3 hand math- will be ahead of the dealer!
I wanted to ask for your advise regarding a 3 hands (simultaneously).
Mathematically, there is no change in the statistics if you play 1, 3, or 1000 hands simultaneously, that's well agreed.
However, my theory is:
- 8 decks
- Playing simple strategy with 0.5% disadvantage.
- 3 hands (simultaneously).
- Flat bests.
You will be ahead of the dealer!
Why?
Because of the blackJack 3/2.
The odds of getting a blackJack is getting higher e.g, you'll get x3 more blackjacks per session (because you play x3 hands).
Now, the dealer will get x3 blackjacks as well, BUT, you'll get 3/2(payout) x 3 as appose to the dealer's 1/1(payout)x 3
Can someone help with a mathematical formula to prove this?
Thanks
Yes, "the odds of getting a blackJack is getting higher e.g, you'll get x3 more blackjacks per session", but you also lose x3 more when you don't get a blackjack.
But, when you take a look of the payout, If you play more hands and get more blackjacks your overall payout will be higher.
for example:
Dealer get 100 blackjacks = 300 hands lost. 300 units lost
player plays 3 hands
Player get 300 blackjacks = 450 units won.
The house advantage on all other hand is the same (0.5%)
How do you explain the double/triple minimum for multiple hands?
Quote: yot21let's say that Casinos don't care.
How do you explain the double/triple minimum for multiple hands?
I have no idea why in the US they have this rule.
The only possible reason that I can thing is that when the casino is busy, by playing 2-3 boxes of minimum there is opportunity cost for the casino because other players could play the extra boxes with more than minimum.
The rule though is good for a Counter who wants to increase his bets and number of boxes with less suspicion.
As a 'tourist' I would go ahead and open another box to 'change the flow'. The dealer would say, if you want to do that you have to play double the minimum.
"Reluctuntly" I would increase my bets as the dealer demended (and of course as the count warranted).
With regard to playing more boxes, as other people have said there is no change in EV. You logic and BJ example are flawed.
There is though a very minor change in EV for a Counter because of the knowledge of extra cards before making his decision.
OR if this a CSM game, there is a minor change for someone using a Composition Dependent Basic Strategy especially in a Single Deck game.
Quote: yot21let's say that Casinos don't care.
How do you explain the double/triple minimum for multiple hands?
I have no idea why in the US they have this rule.
The only possible reason that I can thing is that when the casino is busy, by playing 2-3 boxes of minimum there is opportunity cost for the casino because other players could play the extra boxes with more than minimum.
The rule though is good for a Counter who wants to increase his bets and number of boxes with less suspicion.
As a 'tourist' I would go ahead and open another box to 'change the flow'. The dealer would say, if you want to do that you have to play double the minimum.
"Reluctuntly" I would increase my bets as the dealer demended (and of course as the count warranted).
With regard to playing more boxes, as other people have said there is no change in EV. You logic and BJ example are flawed.
There is though a very minor change in EV for a Counter because of the knowledge of extra cards before making his decision.
OR if this a CSM game, there is a minor change for someone using a Composition Dependent Basic Strategy especially in a Single Deck game.
Quote: yot21let's say that Casinos don't care.
How do you explain the double/triple minimum for multiple hands?
My understanding is that spreading laterally (multiple hands) is most useful to the player at low counts - the times when the house is more likely to win.
The advantage to the player is that more (low) cards are used up per round, meaning one can get on to the "good" cards more quickly.
By requiring the double/triple minimum bet when the house has the edge, the house stands to win more. (There are probably other reasons, too - if someone is playing every round (as opposed to sitting out / dropping a hand from time to time), it further limits their spread - the ratio of low to high bets. There's probably even some completely other reason they teach in gaming management classes.)
When the count is high, my understanding is that it's more useful to spread "vertically" (more chips on one spot), so that the value of each blackjack and double is maximized.
Quote: yot21You will be ahead of the dealer!
Why?
Because of the blackJack 3/2.
The odds of getting a blackJack is getting higher e.g, you'll get x3 more blackjacks per session (because you play x3 hands).
Now, the dealer will get x3 blackjacks as well, BUT, you'll get 3/2(payout) x 3 as appose to the dealer's 1/1(payout)x 3
Can someone help with a mathematical formula to prove this?
Math Fail. Expectation is linear. End of Proof.
Doesn't matter if the same player is playing three spots, or three players are playing three spots.
Quote: yot21let's say that Casinos don't care.
How do you explain the double/triple minimum for multiple hands?
AceTwo is pretty spot on for your answer as to why they make you bet more for multiple spots. In my experience/opinion it's more (on small levels) all around better for the casino to limit a player to one hand. This way more people can play, they can play the game for potentially higher than the minimum, and it keeps counters from spreading more money on the table across multiple hands. While Dieter has a decent point, and another small instance that helps the casino, most counters won't spread to more hands in a negative count to "eat" the small cards, they'll simply wong out =). As a counter I would never want to put more money on a table at any disadvantage, let alone when I know I'm at a greater than normal disadvantage (negative count).
To again agree your BJ logic is pretty much completely flawed... You get a blackjack ~1/20 hands (simplifying just a bit). Also, when you're when you're flat betting at a .5% disadvantage you'll lose approximately 49% of the hands you play (push ~9% and win ~42%). You can look these numbers up to verify on the Wizards site. So out of these 20 hands for just one spot, you'll lose ~10 hands, push ~2 hands, and win ~8 hands. The blackjack you're referring to is counting in to these ~8 wins.
When you spread to 3 spots, absolutely nothing changes. You simply multiply everything by 3... So yes, you will get 3x the blackjacks, but instead of losing ~10 hands, you're going to lose ~30 hands out of the 60 you play (20x3). Of the ~24 hands you'll win (8x3) the 'extra' 2 blackjacks are counted in here. Thus, like others have said your logic is flawed. You get more blackjack's, but you lose more hands. By your logic why don't you just play all 6 spots at the table betting really big? After all, 6x the blackjacks means you'll make way more than 3x the blackjacks! There's a reason you see absolutely no one doing this...
Quote: dwheatleyMath Fail. Expectation is linear. End of Proof.
Love it! Very elegant.
Quote: yot21let's say that Casinos don't care.
How do you explain the double/triple minimum for multiple hands?
Because they don't want some low-roller taking up all the spots at the table min-betting when someone who is going to bet bigger can't get a seat.
Some casinos will only enforce this selectively (ie, during busy times). During slow times they will tell the person that they can bet multiple hands at the table minimum, but they reserve the right to change their mind about that later if things pick up.
Also, some casinos just don't have this rule.
Quote: HughJassLove it! Very elegant.
Yup.
I think that the answer to 99% of the questions on this forum is "because E(X) + E(Y) = E(X+Y)".
Furthermore, from a statistic point of view, there is an issue of dependent vs non-dependent event.
The three hands become a dependent-events.
I see what you're all saying, but I think there is more to it.
Think on the the 3-hands as one event.
I a one hand play you are getting "win" "lose" "bj" or "push"
3-hands as one event is statistically different:
win,win,win
win,win,lose,
win,win,push
win,win,bj
lose,win,win
lose,win,lose
etc.
Quote: yot21I'm talking about payouts, not win/lose rate.
Furthermore, from a statistic point of view, there is an issue of dependent vs non-dependent event.
The three hands become a dependent-events.
I see what you're all saying, but I think there is more to it.
Think on the the 3-hands as one event.
I a one hand play you are getting "win" "lose" "bj" or "push"
3-hands as one event is statistically different:
win,win,win
win,win,lose,
win,win,push
win,win,bj
lose,win,win
lose,win,lose
etc.
While these are the possible outcomes, they're not necessarily the probable outcomes. Ignoring pushes, doing what you did there has 12 wins and 12 loses which would indicate an equal chance of wining and losing, which is NOT the case in blackjack. As I said before you can find the numbers on the Wizard's site. You lose ~49% of the time, push ~9% of the time, and win ~42% of the time. Each one of these hands is subject to these numbers (off the top). They share co-variance, but are still independent hands from one another and...
Eh, you know what, try it out and let us know how it goes =D.
I don't understand how it is you can't see the logic behind 3 different people playing 3 spots, or one person playing 3 spots.
Fyi, there are individual video BJ machines you can play 7 spots.
Quote: yot21Hi to all the math wizards out there.
I wanted to ask for your advise regarding a 3 hands (simultaneously).
Mathematically, there is no change in the statistics if you play 1, 3, or 1000 hands simultaneously, that's well agreed.
However, my theory is:
- 8 decks
- Playing simple strategy with 0.5% disadvantage.
- 3 hands (simultaneously).
- Flat bests.
You will be ahead of the dealer!
Why?
Because of the blackJack 3/2.
The odds of getting a blackJack is getting higher e.g, you'll get x3 more blackjacks per session (because you play x3 hands).
Now, the dealer will get x3 blackjacks as well, BUT, you'll get 3/2(payout) x 3 as appose to the dealer's 1/1(payout)x 3
Can someone help with a mathematical formula to prove this?
Thanks
You will lose 0.5% of the total amount wagered. Blackjack payouts are already figured in. Bet more and lose more. Lose even more at casinos that require two or three times the bet to open extra hands.
Quote: yot21Furthermore, from a statistic point of view, there is an issue of dependent vs non-dependent event.
Expectation is additive regardless of whether the events are dependent (or even correlated). Expectation is extremely easy to work with because of this property.
Quote:3-hands as one event is statistically different
They are statistically different (they have different variances) but the expectation of 3 hands is just 3x the expectation of one hand. That means that by playing 3 hands you lose 3x as much as you do by playing 1 hand. That is a funny definition of "ahead of the dealer"; most people would call that "behind by 3x as much".
Quote: AxelWolfSome other guy thinks the same thing about side bets. Claiming he is beating his buddy for thousands.
Same guy: -300
Quote: Romesmost counters won't spread to more hands in a negative count to "eat" the small cards, they'll simply wong out =).
It's not an ideal play, to be sure. Multihand card eating is vaguely feasible for 2x or 3x minimum bet, but significantly loses appeal for 4x or 9x minimum bet. If you're eating cards, it should be to accelerate an impending shuffle, or to see if a few hands of low cards turns the deck around.
My understanding is that card eating play is different from basic strategy play - no doubles, more hits, even against "bust cards".
Quote: DieterIt's not an ideal play, to be sure. Multihand card eating is vaguely feasible for 2x or 3x minimum bet,
I've never understood this.
Suppose they let you play as many hands as you want for your minimum bet, and you are heads up with the dealer. Each hand (dealer or player) takes 2.7 cards on average. Maybe if you are intentionally eating cards, you can get up to a 3-card average for the player hand (probably generous).
So if you play 1 hand at the table minimum you make 1 bet per 5.7 cards dealt.
If you play 2 hands at the table minimum you make 2 bets per 8.7 cards dealt, or 1 bet per 4.35 cards dealt.
How is this "eating cards" exactly? It seems to have the opposite of the intended effect (which is to bet at little as possible at negative counts)
Quote: AxiomOfChoiceSo if you play 1 hand at the table minimum you make 1 bet per 5.7 cards dealt.
If you play 2 hands at the table minimum you make 2 bets per 8.7 cards dealt, or 1 bet per 4.35 cards dealt.
You would go by the number of hands, not bets.
1 bet (2 players including dealer) = 5.7 / 2 = 2.85
2 bets (3 players including dealer) = 8.7 / 3 = 2.9
I agree entirely that it's a wasted effort.
Card eating in general is a practice best left to the ploppies =). The principal rule of a card counter is to bet more when you have the advantage, and less when you don't. I would never put more money on the table with less of an advantage, and one it hit's TC <= -1, I'm out. I'm even more of a 'straight through' player than someone who constantly Wong's.
Quote: RomesYou would go by the number of hands, not bets.
1 bet (2 players including dealer) = 5.7 / 2 = 2.85
2 bets (3 players including dealer) = 8.7 / 3 = 2.9
I agree entirely that it's a wasted effort.
That doesn't make sense. Why are you dividing by the number of hands, including the dealer? The point is, you want to get through the negative count as cheaply as possible. You want to bet at little as possible per card. Betting 0 (wonging out) is optimal. If that is not an option, the next best is 1 hand. Playing 2 hands does not "eat" more cards per unit bet, which is the only thing that matters.
You said it. Why try to contradict it then?Quote: yot21Mathematically, there is no change in the statistics if you play 1, 3, or 1000 hands simultaneously, that's well agreed.
Quote: AxiomOfChoiceThat doesn't make sense. Why are you dividing by the number of hands, including the dealer? The point is, you want to get through the negative count as cheaply as possible. You want to bet at little as possible per card. Betting 0 (wonging out) is optimal. If that is not an option, the next best is 1 hand. Playing 2 hands does not "eat" more cards per unit bet, which is the only thing that matters.
I was even ignoring the monetary value just to show that even playing another hand doesn't really help at all. I was just showing the average cards per player and how adding another hand and generously rounding up to 3 cards, as you did, still doesn't raise the overall table average by more than .05. Obviously below that I addressed how regardless you shouldn't put more money on the table when you're not at an advantage, let alone less than 'normal' advantage.
Quote: AxiomOfChoiceSame guy: -300
Does not appear to be at the moment.
Quote: AxiomOfChoiceEach hand (dealer or player) takes 2.7 cards on average. Maybe if you are intentionally eating cards, you can get up to a 3-card average for the player hand (probably generous).
My understanding is that the "2.7 cards" number is based on standard dealer draw rules and basic strategy. Card eating strategy should go something like "always hit to at least hard 17 (even with a dealer showing a bust card), don't split aces (hit - you can take more cards, as long as you don't pull a 9 first), always hit soft 18/19..."
Basic strategy is about playing the current hand so that the current hand has the greatest possible expected value.
Card eating is about playing the current hand to create a future expected value.
It probably doesn't make sense to go card eating for more than a few hands - you should be able to win back your losses on the next increased bet.
If it doesn't make sense to you, don't do it.
Quote: AxiomOfChoiceIt seems to have the opposite of the intended effect (which is to bet at little as possible at negative counts)
I am told that there are places where the distance to the next table is measured in hours, rather than footsteps. In some of these places, management refuses to shuffle at the player's request. In some of these same places, management has a policy of disallowing someone who has left a game "dead" to re-enter until after they sort & spread the cards, and a full shoe has been played in between. Some of these places won't let you jump in and out ("If a player plays a hand, and then declines to play any subsequent hand, that player may not play another hand on the same table until after a shuffle has occurred.").
Sometimes, players decide it is preferable to trade money for time.
If you are able to walk 20 steps to a better game and jump right in, that's almost surely a better tactic.
In the meanwhile let me try to explain why I'm thinking that 3 hands is different.
The blackjack combinatorial aspect here is quite unique.
I can't really put my finger on the exact formula, and would love to get any help.
The difference here is not 1:3 (same result as playing one hand x 3) like people here mentioned before, because all three hand are being played against the SAME DEALER'S HAND.
It would be 3:1 ONLY IF the Dealer was using different up-card for each of the payer's hands, and was using the same face-down card for all three hands.
Can someone here have the combinatorial formula for this kind of game?
Quote: yot21
The difference here is not 1:3 (same result as playing one hand x 3) like people here mentioned before, because all three hand are being played against the SAME DEALER'S HAND.
It would be 3:1 ONLY IF the Dealer was using different up-card for each of the payer's hands, and was using the same face-down card for all three hands.
By getting more hands in, you approach the long run expectation more quickly. Since you've said you're playing simple strategy with a .5% disadvantage, that means you'll go broke more quickly.
It's easy to get misled, and quite tempting to think about it incorrectly.
Quote: yot21I'm trying too. So far I am winning un the short run, but very very (very) far from validating it for the long-run.
In the meanwhile let me try to explain why I'm thinking that 3 hands is different.
The blackjack combinatorial aspect here is quite unique.
I can't really put my finger on the exact formula, and would love to get any help.
The difference here is not 1:3 (same result as playing one hand x 3) like people here mentioned before, because all three hand are being played against the SAME DEALER'S HAND.
It would be 3:1 ONLY IF the Dealer was using different up-card for each of the payer's hands, and was using the same face-down card for all three hands.
Can someone here have the combinatorial formula for this kind of game?
Can we put this to rest? Your hands share some co-variance and that's it. It's also pointed out in Standford Wong's Professional Blackjack that spreading to more than 2 hands actually has a negative effect on your EV. If you want to know more about those two subjects, please go buy the book Professional Blackjack. Putting all of that aside, if you can't see how playing 3 hands at a .5% HE is ~3x as worse as playing 1 hands at a .5% HE then you shouldn't be playing blackjack or doing anything that involves numbers in anyway. For the last time the "blackjack" effect is already calculated and counted for in the .5% HE.
Combinatorial? At this point I figure the discussion should be successfully closed. Anything further would indicate simple trolling.
Quote: DieterI am told that there are places where the distance to the next table is measured in hours, rather than footsteps. In some of these places, management refuses to shuffle at the player's request. In some of these same places, management has a policy of disallowing someone who has left a game "dead" to re-enter until after they sort & spread the cards, and a full shoe has been played in between. Some of these places won't let you jump in and out ("If a player plays a hand, and then declines to play any subsequent hand, that player may not play another hand on the same table until after a shuffle has occurred.").
Sometimes, players decide it is preferable to trade money for time.
If you are able to walk 20 steps to a better game and jump right in, that's almost surely a better tactic.
That is all fair enough. My point is just that it is cheaper to get through the deck playing one hand than playing 2, even if you can play 2 at the minimum.
So, if you want to eat cards, eat cards, but do it while playing 1 hand rather than playing 2.
Quote: yot21I'm trying too. So far I am winning un the short run, but very very (very) far from validating it for the long-run.
In the meanwhile let me try to explain why I'm thinking that 3 hands is different.
The blackjack combinatorial aspect here is quite unique.
I can't really put my finger on the exact formula, and would love to get any help.
The difference here is not 1:3 (same result as playing one hand x 3) like people here mentioned before, because all three hand are being played against the SAME DEALER'S HAND.
It would be 3:1 ONLY IF the Dealer was using different up-card for each of the payer's hands, and was using the same face-down card for all three hands.
Can someone here have the combinatorial formula for this kind of game?
The formula is that the expectation of 3 hands is 3x the expectation of 1 hand. The fact that all 3 are being played against the same dealer's hand doesn't change that. The fact that the outcomes of the hands are correlated doesn't change that. Nothing changes that. Expectation is additive, always, no matter what. If you don't understand that one simple concept then you don't understand anything about the mathematics of gambling. It is the first, most basic, most fundamental, and most important concept in gambling.
You should either learn some basic math, or believe what the mathematicians tell you. Refusing to learn even the most basic of math but stubbornly arguing against people who do understand it (and, in some cases, have studied it for years) makes no sense whatsoever.
Quote: AxiomOfChoiceSo, if you want to eat cards, eat cards, but do it while playing 1 hand rather than playing 2.
I guess I'd need to do some stopwatch work to figure if there's a significant improvement in cards-per-minute with one player on 1 vs 2 vs 3 spots.
That's really the tradeoff; either aiming to conserve money, or to conserve time.
Quote: DieterI guess I'd need to do some stopwatch work to figure if there's a significant improvement in cards-per-minute with one player on 1 vs 2 vs 3 spots.
That's really the tradeoff; either aiming to conserve money, or to conserve time.
Oh, I didn't realize that you were aiming to save time rather than money.
