Blackjack Variance

Blackjack Variance Average ratng: 5,0/5 9644 votes

Table Of Contents

  • Ordinary titles are interesting, but adult Slots take the game a step further
  • Adult slots are 'sexy games' where the graphics are….a bit unusual.

Another important factor when describing RTP is variance. Some games have a high variance, this means that the game has a low hit frequency, but when hit, you will more often win big in comparison with a slot that has low variance. Games that have a low variance, have a high hit frequency with a lot of smaller wins. Learn what variance is in blackjack and how we can predict exactly how much we can expect to lose or win on a good or bad day. Knowing the expected variance.

Picking a new favorite from a myriad of online Slots is an exciting process.

To compile this article, I have gathered a more exotic list of titles to give you an alternative to traditional online Casino Slots. They are a bit out of the ordinary as they add a bit of 'extra spice' to the games by placing on the reels something that isn't available in your regular slots.

Blackjack Variance

Wasting no more time, let's dive in this sexy Slots review now.

Adult Slots List: Cleopatra 18+

Cleopatra 18+ comes from MrSlotty and brings a 5-reel, 20-payline Slot to your attention.

The game has an added tempting element, as Cleopatra reveals far more than we're used to see in slots.

Oh, there are some ancient Egyptian erotic scenes around her.

The minimum bet sits at 0.02, with a maximum one of 10.00. There is a Free Spins possibility, a Sphinx Scatter, the Eye of Ra as the highest-value tile, some beetles and lotuses, and Cleopatra herself as the Wild.

Hot Honey 22

Beautiful tattooed women are an honest weakness of mine, so that's Hot Honey 22 ranks high on the Adult Slots table.

Again coming from MrSlotty, this sexy slot machine features different body parts as valuable symbols. Playing it feels a bit like solving a puzzle – and the prize is a beautiful image to gaze upon.

5 reels, 25 paylines, a Free Spins options, a Scatter, and a Gamble feature form the 'boring' aspects of the Slot. Everything else is an uplifting search for the perfect tattoo sequence.

Hot Honey 22 VIP

An upgraded version of the previous MrSlotty title, the Hot Honey 22 VIP doesn't offer a lot more, as the structure and symbols remain the same. As far as I see, the added VIP tag serves just to target High Roller players.

Nevertheless, sexy Slots don't come any better than this, so I don't mind launching the VIP version, too.

Diner of Fortune

Going back to the 1950s, players enter an enhanced pin-up diner to try their luck. Aside from the expected food symbols, you will strive to match stacked reels of sexy waitresses all over the Slot machines.

This Slot machine video game by Spinomenal gets you 5 reels, 15 fixed paylines, a minimum bet of 0.15, and a maximum of 150.

There are Wilds, Scatters, Free Spins, and a portion of low-value symbols to combine on your way to feeding that adult Slots hunger.

Live Slot

Soothing lounge music accompanies six different impulse-provoking ladies. Five of them form the high-value symbols, while the sixth is placed among the low-value symbols. (which doesn't make sense to me, but hey, who am I to judge?)

Spinomenal is the creator of this one, too – 5 reels, 3 rows, and 15 paylines to maximize your winnings while looking at well-drawn pictures of Slot beauties.

There are also Wilds and Scatters to comfort you even when you miss the real-deal combos.

9 Figures Club

Yet another Spinomenal title, 9 Figures Club switches things a bit.

While many other adult Slots bet on sexy symbols for their main attraction, this one only shows them as Wilds and Scatters.

All other tiles are filled with High Roller lifestyle items – watches, cars, bags of cash, planes, yachts, and more.

It is a standard 5x3 online Slot, with 5 paylines going both ways – you can win by combining symbols from left to right and vice-versa.

Booming Gold

A Wild-reel Slot by Booming Games, with 5 reels and 20 paylines to get you going. The sexy online gaming here is rather simplified, as the adult element is presented by a girl in a yellow bathing suit and a woman's smile with grillz.

There are some flashy low-value symbols and the 4th reel is always Wild, except for when Scatters decide to join the party.

Devil's Heat

Femme Fatales and sexy nerdy chicks are the main views in this Booming Games title. There are two interacting symbols available, which award a special bonus if aligned properly.

The one thing that made me lift my eyebrow? The male symbol looks a lot like Antonio Banderas, but I guess this is intentional.

Aside from that, you get a wink from any of the tempting girls when you hit a combo with them.

Golden Girls

Apparently, Booming Games have a strong adult Slots side. Golden Girls presents a 5 reel, 25 payline game to hit the beach with a great company.

Flip-flops, surfboards, Wilds, Scatters, and three inviting ladies are pretty much all you need for a sexy Slot session. If you've ever seen it live, I suggest rethinking whether you even need to spin the reels.

Jetsetter

Jetsetter comes from the hands of Endorphina. Which should be enough to spark the interest of adult Slots enthusiasts.

5 reels, 20 paylines, and the main sexy symbol in the image of a blonde holding a dollar bill. Whenever you manage to combo her in a winning line, she multiplies the bill and spreads a money-fan. Oh yes, and all the bills have her face on them, too.

Twerk

Endorphina also created a fant-ass-tick 3x3 Slot game – yes, the variance is high, but winning combinations literally twerk before your eyes.

Not the most consistent Slot to play, but it's definitely done masterfully. And with a maximum win of 250,000 coins, who actually needs to hit it every five spins, eh?

I didn't include the Cherry Love Slot, but I think those are enough for now.

The promotion presented on this page was available at the time of writing. With some Casino promotions changing on daily basis, we suggest you to check on the site if it still available. Also, please do not forget to read the terms and conditions in full before you accept a bonus.

Introduction


The Kelly Criterion is a bet-sizing technique which balances both risk and reward for the advantage gambler. The same principle would work for any investment with an expectation of being profitable. For the gambler/investor with average luck bankroll and a fixed bet size, the expected bankroll growth after one bet is:

For example, suppose a casino ran a promotion in craps where the 2 paid 3 to 1 and the 12 paid 4 to 1. A 3, 4, 9, 10, or 11 still pay 1 to 1 and every other total loses. The probability of a 2 or 12 is 1/36 each, of any even money win is 14/36 and of a loss is 20/36. Suppose also the player bets 1% of his bankroll every bet. Then the expected bankroll growth per bet would be:

(1 + (0.01*3))^(1/36) * (1 + (0.01*1)^(14/36) * (1 + (0.01*-1))^(20/36) * (1 + (0.01*4))^(1/36)) - 1 = 0.00019661.

This product is maximized by Kelly betting. Kelly betting also minimizes the expected number of bets required to double the bankroll, when bet sizing is always in proportion to the current bankroll.

The Kelly bet amount is the optimal amount for maximizing the expected bankroll growth, for the gambler with average luck. While betting more than Kelly will produce greater expected gains on a per-bet basis, the greater volatility causes long-term bankroll growth to decline compared to exact Kelly bet sizing. Betting double Kelly results in zero expected growth. Anything greater than double Kelly results in expected bankroll decline. What is more commonly seen is betting less than the full Kelly amount. While this does lower expected growth, it also reduces bankroll volatility. Betting half the Kelly amount, for example, reduces bankroll volatility by 50%, but growth by only 25%.

For simple bets that have only two outcomes, the optimal Kelly bet is the advantage divided by what the bet pays on a 'to one' basis. For bets with more than one possible outcome, the optimal Kelly wager is that which maximizes the log of the bankroll after the wager. However, for bets with more than one outcome, that can be hard to determine. Most gamblers use advantage/variance as an approximation, which is a very good estimator. For example, if a bet had a 2% advantage, and a variance of 4, the gambler using 'full Kelly' would bet 0.02/4 = 0.5% of his bankroll on that event. Remember that variance is the square of standard deviation, which is listed for many games in my Game Comparison Guide.

Let’s look at three examples.

Example 1: A card counter perceives a 1% advantage at the given count. From my Game Comparison Guide, we see the standard deviation of blackjack is 1.15 (which can vary according to the both the rules and the count). If the standard deviation is 1.15, then the variance is 1.152 = 1.3225. The portion of bankroll to bet is 0.01 / 1.3225 = 0.76%.

Example 2: A casino in town is offering a 5X points promotion in video poker. Normally the slot club pays 2/9 of 1% in free play. So at 5X, the slot club pays 1.11%. The best game is 9/6 Jacks or Better at a return of 99.54%. After the slot club points, the return is 99.54% + 1.11% = 100.65%, or a 0.65% advantage. The Game Comparison Guide shows the standard deviation of 9/6 Jacks or Better is 4.42, so the variance is 19.5364. The portion of bankroll to bet is 0.0065 / 19.5364 = 0.033%. By the way, this exact promotion is going on at the Wynn as I write this, for September 2 and 3, 2007.

Example 3: A sports wager has a 20% chance of winning, and pays 9 to 2. The advantage is 0.2×4.5 + 0.8×-1 = 0.1. The optimal Kelly wager is 0.1/4.5 = 2.22%.

Following is the exact math of example 3. Let x be optimal Kelly bet, with a bankroll of 1 before the bet. The expected log of the bankroll after the bet is...

f(x) = 0.2 × log(1+4.5x) + 0.8 × log(1-x)

To maximize f(x), take the derivative and set equal to zero.

f'(x) = 0.2 × 4.5 / (1+4.5x) - 0.8 / (1-x) = 0

0.9 / (1+4.5x) = 0.8/(1-x)

0.9 - 0.9x = 0.8 + 3.6 x

4.5x = 0.1

x = .1/4.5 = 1/45 = 2.22%

The math gets much messier when there is more than one possible outcome, such as in video poker. The method is still the same, but getting the solution for x is harder. The easiest way to solve for x in such cases, in my opinion, is experimenting with different values, using the higher and lower techniques (like the Clock Game on the 'Price is Right'), until the f'(x) gets very close to zero.

I did this for two common video poker games with greater than 100% return. For 'Full Pay Deuces Wild,' with a return of 100.76%, the optimal bet size is 0.0345% of bankroll. For ' 10/7 Double Bonus,' with a return of 100.17%, the optimal bet size is 0.0062637% of bankroll. I have heard a rule of thumb that to make it in video poker you should have a bankroll of 3 to 5 times the royal amount you play for. If playing Full Pay Deuces wild, the exact amount is 3.66 royals. For 10/7 Double Bonus it is 19.96 royals.

Simulations

To prove my statement that Kelly minimizes the number of bets to double the bankroll I assumed an even money bet with a 51% chance of winning, for a 2% advantage, and 2% Kelly bet size. Here is how many bets were required on average to double the bankroll at various bet sizes. If a winning wager would put the bettor over double the bankroll, he would only bet what was needed to exactly double the bankroll.

Average Bets to Double Bankroll

Bet SizeAverage Bets
0.5%7,901
1%4,617
2%3,496
3%4,477

Kelly Vs. Optimal Video Poker Strategy

In my Sep. 20, 2007 Ask the Wizard column I suggested the Kelly bettor should sometimes not play optimal video poker strategy. My reasons are explained there.

Links on Kelly

German translation of this page.

Fortune’s Formula by William Poundstone. Read my review.

Negative Variance Blackjack

A good source on Kelly, especially as it pertains to blackjack, is Blackjack Attack by Don Schlesinger.

SBRForum.com has good material on Kelly, including the article 'A Quantitative Introduction to the Kelly Criterion', part I and part II, and a Kelly calculator.

The Kelly Criterion at Wikipedia.

Poker Variance Calculation


Written by: Michael Shackleford