Multiples Accumulators Explained

Opening multiple betting accounts is a popular method to bypass account restriction by the bookmaker and is often used in the work of arbers and bonus hunters. Certainly, every year it becomes. With multiples featuring a large number of selections, multiple selections at long odds, or placed with a high-value stake, the combined odds of your accumulator can sometimes exceed your bookmaker’s maximum win limits – though this is usually a six figure sum. 2.1.7 Multiple Bets / Accumulators 2.1.7.1. Multiple bets (or Accumulators) means bets in a combination of two up to 20 selections.

In computing, especially digital signal processing, the multiply–accumulate operation is a common step that computes the product of two numbers and adds that product to an accumulator. The hardware unit that performs the operation is known as a multiplier–accumulator (MAC, or MAC unit); the operation itself is also often called a MAC or a MAC operation. The MAC operation modifies an accumulator a:

${\displaystyle a\leftarrow a+(b\times c)}$

When done with floating point numbers, it might be performed with two roundings (typical in many DSPs), or with a single rounding. When performed with a single rounding, it is called a fused multiply–add (FMA) or fused multiply–accumulate (FMAC).

Modern computers may contain a dedicated MAC, consisting of a multiplier implemented in combinational logic followed by an adder and an accumulator register that stores the result. The output of the register is fed back to one input of the adder, so that on each clock cycle, the output of the multiplier is added to the register. Combinational multipliers require a large amount of logic, but can compute a product much more quickly than the method of shifting and adding typical of earlier computers. Percy Ludgate was the first to conceive a MAC in his Analytical Machine of 1909,^[1] and the first to exploit a MAC for division (using multiplication seeded by reciprocal, via the convergent series (1+x)⁻¹). The first modern processors to be equipped with MAC units were digital signal processors, but the technique is now also common in general-purpose processors.

In floating-point arithmetic[edit]

When done with integers, the operation is typically exact (computed modulo some power of two). However, floating-point numbers have only a certain amount of mathematical precision. That is, digital floating-point arithmetic is generally not associative or distributive. (See Floating point § Accuracy problems.)Therefore, it makes a difference to the result whether the multiply–add is performed with two roundings, or in one operation with a single rounding (a fused multiply–add). IEEE 754-2008 specifies that it must be performed with one rounding, yielding a more accurate result.^[2]

Fused multiply–add[edit]

A fused multiply–add (FMA or fmadd)^[3]is a floating-point multiply–add operation performed in one step, with a single rounding. That is, where an unfused multiply–add would compute the product b×c, round it to N significant bits, add the result to a, and round back to N significant bits, a fused multiply–add would compute the entire expression a+b×c to its full precision before rounding the final result down to N significant bits.

A fast FMA can speed up and improve the accuracy of many computations that involve the accumulation of products:

• Polynomial evaluation (e.g., with Horner's rule)
• Newton's method for evaluating functions (from the inverse function)
• Convolutions and artificial neural networks

Fused multiply–add can usually be relied on to give more accurate results. However, William Kahan has pointed out that it can give problems if used unthinkingly.^[4] If x² − y² is evaluated as ((x×x) − y×y) using fused multiply–add, then the result may be negative even when x = y due to the first multiplication discarding low significance bits. This could then lead to an error if, for instance, the square root of the result is then evaluated.

When implemented inside a microprocessor, an FMA can be faster than a multiply operation followed by an add. However, standard industrial implementations based on the original IBM RS/6000 design require a 2N-bit adder to compute the sum properly.^[5]

Another useful benefit of including this instruction is that it allows an efficient software implementation of division (see division algorithm) and square root (see methods of computing square roots) operations, thus eliminating the need for dedicated hardware for those operations.^[6]

Dot product instruction[edit]

Some machines combine multiple fused multiply add operations into a single step, e.g. performing a four-element dot-product on two 128-bit SIMD registers a0×b0+a1×b1+a2×b2+a3×b3 with single cycle throughput.

Support[edit]

The FMA operation is included in IEEE 754-2008.

The Digital Equipment Corporation (DEC) VAX's POLY instruction is used for evaluating polynomials with Horner's rule using a succession of multiply and add steps. Instruction descriptions do not specify whether the multiply and add are performed using a single FMA step.^[7] This instruction has been a part of the VAX instruction set since its original 11/780 implementation in 1977.

The 1999 standard of the C programming language supports the FMA operation through the fma() standard math library function, and standard pragmas (#pragma STDC FP_CONTRACT) controlling optimizations based on FMA.

The fused multiply–add operation was introduced as 'multiply–add fused' in the IBM POWER1 (1990) processor,^[8] but has been added to numerous other processors since then:

• HPPA-8000 (1996) and above
• HitachiSuperH SH-4 (1998)
• SCE-ToshibaEmotion Engine (1999)
• Intel Itanium (2001)
• STI Cell (2006)
• FujitsuSPARC64 VI (2007) and above
• (MIPS-compatible) Loongson-2F (2008)^[9]
• Elbrus-8SV (2018)
• x86 processors with FMA3 and/or FMA4 instruction set
  • AMD Bulldozer (2011, FMA4 only)
  • AMD Piledriver (2012, FMA3 and FMA4)^[10]
  • AMD Steamroller (2014)
  • AMD Excavator (2015)
  • AMD Zen (2017, FMA3 only)
  • Intel Haswell (2013, FMA3 only)^[11]
  • Intel Skylake (2015, FMA3 only)
• ARM processors with VFPv4 and/or NEONv2:
  • ARM Cortex-M4F (2010)
  • ARM Cortex-A5 (2012)
  • ARM Cortex-A7 (2013)
  • ARM Cortex-A15 (2012)
  • Qualcomm Krait (2012)
  • Apple A6 (2012)
  • All ARMv8 processors
    • Fujitsu A64FX has 'Four-operand FMA with Prefix Instruction'.
• GPUs and GPGPU boards:
  • Advanced Micro Devices GPUs (2009) and newer
    • TeraScale 2 'Evergreen'-series based
    • Graphics Core Next-based
  • NVidia GPUs (2010) and newer
    • Fermi-based (2010)
    • Kepler-based (2012)
    • Maxwell-based (2014)
    • Pascal-based (2016)
    • Volta-based (2017)
  • Intel GPUs since Sandy Bridge
  • Intel MIC (2012)
  • ARM Mali T600 Series (2012) and above
• Vector Processors:

References[edit]

1. ^'The Feasibility of Ludgate's Analytical Machine'. Archived from the original on 2019-08-07. Retrieved 2020-08-30.
2. ^Whitehead, Nathan; Fit-Florea, Alex (2011). 'Precision & Performance: Floating Point and IEEE 754 Compliance for NVIDIA GPUs'(PDF). nvidia. Retrieved 2013-08-31.
3. ^'fmadd instrs'.
4. ^Kahan, William (1996-05-31). 'IEEE Standard 754 for Binary Floating-Point Arithmetic'.
5. ^Quinnell, Eric (May 2007). Floating-Point Fused Multiply–Add Architectures(PDF) (PhD thesis). Retrieved 2011-03-28.
6. ^Markstein, Peter (November 2004). Software Division and Square Root Using Goldschmidt's Algorithms(PDF). 6th Conference on Real Numbers and Computers. CiteSeerX10.1.1.85.9648.
7. ^'VAX instruction of the week: POLY'. Archived from the original on 2020-02-13.
8. ^Montoye, R. K.; Hokenek, E.; Runyon, S. L. (January 1990). 'Design of the IBM RISC System/6000 floating-point execution unit'. IBM Journal of Research and Development. 34 (1): 59–70. doi:10.1147/rd.341.0059.
9. ^'Godson-3 Emulates x86: New MIPS-Compatible Chinese Processor Has Extensions for x86 Translation'.
10. ^Hollingsworth, Brent (October 2012). 'New 'Bulldozer' and 'Piledriver' Instructions'. AMD Developer Central.
11. ^'Intel adds 22nm octo-core 'Haswell' to CPU design roadmap'. The Register. Archived from the original on 2012-03-27. Retrieved 2008-08-19.

Sports betting has come a long way since the regular outright (Moneyline) wagers. There are plenty of bet types for most popular sports, and in this article, we will explain some of the most popular and unusual bet types – accumulators. Read the full article to understand everything you need to know to place these bets on your favorite Sportsbook.

Get here our best acca tips for today.

Accumulator Bets – Explanation and Examples

If you aren't well informed on multiple bets, you probably aren't acquainted with accumulators, which are sometimes called “ACCA” for short. They are a form of multiple bet that combines several selections in a single wager. This bet type is trendy in the UK, and punters mostly use it on football matches, but some people also place accumulators on other sports, such as, but not limited to:

• American Football
• Cricket
• Rugby
• Basketball
• Tennis
• Horse Racing

People place ACCAs in both online Sportsbooks and betting shops. These types of bet have high potential, but there is a catch. To win your wager, you must guess all the legs of the accumulator bet correctly. Even if one selection loses, you will lose the whole wager. Different bookmakers sometimes offer promotions where if you lose one leg of the accumulator bet, you can still win the entire bet. Still, there are specific terms and conditions you have to follow for these types of bonuses.

For your bet to be considered an ACCA, you have to have at least four selection on your betting slip. There are, of course, ACCAs with more than four selections, or also called legs. There isn't any upper limit to the number of legs you can wager. Each of the bets you put in the ACCA bet has different odds, so before you place the bet, all the odds are combined, which means that you might get a very high payout if you win the bet.

An Example of a Six-Fold Accumulator Bet

Let’s say that you place the following ACCA wager on any online Sportsbook or in any betting shop:

1. Liverpool to beat Manchester City at 2/1
2. Chelsea to beat Arsenal at 2/1
3. Manchester United to beat West Ham United at 4/1
4. Leicester City to beat Bournemouth at 3/1
5. Cardiff City to beat Newcastle United at 3/1
6. Wolverhampton Wanderers to beat Tottenham Hotspur at 4/1

If you stake £2 on this ACCA wager, in the end, you could win £7,200. Each time a selection wins, the amount you win gets transferred as the stake of the next event in the ACCA bet slip. That is why these sorts of bets have a huge payout potential, as shown in the example above, from a £2 bet, and you can win £7,200. But if any of the selections lose, you lose the whole wager, unless you participate in ACCA Insurance promotion of some kind.

Types of Accumulator Bets

Even though ACCAs don't have an upper limit, not many people risk placing wagers with high legs because their chances of winning get slimmer with each new leg, but the good news is that the profit also grows. People sometimes put bets with two or three selections in the ACCA bet category, which isn't accurate because ACCAs are only multiple bets with four or more wagers combined.

• Accumulators with four legs are called Four-Fold Accumulator bets.
• Accumulators with five legs are called Five-Fold Accumulator bets.
• Accumulators with six legs are called Six-Fold Accumulator bets.
• Accumulators with seven legs are called Seven-Fold Accumulator bets.
• Accumulators with eight legs are called Eight-Fold Accumulator bets.

You can also place each-way accumulator bets. If you place them, you bet on one selection to win and the second one to be placed. These bets increase your chances of winning something, but the amount you win is less than betting with normal accumulators.

ACCA Insurance

Multiples Accumulators Explained Meaning

ACCA Insurance is a popular bonus that many bookmakers offer on their Sportsbooks. The cool thing about it is that even if you lose one leg on your selection, you can still win the bet. For example, let's say you place a wager for Everton, Arsenal, Tottenham, West Ham, and Liverpool to win against their opponents. The results of the games are that all teams win in their matches except for West Ham. If ACCA Insurance is available and you opted-in and placed an ACCA bet with the minimum required selection number, you would still receive the winnings from your wager. Sometimes if you lose a leg, the bookmaker offers a refund in the form of a free bet. The free wagers last for different periods, and you need to read the terms of the offer to find out which events you would be able to use them. Most bookmakers offer ACCA Insurance on football matches, but some offer the bonus on other sports like Paddy Power and 888 Sport.

Popular Bookmakers that Offer ACCA Insurance and other ACCA-related Promotions

Many fantastic bookmakers offer ACCA Insurance; the offer is mostly the same on all of the Sportsbooks. Here are the top bookmakers who offer ACCA Insurance:

• BetVictor
• 888 Sport

Multiples Accumulators Explained Definition

Some bookmakers provide different types of ACCA bonuses, such as ACCA bet boosts. You can find these types of bonuses at William Hill, Betfair, and Coral.

Final Conclusion on Accumulator Bets and Promotions

Multiples Accumulators Explained 3

ACCA wagers are quite popular among customers on all the popular Sportsbook platforms. They are easy-to-place wagers and don't require placing large stakes. But if you win, the benefits can be exhilarating. That is what people most enjoy about ACCA bets – they have to potential to win a large amount with a small stake. The bookmakers also attract people to this betting by providing ACCA-related bonuses like Bet Boosts or ACCA Insurance. While there are Sportsbooks who offer ACCA bonuses both online and offline, not all of the bookmakers make a habit of providing this type of bonus. Don't hesitate to try out ACCA bets, and if you don't like them, that's okay, but you may end up enjoying them.

Multiples Accumulators Explained 2

The best Accumulator Betting Calculator we tested is the one developed by OddsMonkey.