Table Games odds and multiple hands

Are there odds stats for multiple hand play? For any and all games with hands.

 

If there are three players at a BJ table, I would think the odds for player #1, #2 and #3 are equal. Right?

So, the fact that you are the player #1, #2 and #3 - I can not see where it would be different.

There are non mathematic reasons that your eventual play might be different such as trying to manage multiple hands or the impact on hand 2 because of how YOU played hand #1, etc.

 

Is this a riddle?

 

Individually played, it's one game per person (even in the event of multiple players). Here is one model. Multiplay is multiple games for one person. This is another model. Each individual hand in the multiplay by this one player has its own odds but combined *together* (as a model) for all of his/her hands they would have different odds. If it does not make sense that the latter would have a different impact than the former then my entire statistical and probability training is null and void.

Now, if there are no statistics out there on it, fine. If it has been said time without number by a mathematician that multiple hands by ONE player makes no difference, show me. And believe me, I will humbly accept. Thanks.

 

OK, I'm only on my second cup of copy, so that might be the problem ...

 

I think its the way you worded it, sco5123. Its not entirely clear what you were after.

Are you asking whether the house edge changes when you play multiple spots?

If so, then no. At blackjack, playing multiple hands your expected loss will be the same. The hands are not completely independent, but are governed by the same odds. Playing 2 hands at $5 50 times should be similar to playing 1 hand of $5 100 times, except the former will have a more variance. Same goes for just about any game I can think of.

 

I'm very confused by what you're asking as well, even after you've attempted to clarify.

Assuming each hand is independent, the odds for each hand are the same whether you play one hand or multiple hands.

Multiple hands by ONE player does make a difference in terms of the overall variance of their game (it INCREASES) but the overall volatility (e.g. standard deviation) per $ bet DECREASES.

Basic stats. Let's say we simplify and assume completely uncorrelated independent variables the total variance is just the sum of the variances. Standard deviation is the square root of that. St dev is what matters because its expressed in terms of the same unit (e.g. dollars).

e.g. sqrt(50) < (sqrt(25) + sqrt(25))

Overall variance increases linearly (in this example) but overall volatility per dollar bet decreases. If we're talking about correlated variables we sum the variances differently but the basic idea is the same that as overall var increases by adding n units the overall st dev per unit decreases.

 

Thank you Nevyn and Kickin! I see!

 

Now, if you had been talking about multiple hands in video poker ... like Triple Play, or 5-Play, or 10-Play ... the payoff EV on each and every line is the same, as each line is dealt from its own separate deck. For example, if you were playing 9/6 JOB (a 99.54% game), every line has a "theoretical" EV of 99.54% ... no more, no less, unless you are making straegical errors in how you play the starting hand.

 

I have no idea what you're asking, but if you're talking about blackjack, in theory there's no difference in playing one hand or multiple hands because the odds are the same. Just like what you do (hit or stay) has no mathematical impact on the outcome of another player's hand.

In practice, this might not be the case. In an extreme example, consider a single deck blackjack table with six players. Before the deal, everyone has the same odds, but since you can see a lot of the cards from the deck, if you're the sixth player the odds could often shift enough where you'd change your play.

So it doesn't change your odds, because the cards are random before they're dealt and you can't change your bet based on the cards, but you could theoretically avoid doubling (or on the other hand, you could double where you normally wouldn't...like doubling 9 against a dealer 3 if there are a ton of high cards left) which would change your EV on that hand if you knew what you were doing (which would go beyond just knowing basic strategy.)

 

It ~could~ make a difference...

...if you're alone at a two-deck table, playing a single hand on negative counts and neutral counts and 5 or 6 hands on positive counts, then the circumstances required for the multi-hand play would, by virtue of math, give you a greater probability of winning for the session versus playing one hand in all circumstances.

This is only true because, with you playing 5 or 6 hands, you will have a greater chance at depleting the (fleeting) abundance of tens and aces even before the dealer gets her cards - (Your initial draw of 10 or 12 cards from a positive deck versus the dealer's 2 cards.)

You can practice this at home with a single deck.
Shuffle.
Then pull out the first five "2 thru 6 value" cards from the top of the deck, leaving the rest of the cards in their original order...(they will all be 7s or better - at least for awhile).
Then, deal out six two-card hands, with the last hand dealt being the "dealer's".
Play the 5 player-hands as you normally would, assuming a "base bet" equally placed on all 5. Play the "dealer" hand using H17.

Then try the same experiment but only deal two hands - yours and the dealer's, with an assumption that you have bet 5x your base bet (instead of playing 5 hands).

You should find that the multi-hand play at a base bet is far more profitable than simply pressing your bet for a single hand on the same positive count.

 

First, I think it's obvious that at games like craps and roulette, the number of players doesn't affect anything. In card games where they shuffle a single deck every time, (all the poker make-a-hand games), the same will be true.

In blackjack, there are some minor effects available. First, there isn't anything that would say playing a single hand against the dealer vs. playing a single hand with 4 other players seated changes anything in any significant way, EXCEPT the number of hands per hour, (so heads-up costs you more per hour, even though each hand is still the same).

Playing two or more hands doesn't change the edge on the game, but reduces the volatility of the overall game, (reduced variance), because you'll get some win/lose combinations you won't get playing a single hand. The two hand are correlated to some degree because they both play against the same dealer hand, but the variance will go down.

And if counting, you can try to play more hands when the count is high, but again, the difference is mostly variance, not edge. Mostly you're putting more money in play when you have the advantage, so you could get a similar result edge-wise just by raising your bet on a single hand.

Somewhere I read that the variance on one hand of $100 is similar to the variance on two hands of $75 each.

 

Not to nitpick (but I will), the overall variance goes UP while standard deviation per dollar bet goes DOWN. You can say its just semantics, but variance isn't expressed in any practical units while st dev always is (e.g. dollars)....var would be square dollars but the wtf is that? There's no linear relationship. Gamblers always say variance goes down in multi-hand play and everyone knows what they mean by it but its just bad terminology. It should be said that standard dev goes down since by default that is expressed in the base units.

On the Wizards site he lists the standard deviation for 1, 2, and 3 hands of BJ play. (http://wizardofodds.com/games/blackjack/appendix/4/)

1. 1.15514
2. 1.34942
3. 1.51957

Therefore....
For 1 hand at $100 the st dev is simply: $100 * sqrt(1) * 1.15514 = $111.514
For 2 hands at $75 each the st dev is: $75 * sqrt(2) * 1.34942 = $143.1276

The variances are just the squares of those....so the overall standard deviation is higher and therefore the overall variance is higher, but the former can be expressed per $ bet in which case the 2 hands at $75 are lower than a single hand at $150.

 

Wade... given the relatively small quantity of cards to be dealt with a positive count on a two-deck game, I would think that playing multiple hands when it happens is better than pressing a single hand - by virtue of there being a greater chance that your multiple hands will consume the majority of the 'positive' cards that immediately exist in the deck. Chances are that, with playing the multiple hands, that next hand will be the last prior to the shuffle...and may very well result in the deck being dealt deeper after the cut card than it might normally be playing head-to-head.
Think of it this way: if the next ten cards are all 9s and 10s - and you're playing head-to-head, you are mathematically 'even' with the dealer it terms of expected outcome on one hand.
If you play 5 hands, at least 4 of your 5 will be either 18, 19 or 20...the dealer's first card will be a 9 or 10, and the second card will be face up.
It would seem to me to far more advantageous to play multiple hands (5) with a very positive count (let's say +5) in a 2-deck game than it is to play head-to-head with a 5x increased bet.

 

Good post, I hadn't seen that page from the WizOfOdds.

I agree I used 'variance' and 'volatility' loosely in my post.

 

There is something to what you say here, but it's not a gigantic factor. And you should modify your bet size, 5 hands at $100 is not the same deviation than 1 hand of $500. (See KChicken's post).

You'll also get bounced pretty quickly if you spread to 3 or more hands every time the count goes up. I think this is much harder to get away with than just raising your bet on one hand. And if anyone else is at the table, you'll usually piss them off (attracting attention from the pit) when you switch from one to many hands.

 

Thanks for that post. It's very informative. I've used variance and SD interchangably, and what I meant was correct, but what I was saying was probably not.