Extra Bet Blackjack
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6 members have voted
Depending on the rules, if the player has a 10-point card as his first card, lacking any other information, he will have an advantage of about 14%, depending on the rules. Let's look at these rules, for sake of discussion:
Six decks
Dealer hits soft 17
Double any first two cards
Double after split allowed
Re-split any pair, including aces, up to three times (or four hands)
I'm showing under these rules a player advantage of 14.14%. Paying a fee of 20% is obviously steep. I would define the expected loss as (0.2-0.1414)/1.2 = 4.88%. (edited)
BTW, if the number 1.414 looks familiar, it is the first four digits of the square root of 2.
Does anyone have any other information to shed on this bet? Any comments or disagreements?
The question for the poll is would you invoke this "Extra Bet" option?
Quote: WizardI heard the Grand Sierra in Reno introduced a blackjack variant called Extra Bet Blackjack earlier this month. If my understanding is correct, the concept is pretty simple -- if the player is dealt a 10-point card as his first card, before the dealer's up card is dealt, he has the option to increase his bet. I think by up to 5x. That catch is that he must pay a fee of 20% of this additional wager. This fee is a one-time only thing and is totally non-refundable.
Depending on the rules, if the player has a 10-point card as his first card, lacking any other information, he will have an advantage of about 14%, depending on the rules. Let's look at these rules, for sake of discussion:
Six decks
Dealer hits soft 17
Double any first two cards
Double after split allowed
Re-split any pair, including aces, up to three times (or four hands)
I'm showing under these rules a player advantage of 14.14%. Paying a fee of 20% is obviously steep. I would define the expected return as 1.414/1.2 = 70.7%, or a house edge of 29.3% (ouch!).
BTW, if the number 1.414 looks familiar, it is the first four digits of the square root of 2.
Does anyone have any other information to shed on this bet? Any comments or disagreements?
The question for the poll is would you invoke this "Extra Bet" option?
Would a player who made the extra bet be allowed to split his 10s for the extra bet amount without a second fee? If so, perhaps in some situations it might not be such a bad bet.
I'm trying to understand the HE calculation. I'm missing something, because if there's a 14% PA to the bet, and they charge 20%, I would have thought the HA was a simple 6%. Still too much, but not nearly 30% (Yikes!).
Would you mind getting into more detail about how you arrived at the formula, and/or correct the flaw in my thinking?
Also why do you do 1.41? It should be 1.14, I think? 1.14 = 114% = 100% + 14% advantage?
I'd think 1.14/1.2 = 0.95 = 95% = 5% HE.
You then add $100 bet and lose $20 immediately (up front vig).
Expected return is $114 on your $100 bet. But of course, you've already lost $20. So you're expected return is $94.
I don't really understand or like adding in the vig to determine the HE. You wouldn't include the vig as part of your bet if you had to pay it after the fact, would you? Now what if you ALWAYS had to pay vig afterwards, even if you lose?
IE: You have a $100 buy bet on the 4 in craps and you pay vig after win only. 2/3 the time you lose $100. 1/3 the time you win $195. Overall you're down $5 over $300 in action = 1.66% HE.
I say a 6% HE.
Quote: IbeatyouracesI'm curious to know how the house edge is affected at various true counts.
+EV at TC +9 lol
https://blackjackincolor.com/z800Chart.gif
Quote: RSWell you're going to be getting a T first in regular blackjack, so that part shouldn't change. The calculation should only be based on the additional bet(s). Otherwise, you'd have to remove the advantage in the base game for situations where you're getting a T first. So instead of the base game having a 0.5% HE (for example), you'd have to increase that number (it's the HE). But that doesn't even make sense.
Once you are starting off with a ten you are no longer at a 0.5 disadvantage, you are at a 14 % advantage, so I thought you would include it in the calculation.
Quote: beachbumbabs
Would a player who made the extra bet be allowed to split his 10s for the extra bet amount without a second fee? If so, perhaps in some situations it might not be such a bad bet.
It's my understanding that the answer is he wouldn't have to repay the fee to split. At some count, yes, the odds would favor paying the fee. I may do some math to calculate at what count the player should do so.
BTW, I did a long simulation overnight. For the rules stated above, the player advantage with a 10 as the first card is 14.1384%.
Quote:I'm trying to understand the HE calculation. I'm missing something, because if there's a 14% PA to the bet, and they charge 20%, I would have thought the HA was a simple 6%. Still too much, but not nearly 30% (Yikes!).
Would you mind getting into more detail about how you arrived at the formula, and/or correct the flaw in my thinking?
Let's say the player bets an extra $100 as his supplemental bet after a 10, plus the $20 fee. His expected win from the $100 is $14.14. However, he is still down $20 from the fee, so a net loss of $5.86. $5.86/$120 = 4.88%. So, let me amend my answer to say a house edge of 4.88%. I previously was incorrectly dividing by the fee.
Quote: RSI'd think 1.14/1.2 = 0.95 = 95% = 5% HE.
I agree. See my post above.
Quote: WizardIt's my understanding that the answer is he wouldn't have to repay the fee to split. At some count, yes, the odds would favor paying the fee. I may do some math to calculate at what count the player should do so.
BTW, I did a long simulation overnight. For the rules stated above, the player advantage with a 10 as the first card is 14.1384%.
Let's say the player bets an extra $100 as his supplemental bet after a 10, plus the $20 fee. His expected win from the $100 is $14.14. However, he is still down $20 from the fee, so a net loss of $5.86. $5.86/$120 = 4.88%. So, let me amend my answer to say a house edge of 4.88%. I previously was incorrectly dividing by the fee.
So if you were to look at this like a pass line bet and taking odds what would be the edge on the total amount of money in action ie..$120?
Quote: ZenKinG+EV at TC +9 lol
https://blackjackincolor.com/z800Chart.gif
The text that goes with this: https://www.blackjackincolor.com/cardcountingextra4.htm
Ten is the second line from the top.
Quote: HunterhillSo if you were to look at this like a pass line bet and taking odds what would be the edge on the total amount of money in action ie..$120?
Yes. I have in my craps page a blended house edge between the pass and maximum odds.
Quote: QFITThe text that goes with this: https://www.blackjackincolor.com/cardcountingextra4.htm
Ten is the second line from the top.
Thanks. Looks like the advantage of the 10 reaches 20% at about a true count of +8.
As always, I welcome all questions, comments, and especially corrections.
However, I can see players with bankroll and/or alcohol in their system putting down $60 (to bet $50) on a $10 bet and lose $3.00 ($2.90 + $.10 on the original hand) on average vs .$10 if the bet had not been available. A casino might see that potential gain reason enough to make it available and slow down the rest of the game.
Quote: boymimboIn my opinion, this would slow the game down tremendously. I am not sure whether a 4.88% HA is worth slowing the game down by a decent factor. The whole reason why BJ is so profitable for a casino is hands per hour (and stupid players).
I disagree there. I'm sure the casino would rather have a 4.88% edge than the 0.6% they currently have under the base rules. It also isn't like this is a 5% edge on $1. Players can bet up to 5x the original wager on the Extra Bet.
Quote: boymimboIn my opinion, this would slow the game down tremendously.
I agree with this- all these sidebets slow down the game, and the reason, from the casino's point of view, is that the slowdown is to its benefit, since the house edge on any sidebet is higher than the regular game. Otherwise, why halt play with an option that is worse from the house's point of view?
There are two other factors that I think will detract from this one.
First is complexity. Sidebet players are not the brightest bulbs on the tree. Match The Dealer is about the limit of the recreational player's mental capacity. FreeBet and Super 4 Progressive? How many times can you say "Dealer 22 is a push" or "dealer has to have blackjack". Maybe the complexity hides the bad HE, and the ploppies do bet the sidebets out there already. But I think this one might be off-putting because of the need to make decisions in the middle of the hand.
Second is dealer acceptance. I've heard that ASMs have a tendancy to break down for unknown reasons - mysteriously so - due to dealer resistance. They become dealing robots, they don't get any pause in the routine, they can't talk up the players, it's just deal, deal, deal. Freebet was resisted where I play - somewhat because the casino didn't train the staff adequately, but also because the dealers didn't want to bother. Match the Dealer works for them because it's a fluid, constant part of the flow of the game. This one sounds like a lot of back and forth between the dealer and the player, rinse and repeat for each one at the table.
I hate all of the sidebets. They slow down the game too much, Although they do add to the casino's take, and NONE of that money comes from me.
Quote: racquetI agree with this- all these sidebets slow down the game,
I agree with that as a generality but not for every single game. I'd like to see information on how often players invoke the Extra Bet there in Reno before making any judgments specifically on that game. If usage is high, I think it will increase revenue at the table.
That mindset influences where they put the cut-card, how fearful they are of APs, how they award comps.
Their scientific method will involve putting the game in a few pits, without spending valuable down-time training and motivating dealers to promote the game. Dealers will show up at a table and need to have the players tell them the rules of the game. I've seen that with my own eyes. Why bother training the dealers for a game that has a limited half-life, and differs from business-as-usual.
I've played FreeBet at a casino in downtown Las Vegas where ALL the dealers could deal it faster than I could play, and talked it up at the same time. I've read that FreeBet has a higher HE than regulation BJ. But my bet is that it's true ONLY at a casino where the dealers are committed to it and know how to deal it. I also played it back East where it on;y lasted for a couple of months.
If I were a game developer, I'd be scared that as good as my game is, I'm at the mercy of an old-school director of table games and a bunch of apathetic, untrained dealers.
Also, 14.02% is the value from the BJSTRAT.net calculator, which is a highly respected calculator (e.g., J.B. has spoken highly of it!)
Given an initial 10, there is no chance of splitting (or doubling), so those kind of complications don't exist.
Quote: gordonm888I got EV of 14.02% for 6-deck, H17, BJ pays 3-2: not sure why the difference from your 14.16% result. I get 13.99% for single deck.
Also, 14.02% is the value from the BJSTRAT.net calculator, which is a highly respected calculator (e.g., J.B. has spoken highly of it!)
Given an initial 10, there is no chance of splitting (or doubling), so those kind of complications don't exist.
Why couldn't you split with an initial 10?
Quote: gordonm888I got EV of 14.02% for 6-deck, H17, BJ pays 3-2: not sure why the difference from your 14.16% result.
What did you put in for:
Surrender
Re-splitting aces
Doubling restrictions
Maximum number of hands to re-split to
Quote: HunterhillWhy couldn't you split with an initial 10?
It's not that you can't, it's that you wouldn't ever want to, since splitting is -EV. Same with doubling down.
Quote: boymimboIn my opinion, this would slow the game down tremendously.
1. Deal all of the players first card only. Do not deal a card for the dealer yet.
2. Anyone with a 10 decides to make the 5x raise or not.
3. Finish dealing the rest of the hand as normal.
Of course #1 is true.
Number 2 is as follows:
- Dealer has to offer the 5x bet.
- Player has to decide and fumble for bet which must be in increments of $5.
- Dealer has to make change for 20%, which will be to:
-- count out the bet-
-- calculate 20%
-- exchange greens for reds, and reds for whites at 4:5.
- and better not error!
Then do #3
- Then deal out the rest of the hand.
I think it will slow down the game by a factor 2 or 3.
A thought to speed it up slightly:
- Player makes decision to bet the 10x before the deal.
- When the player receives a 10, dealer either pushes the bet back (no 10) or leaves the bet up.
- At decision time, dealer either takes entire bet (lose), 20% of bet (push) or pays the player 80% (win)
Quote: WizardWhat did you put in for:
Surrender
Re-splitting aces
Doubling restrictions
Maximum number of hands to re-split to
No surrender. Resplitting aces, resplitting other pairs and doubling are not relevant to a probabilistic calculation of a single hand, which is what I did. Maybe they were relevant to your shoe calculation, if you are factoring in depletion of small cards as you run through a shoe ???
edit: if you are modeling millions of hands from a shoe and just keeping statistics on the player hands starting with a 10, then perhaps you are averaging over the fluctuations in card composition: e.g., if you were to "average" the player EV when the shoe is ace-rich, ace-poor and ace neutral it will not be the same as when the shoe is ace-neutral. I am doing a probabilistic (or combinatorial) calculation, which is correct for a statistically average deck, but is not the statistical average over fluctations in card composition, which may be what you are calculating.
Quote: gordonm888No surrender. Resplitting aces, resplitting other pairs and doubling are not relevant to a probabilistic calculation of a single hand, which is what I did. Maybe they were relevant to your shoe calculation, if you are factoring in depletion of small cards as you run through a shoe ???
I assumed surrender is allowed.
Quote:edit: if you are modeling millions of hands from a shoe and just keeping statistics on the player hands starting with a 10, then perhaps you are averaging over the fluctuations in card composition: e.g., if you were to "average" the player EV when the shoe is ace-rich, ace-poor and ace neutral it will not be the same as when the shoe is ace-neutral.
I did a simulation with 75% penetration, looking only at hands where the first card was a 10.
Quote: WizardI assumed surrender is allowed.
Okay, when I add late surrender to my calculation, the EV of a Ten-valued card goes from 14.04% to 14.14%
Quote: WizardI did a simulation with 75% penetration, looking only at hands where the first card was a 10.
So this difference in methodology presumably accounts for the difference between 14.16% (your value) and the 14.14% I calculate. I believe that my result is rigorously correct for the case when a player is dealt a 10 from a fresh 6-deck shoe. Your calculation is more meaningful than mine, however, because it factors in the fluctuations in card composition (and count) of the shoe during the course of play. When drawing to a 10, I would expect that simulations that include the fluctuation in card composition of a shoe would yield a slightly higher EV than the combinatorial calculation that assumes a fresh shoe. And, that is exactly what we see! - apparently the composition variations increase the effective EV of drawing to a 10 by 0.02%. Interesting.
Quote: gordonm888Okay, when I add late surrender to my calculation, the EV of a Ten-valued card goes from 14.04% to 14.14%
Glad to hear it.
Quote:So this difference in methodology presumably accounts for the difference between 14.16% (your value) and the 14.14% I calculate. I believe that my result is rigorously correct for the case when a player is dealt a 10 from a fresh 6-deck shoe. Your calculation is more meaningful than mine, however, because it factors in the fluctuations in card composition (and count) of the shoe during the course of play. When drawing to a 10, I would expect that simulations that include the fluctuation in card composition of a shoe would yield a slightly higher EV than the combinatorial calculation that assumes a fresh shoe. And, that is exactly what we see! - apparently the composition variations increase the effective EV of drawing to a 10 by 0.02%. Interesting.
We could probably spend a long time and some very rigorous analysis on that 0.02%. I will say that I don't think that the your "neutral shoe" is a good explanation. In a six-deck shoe, the beginning of the shoe is just as likely to be rich in high or low cards as any other point in the shoe. Before going further, let me do another simulation that is just the first 30 hands in the shoe and see what happens. The result should be the same as just the first hand after a shuffle.
Alternately, when the shoe is depleted in low cards, you will make a 12-16 less frequently but the probability of busting a 12-14 is now higher than average -because, by definition, the shoe is depleted in low cards.
These effects tend to wash each other out but they don't perfectly cancel each other - because there are more stiff hands when the deck is rich in low cards (as compared to when the deck is depleted in low cards), so overall there is a net bias towards higher EV when hitting a Ten.
Quote: gordonm888When the count is high (shoe is rich in low cards) there will be a higher frequency of making 12-16, but the outcomes will be better than normal for hitting those stiff hands (at least for hands that are not surrendered such as 12-14) because there are more low cards in the shoe (so player busts less frequently than normal.).)
Alternately, when the shoe is depleted in low cards, you will make a 12-16 less frequently but the probability of busting a 12-14 is now higher than average -because, by definition, the shoe is depleted in low cards.
These effects tend to wash each other out but they don't perfectly cancel each other - because there are more stiff hands when the deck is rich in low cards (as compared to when the deck is depleted in low cards), so overall there is a net bias towards higher EV when hitting a Ten.
I don't dispute any of that.
I'm sure this mathematical issue has been discussed before in several BJ books/forums (fora?) and has some quasi-official name. It probably has not been previously quantified for the specific case of a player 10 versus a "TBD dealer upcard." And no one who is not a complete nerd would care about it, anyway.
Quote: gordonm888Bingo! Good news, thank for doing that calc.
You're welcome. Thanks also to you for your work on this.
Quote:I'm sure this mathematical issue has been discussed before in several BJ books/forums (fora?) and has some quasi-official name. It probably has not been previously quantified for the specific case of a player 10 versus a "TBD dealer upcard." And no one who is not a complete nerd would care about it, anyway.
I still say this is a tangent to the cut card effect. It has been discussed here and there for years. If I didn't have to put rice on my table I'd love to do a rigorous academic-level paper on the topic. However, the number of people who would care could probably be counted on two hands.
Quote: QFITBut, I'm still one of those fingers, however many you might have.
Count me as another finger. I'm not going to fuss with simulating it but would be interested should someone else bother with it.
