peeves/120/#post815219
CrystalMath
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June 14th, 2012 at 3:08:43 PM permalink
I didn't read most of this thread, so forgive me if this has already been covered.

If you do a side bet like this, I would just base it on the dealer's cards. This way if a 10 or an Ace is showing, there's a good chance that the player will lose their main bet, but walk away with a decent pay for a dealer blackjack or 20.

This won't change basic strategy, but I suspect that it is very countable (which I know has been addressed in this thread).
I heart Crystal Math.
Mission146
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June 14th, 2012 at 3:12:33 PM permalink
Quote: CrystalMath

I didn't read most of this thread, so forgive me if this has already been covered.

If you do a side bet like this, I would just base it on the dealer's cards. This way if a 10 or an Ace is showing, there's a good chance that the player will lose their main bet, but walk away with a decent pay for a dealer blackjack or 20.

This won't change basic strategy, but I suspect that it is very countable (which I know has been addressed in this thread).



That's a fantastic idea! If the dealer wins, you win!!!

It still also has the benefit of the player not finding out until the end of a hand, so a player can bust (and if the dealer is showing a 9, 10, J, Q, K or A) the player still has his horse in the race!

The Wizard addressed this countability issue with me. I have decided that there is no choice but to make 20 a, "Push," so I'm waiting to see what he thinks of that.

He scored the game, as before, a "2" on a 0-10 scale, so that could have been worse.
https://wizardofvegas.com/forum/off-topic/gripes/11182-pet-peeves/120/#post815219
MonkeyMonkey
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June 15th, 2012 at 1:21:12 AM permalink
Quote: Mission146

Do you really think the sidebets simply being paid (or raked) during the round would be that much of a distraction?



Now that you're not looking at basing it on the cards drawn by the players it may be a moot point, but yeah, I think if you had to settle the sidebets in the middle of a player hitting it would be very procedurally awkward.
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