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What Are Blackjack Side Bets?Side bets are bonus bets placed on a round of Blackjack on outcomes beyond whether the player or dealer will win. The majority are staked at the start of the round before the cards have been dealt alongside regular bets and many have fixed odds that usually offer greater payouts than the simple 2:1 rewarded for beating the dealer.Play Blackjack at Pinnacle Casino

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Side bets provide an exciting way to make Blackjack games more interesting whilst offering you a greater number of ways to win. So what are side bets, what side bets are available and are they worth it? Read on to find out.

Blackjack Side Bets Explained

Finding a niche market in betting can often lead to value. This can be anything from specialist knowledge of handball betting to extensive experience in betting on Japanese baseball. Providing you know more than the bookmaker, there is money to be made.  &lt;Bet on soccer at Pinnacle&gt; They also make for interesting and potentially profitable bets, as they can be a little more reliable

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A corner is one of the most inexplicably exciting events in soccer. Only around three per cent of them lead to a goal, but you can guarantee that the attacking team’s fans will roar their approval and encouragement if their team are awarded one. Read on to find out how you can benefit from betting on corners.

Corners betting in soccer: Value in a lesser-known market

Poisson Distribution is a mathematical concept for translating mean averages into a probability for variable outcomes across a distribution. For example, if we know Manchester City average 1.7 goals per game, so by putting the Poisson Distribution formula tells us that this average equates to Manchester City&nbsp;scoring 0 goals 18.3% of the time, 1 goal 31% of the time, 2 goals 26.4% of the time and 3 goals 15% of the time.

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Poisson Distribution: Predict the score in soccer betting

What is Expected Value?The amount a player can expect to win or lose if they were to place a bet on the same odds many times over, calculated through a simple equation multiplying your probability of winning with the amount you could win per bet, and subtracting the probability of losing multiplied by the amount lost per bet.A simple example of Expected Value (EV) put into practice -&nbsp;if you were

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The Expected Value of a bet shows us how much we can expect to win (on average) per bet, and as such is the most valuable calculation a bettor can make when comparing bookmakers' odds. How can you calculate Expected Value in sports betting in order to predict your winnings? Read on to find out.

How to Calculate Expected Value

Dan is a professional engineer and part-time sports betting analyst. He has previously written several articles on hedging and bankroll management and is the author of the book But How Much Did You Lose? which looks at ways that bettors can use risk management to optimize their expected bankroll growth and increase their bankroll more quickly.

Dan Abrams

In his recent book ‘Monte Carlo or Bust’, Joseph Buchdahl introduced a new staking method that he called “unit-z”.
The goal of this method is to adjust your stake size between bets of different odds such that the statistical z-score is the same for each one. I won’t embarrass myself by trying to explain to you what that means, so please read Joseph’s explanation if you haven’t already.
<div class="articleV2 unordered-list">
<ul>
<li><a style="color: #f50;" id="articleLink" href="/betting-resources/en/educational/monte-carlo-or-bust-book-review/sha274ccu45t7n7b" target="_blank">Book review: Monte Carlo or Bust</a></li>
</ul>
</div>
The great thing about this new method is that when he tested its effectiveness against a huge dataset of profitable soccer bets, it estimated the Expected Value (EV) attainable at any given odds much more accurately than the more common unit-loss (i.e., flat staking) and unit-win (i.e., bet “to win” one unit) methods.
Even the creative unit-impact method (introduced by Andrés Barge-Gil and Alfredo García-Hiernaux of the tipster platform Pyckio and published in the Journal of Sports Economics) proved inaccurate at longer odds. The not-so-great aspect of his method is that the formula he had to derive to calculate your Maximum Probable EV (or Expected Edge) based on the z-score is quite difficult.
To save you from too many complicated formulas, I won’t repeat it here. Instead, I’ll recreate his graph of the results of EV available vs. decimal odds: <img src="/sites/default/files/media-image/EV-1.jpg" alt="EV-1.jpg" title width="600" height="400" loading="lazy">

Since the unit-z staking curve very closely matches the real-life data, let’s use Joseph’s method as a reference to represent actual results.
Why do you think the curve takes this shape, and is there any significance to it? What if, like with so many of the other questions about sports betting that I’ve investigated, the answer is that it depends on the Expected Growth (EG) available to the bettors?
Since each bettor has a different bankroll size, we would need to use the Maximum Expected Growth (MEG) to compare the EV available at different odds.
If we compute the MEG for one of the unit-z data points, and then plot a Line of Constant Optimal EG (LOCO EG) across the same range of odds as in the first graph, then it looks like this: <img src="/sites/default/files/media-image/EV-2.jpg" alt="EV-2.jpg" title width="600" height="400" loading="lazy"> 

It’s an exact match to unit-z. In fact, the relationship between the EV at any given odds and the EV at even money becomes incredibly simple if we use fractional odds to calculate and plot it instead of decimal ones, like so: <img src="/sites/default/files/media-image/ev-3.jpg" alt="ev-3.jpg" title width="600" height="400" loading="lazy">
The black trend line, Power (LOCO EG), overlaying our LOCO EG curve in the graph above is a perfect fit too. Since the y-axis is the EV or edge in this graph, and the x-axis is the fractional odds “b”, the formula for the edge “e” on our curve is:
e = 1.46% * √b
Why 1.46%? Because that’s exactly the Expected Edge for even Money Lines in the dataset that Buchdahl used to set up the variables for his unit-z formula. If all you need to do is compute the same MEG at a given odds as you’d get at even money, it’s not hard to derive the formula for your Expected Edge. First, we must use a handy approximation for the MEG:
<div style="text-align: center;">MEG = edge2/(2*odds)</div>
This “edge squared over twice odds” amount is typically very small, because it calculates the median change to your total bankroll from just one bet. Yet, it’s very powerful because, by setting it equal across all possible odds, we can derive the same exact formula that fits our unit-z curve:
MEG = edge2/(2*odds) = edge02/(2*1)
e2/2b = e02/2
e2 = e02b
e = e0√b
e = 1.46% * √b
Where:
e = edge or EV at the given odds
e0 = edge or EV at even money
So, what does this all actually mean? Well, over a dataset of 55,000 points, the best available line in the market produced the same amount of MEG for bettors when compared to Pinnacle’s margin-free line regardless of the actual odds that were offered.
Favourites, longshots, and pick ‘ems all had the same bankroll growth potential if you could get your bet down on the best line before it was gone, and if you staked optimally.
Is the treasure trove of European soccer data that Joseph used representative of all sports?
That’s the key question, because if so, it would mean that we could easily set our expectations for how much value can likely be found for different values of true odds based on our expected ROI at even odds. Then we can stake appropriately so that we take optimal advantage of our edge but don’t overbet.
<h3>“Root-unit” staking</h3>
For us to stake the optimal amount based on the LOCO EG, we just need to remember the old mantra from the Kelly Criterion method that your stake size should be “edge over odds.”
<div class="articleV2 unordered-list">
<ul>
<li><a style="color: #f50;" id="articleLink" href="https://www.pinnacle.com/en/betting-strategy/how-to-use-kelly-criterion-for-betting" target="_blank">How to use Kelly Criterion for betting</a></li>
</ul>
</div>
When we write the simple Kelly equation that way, and substitute our estimate of the edge at even money, we get another very simple equation:
f = edge/odds
f = e/b
f = e0√b/b
f = e0/√b
And, since the optimal fraction to bet at even money, f0, is the same as e0, then we end up with this formula:
f = f0/√b
In other words, to stake an amount that will give you the same EG at the current odds as you would get in a similar market at even money, just bet your usual even-money unit size divided by the square root of the odds.
That’s why I call this new technique the “root-unit” staking method.
Say that you are a one-unit bettor for NBA spreads and Totals, but spotted a good Money Line bet on the Pistons to beat the Sixers in tomorrow night’s game at +400 (or 5.0 in odds)?
Then you’d want to bet one unit divided by √4 in that case. Which means you bet half a unit. What if your model says the value is on the Sixers at -400 (1.250 decimal) instead?
Then you’d bet one unit divided by √0.25, or two units. Since you don’t have to get these values exactly right (and you may look far too sharp by betting amounts like $103.58 even if you did), you can use the following table as a guide:
<table class=" article-table">
<tbody>
<tr>
<td style="text-align: center;">
American Odds
</td>
<td style="text-align: center;">
Decimal Odds
</td>
<td style="text-align: center;">
Net Fractional Odds
</td>
<td style="text-align: center;">
Units Staked
</td>
</tr>
<tr>
<td style="text-align: center;">
-1000
</td>
<td style="text-align: center;">
1.100
</td>
<td style="text-align: center;">
1/10
</td>
<td style="text-align: center;">
3.00
</td>
</tr>
<tr>
<td style="text-align: center;">
-600
</td>
<td style="text-align: center;">
1.167
</td>
<td style="text-align: center;">
1/6
</td>
<td style="text-align: center;">
2.50
</td>
</tr>
<tr>
<td style="text-align: center;">
-400
</td>
<td style="text-align: center;">
1.250
</td>
<td style="text-align: center;">
1/4
</td>
<td style="text-align: center;">
2.00
</td>
</tr>
<tr>
<td style="text-align: center;">
-200
</td>
<td style="text-align: center;">
1.500
</td>
<td style="text-align: center;">
1/2
</td>
<td style="text-align: center;">
1.40
</td>
</tr>
<tr>
<td style="text-align: center;">
-110
</td>
<td style="text-align: center;">
1.909
</td>
<td style="text-align: center;">
10/11
</td>
<td style="text-align: center;">
1.05*
</td>
</tr>
<tr>
<td style="text-align: center;">
+100
</td>
<td style="text-align: center;">
2.000
</td>
<td style="text-align: center;">
1
</td>
<td style="text-align: center;">
1.00
</td>
</tr>
<tr>
<td style="text-align: center;">
+200
</td>
<td style="text-align: center;">
3.000
</td>
<td style="text-align: center;">
2
</td>
<td style="text-align: center;">
0.70
</td>
</tr>
<tr>
<td style="text-align: center;">
+400
</td>
<td style="text-align: center;">
5.000
</td>
<td style="text-align: center;">
4
</td>
<td style="text-align: center;">
0.50
</td>
</tr>
<tr>
<td style="text-align: center;">
+600
</td>
<td style="text-align: center;">
7.000
</td>
<td style="text-align: center;">
6
</td>
<td style="text-align: center;">
0.40
</td>
</tr>
<tr>
<td style="text-align: center;">
+1000
</td>
<td style="text-align: center;">
11.000
</td>
<td style="text-align: center;">
10
</td>
<td style="text-align: center;">
0.30
</td>
</tr>
</tbody>
</table>
*If you still prefer to stake 1.1 units to win 1 for accounting purposes, you can.

Make a copy and tape it up next to your monitor if you want to.
If you have equal confidence in your ability to sniff out an edge at different odds, this method is how you can quickly stake in a Kelly-like way adjusted for the different levels of risk you’re accepting.
Remember that you can use root-unit staking for any fraction of Kelly that you feel comfortable with. It will simply allow you maintain that same balance of risk vs. reward for any odds you bet on.
 Read more insightful and educational articles from <a href="/author/simon-edwards---copy" target="_blank">Dan Abrams</a> at Pinnacle Betting Resources. <a href="https://bit.ly/3sbs8Ec" target="_blank">Sign up</a> today and bet on your favourite sports with Pinnacles exceptional odds.

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Looking to more accurately predict Expected Value? Dan Abrams expands on the "Unit-Z" method and guides sports bettors through the new Root-Unit staking method to help you find the betting edge more efficiently and accurately.

Developing the Root-Unit staking method

Once a bettor decides to place a bet on a market, what’s the best way to decide how much to stake on it? There are several methods that are commonly used, but which one is optimal?
Or is there another way? Read on to find out.