Floating Point Variance

[assume_R]

So as I understand it, the floating point advantage measures how the TC advantage changes as you get deeper into the shoe.

My thought is that wouldn't the variance decrease as you get deeper also? Because a TC=+10 early means that it could be spread out over a lot more cards, while a TC=+10 towards the cut card means that there are less cards that the "advantage cards" are spread out over, and hence the variance would be lower.

Correct logic?

 

[creeping panther]

Assume

So as I understand it, the floating point advantage measures how the TC advantage changes as you get deeper into the shoe.

My thought is that wouldn't the variance decrease as you get deeper also? Because a TC=+10 early means that it could be spread out over a lot more cards, while a TC=+10 towards the cut card means that there are less cards that the "advantage cards" are spread out over, and hence the variance would be lower.

Correct logic?

Let me ask you this, would you rather go to Max bet with a TC+10 with 1 deck left or 3,,,Hmmmmm.

You know the answer...it is called the floating advantage.

CP

 

[assume_R]

Yeah, definitely with 1 deck left, because I know the EV at each TC increases a bit, but I was wondering if, in addition to the EV increasing, the variance decreases.

 

[jack.jackson]

Not only are your bets influened, but your hands are as well. I double,split, and stand more frequently late in the deck. Depending on your TC of course.

 

[assume_R]

Yeah, I was actually just reading the Index Deviation thread you linked to, a few minutes ago http://www.blackjackinfo.com/bb/showthread.php?t=16797&highlight=index+deviation

and it's interesting, because let's see even for balanced systems, different indices can be generated for different # of decks used (2D indices can be pretty different from 8D indices), which logically means that the TC does NOT mean the same with 1 deck remaining in each situation.

So we've established that indices, and EV are affected. Only that one last question I was wondering about variance

 

[creeping panther]

assume

Yeah, definitely with 1 deck left, because I know the EV at each TC increases a bit, but I was wondering if, in addition to the EV increasing, the variance decreases.

I only play LS games, with one deck left with tc+10 I say it decreases,:laugh: if I make the hands, great, if not I use LS with aggression. I would always be prepared for the dealer to make their hands, and if playing dd with the ace SC, I would be even better prepared. last weekend I ran into just such a situation, DD, 3 aces left, tc +12, 20 cards left, I had to do it, pushed out all my chips on 2 spots, $200 each, the extras were pushed back, I had to sweat the dealer having a 10 up or ace up, dealer pulled the ace, I checked under first hand 20, second hand BJ, took even on the BJ and insured the 20, dealer had no BJ, pulled to pat hand, I won....but I was sweating. Ya, one other player with a $5 bet also had a BJ. The pit gave me a very disgusting look as my prior bet was $30 on each hand of two.

CP

 

[assume_R]

ha thanks cp for the advice and story, i always do enjoy reading about your experiences :eyepatch:

 

[bj bob]

I had to do it, pushed out all my chips on 2 spots, $200 each, The pit gave me a very disgusting look as my prior bet was $30 on each hand of two.

CP

Jesus, CP. You got away with a (launch?) ramp like that? You've either got a classic set or they must really love you there.

 

[bigplayer]

Floating Advantage

Let me ask you this, would you rather go to Max bet with a TC+10 with 1 deck left or 3,,,Hmmmmm.

You know the answer...it is called the floating advantage.

CP

I'd go to a max bet on both without hesitation, but if I have a choice between TC +10 with 1 deck left or 3 decks left I'll take the 3 decks left as long as I can keep on playing out the rest of the shoe. Obviously if I can only play one round I'll take the TC of +10 with 1 deck left as the Floating Advantage yields about +0.5% extra edge. With 2 decks left FA would get an about an extra 0.2%.

The floating advantage comes from the relatively increased effect that the removal of individual cards has on the percentage composition of the remaining cards. If the count is +10 with 1 deck left and Aces are balanced if you catch a 10 as your first card you have a better chance of a blackjack than you do with the same +10 TC and balanced Aces with 5 decks left. This same effect is why the house advantage is lower for single deck games than it is for six deck games.

 

[creeping panther]

Big

I'd go to a max bet on both without hesitation, but if I have a choice between TC +10 with 1 deck left or 3 decks left I'll take the 3 decks left as long as I can keep on playing out the rest of the shoe. Obviously if I can only play one round I'll take the TC of +10 with 1 deck left as the Floating Advantage yields about +0.5% extra edge. With 2 decks left FA would get an about an extra 0.2%.

The floating advantage comes from the relatively increased effect that the removal of individual cards has on the percentage composition of the remaining cards. If the count is +10 with 1 deck left and Aces are balanced if you catch a 10 as your first card you have a better chance of a blackjack than you do with the same +10 TC and balanced Aces with 5 decks left. This same effect is why the house advantage is lower for single deck games than it is for six deck games.

Thanks for the post, very good info on the Floating Advantage.

CP

 

[chessplayer]

Nope. If you have 10 as first card and the TC is the same(If the average number of ACe removced is the same), you have the equal chances of catchin the ACe .

Your chance of getting 4/52 = 20/260.

Floating Advantage arises out of the positional varience of the extra high cards

If the count is +10 with 1 deck left and Aces are balanced if you catch a 10 as your first card you have a better chance of a blackjack than you do with the same +10 TC and balanced Aces with 5 decks left. This same effect is why the house advantage is lower for single deck games than it is for six deck games.

 

[Sonny]

My thought is that wouldn't the variance decrease as you get deeper also?

It depends on how you are measuring the variance.

If you are measuring variance in terms of initial bets then it might decrease. There may be less splitting/re-splitting and more insurance bets to smooth out the bankroll fluctuations. Possibly more surrendering too. I don't know for sure, but that would be the place to look.

If you are measuring it in terms of absolute dollars (or minimum bets, or "units", or whatever) then it will go up. The majority of high counts will occur deeper in the shoe so your average bet will be increasing as the cards are dealt. Those higher bets are going to affect the variance much more than the play of the hands. A double down or even a few re-splits are going to be insignificant compared to dropping a 16-unit bet on the table.

Because a TC=+10 early means that it could be spread out over a lot more cards, while a TC=+10 towards the cut card means that there are less cards that the "advantage cards" are spread out over, and hence the variance would be lower.

From this sentence it sounds like you are talking about the volatility of certain cards, not the volatility of the bets. That would be a very different question. If we look at different shoe depths with the same TC, the probability of any card being dealt will be the same but the variance might be different.

-Sonny-

 

[assume_R]

It depends on how you are measuring the variance.

If you are measuring variance in terms of initial bets then it might decrease. There may be less splitting/re-splitting and more insurance bets to smooth out the bankroll fluctuations. Possibly more surrendering too. I don't know for sure, but that would be the place to look.

If you are measuring it in terms of absolute dollars (or minimum bets, or "units", or whatever) then it will go up. The majority of high counts will occur deeper in the shoe so your average bet will be increasing as the cards are dealt. Those higher bets are going to affect the variance much more than the play of the hands. A double down or even a few re-splits are going to be insignificant compared to dropping a 16-unit bet on the table.

From this sentence it sounds like you are talking about the volatility of certain cards, not the volatility of the bets. That would be a very different question. If we look at different shoe depths with the same TC, the probability of any card being dealt will be the same but the variance might be different.

-Sonny-

Ah, this post perhaps means I wasn't even understanding my own question entirely. I see how you mean that the variance of the betting units might increase.

I suppose my question was actually related to the volatility. So would this be a more appropriate question:

Given a constant TC, and comparing different depths, would there be less volatility in how often that TC would yield a profitable outcome.

I know that on average it could lead to a profitable situation maybe 60/100 times (just came up with that number randomly), which is equal to 120/200 times, which is equal to 3/5 times. But deeper into the shoe won't there be less variance in that number?

 

[Renzey]

So as I understand it, the floating point advantage measures how the TC advantage changes as you get deeper into the shoe.

My thought is that wouldn't the variance decrease as you get deeper also? Because a TC=+10 early means that it could be spread out over a lot more cards, while a TC=+10 towards the cut card means that there are less cards that the "advantage cards" are spread out over, and hence the variance would be lower.

Correct logic?

Assume R
Let's try to stay on point with your question. The floating advantage arises from the fact that at a given positive true count (let's say +5 true) your advantage if there are 4 decks left in the shoe will be a bit smaller than if there was only 1 deck left. This is so because were talking about a 4 deck pack of cards that has 20 more high cards than low cards, as compared to a single deck that has 5 more highs than lows.

Why an advantage difference? Because with 4 decks left and a +5 true, your chances of being dealt a blackjack are 1 in 13.5 -- where with 1 deck left, your chance for a blackjack is 1 in 13.25.
If you had 6/5 against an 8 with 4 decks left and doubled down, you'd have a 39.0% chance to be dealt a 10. But with 1 deck left you'd be dealt a Ten 40.8% of the time.
Remember that you started out with an identical proportional composition of cards, but the cards you removed to form your hand had a greater affect on the balance if there were fewer cards left at the beginning of the deal. These, I believe are two simple examples of why single deck has better percentages for the player than an 8 deck shoe -- and why the indices can be a bit different.

With regard to changing variance, there may be technical differences, I don't know. But doubling down with 6/5 when when there are 80 Tens among 205 cards (39.0%) and doubling when there are 20 Tens among 49 cards (40.8%) will both bring a poopload of variance. Single deck variance can be wicked pretty much the same as with a shoe.

Taking that thought to an extreme, let's think about having only 10 cards left in the shoe with a +1 RC. That's a +5.2 TC. Again you're dealt that 6/5 against an 8 and double down. Now your chance to be dealt a 10 is 55.4%. A better deal, but still tons of variance even in this unrealistic scenario. From this last example, I guess we can see that you will indeed yield a favorable outcome more often than with more cards left -- on this particular hand. But what if you're dealt a bad hand such as 6/6 against that 8? With only 7 cards left, it looks like you'd be a bigger dog than with 4 decks left because of your severely limited proportion of "outs".

This is no be-all end-all answer, but I think you can just look at the floating advantage as giving you a little better EV deeper than earlier, with favorable results coming in those relative proportions.

Critiques or corrections are welcomed.

 

[assume_R]

From this last example, I guess we can see that you will indeed yield a favorable outcome more often than with more cards left -- on this particular hand. But what if you're dealt a bad hand such as 6/6 against that 8? With only 7 cards left, it looks like you'd be a bigger dog than with 4 decks left because of your severely limited proportion of "outs".

So it would follow logically from this statement that whatever your expected return for a particular hand would have less variance later in the shoe. By this, I mean that an 11v8 at TC=+5.2 has a high EV, and it would actually converge to that EV faster if you only have 10 cards left (vs. 200 left, where there's a lot of chances to not get that 10). And a bad hand of 12v8 at TC=+5.2 has a low EV, and it would actually converge to that low EV faster if you only have 10 cards left (vs. 200 left, where there's a lot of outs)

How's that sound?

 

[chessplayer]

Hmm..I have no idea if Arnold is right or you are right because I have no simulation to prove either case.

However according to Arnold Snyder, the advantage of the same TC +2 At 50%penetration as compared to 87.5% penetration is 0.57 is 0.87. 0.3 seems quite a bit.

http://www.blackjackinfo.com/bb/showthread.php?t=17743

Assume R
Let's try to stay on point with your question. The floating advantage arises from the fact that at a given positive true count (let's say +5 true) your advantage if there are 4 decks left in the shoe will be a bit smaller than if there was only 1 deck left. This is so because were talking about a 4 deck pack of cards that has 20 more high cards than low cards, as compared to a single deck that has 5 more highs than lows.
Taking that thought to an extreme, let's think
This is no be-all end-all answer, but I think you can just look at the floating advantage as giving you a little better EV deeper than earlier, with favorable results coming in those relative proportions.

Critiques or corrections are welcomed.

 

[Renzey]

So it would follow logically from this statement that whatever your expected return for a particular hand would have less variance later in the shoe. By this, I mean that an 11v8 at TC=+5.2 has a high EV, and it would actually converge to that EV faster if you only have 10 cards left (vs. 200 left, where there's a lot of chances to not get that 10). And a bad hand of 12v8 at TC=+5.2 has a low EV, and it would actually converge to that low EV faster if you only have 10 cards left (vs. 200 left, where there's a lot of outs)

How's that sound?

Remember though, even with very few cards, sometimes you get the good hand and sometimes you get the bad hand. And together, volatility still reigns supreme.

Regarding Chessplayer's comment about Arnold Snyder and the floating advantage: That 0.30% difference between 3 decks and 1 deck at the same true count seems in the ballpark. I guess you could say that seems like a lot. But look at it from the perspective that when 3 decks are left, you need a +2.6 TC to have the same advantage that you get from a +2.0 TC with 1 deck left.