Casino Bonuses and EV
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WARNING – Apart from specific risk-free strategies (which are often not allowed) all casino play is risky. Even with a +EV bonus you can easily lose all of your money on an individual offer.
To the novice casino player the various different bonuses, games, strategies and terminology provide a bewildering and off-putting mountain of often incomprehensible information. The purpose of this post is to clarify the definitions of some of the terms used and to unravel the meaning of that often quoted term EV.
Cashable bonus – a bonus which is added to your deposit and can be withdrawn as cash, usually after a wager requirement (WR) has been completed.
Sticky bonus – a bonus which can be played with but cannot be withdrawn. Your cash balance will be used before your bonus, and withdrawing before the wagering requirement has been completed usually voids the bonus and any winnings.
Clearplay bonus – These bonuses have a WR but you can withdraw your winnings at any time. Most clearplay bonuses have now been modified so that the cash is released incrementally as you work through the WR, making them like a sticky bonus if you don’t finish the WR but like a cashable bonus if you do.
Free spins/freeplay bonus – no deposit is required in order to get the bonus, although you may be required to deposit before you can withdraw any winnings.
Cashback bonus – a refund of a percentage of losses during a specific period, usually without a WR on the refund (but always check).
Post wager bonus – a bonus which is added after the WR has been completed. If you have a bad run these can become very expensive.
Wager requirement – the amount of money which has to be wagered before a withdrawal is allowed or a bonus is released for play. Usually expressed in terms of multiples of the deposit and/or bonus amounts.
EV is estimated value. A bonus strategy with a +EV will return a profit if repeated a large number of times. One with a -EV will return a loss.
House Edge – The average loss per initial bet, ie the percentage of money the casino takes out of the game. Different games have different house edges.
Busting out – losing all of your deposit and the bonus money.
Variance – a measure of the variation you are likely to encounter in returns from playing identical bonus amounts and strategies. A high variance means you are more likely to either bust out or win big. The mathematical definition of variance is the square of the standard deviation from the mean.
How to Calculate EV
The EV of an offer depends on the WR, the house edge and the chance of busting out. At first it is extremely surprising to discover that the EV increases as the chances of busting out increase. This is a similar concept to the idea that potential rewards increase with increasing risk. If you play small stakes you will probably complete the WR without busting out, but you will probably not win large amounts. If you play with large stakes it is much more likely that you will bust out early in the WR, but if you have a good run you will win much more.
The formula you use depends on whether or not it is possible to bust out.
For post wager bonuses where it is not possible to bust out:
EV = Bonus – (WR x house edge per unit wagered).
Example: Post wager £100 bonus playable on blackjack with 20 x WR
EV= 100 – (2000 x 0.005) = 90
This illustrates that playing blackjack with a 20 x WR should produce a good profit over time.
For bonuses where it is possible to bust out:
EV = (chance of bust x bonus) – (average wagering x house edge per unit wagered).
Working out the chance of busting out is far from easy unless your stakes are so large that you put the whole lot on one hand. In these cases, although the actual EV may be larger than for the same game using small stakes and with no chance of busting out, the variance is hugely increased and the risk of losing an individual bonus is much higher. Usually the increase in risk is vast compared to the increase in EV. Unless you are prepared to lose large amounts before you win anything the best way to tackle bonuses is to keep the stakes small (and therefore the chance of bust small) and accept a slightly lower EV. If you do this, the first equation will give a good approximation to the EV.
Approximate House Edge of some common Casino Games
The exact house edge varies a bit between software providers and also between different variations of the same game (for example in blackjack the house edge will be slightly different depending on whether the dealer stands or hits on a soft 17). There is a comprehensive table of casino games with their house edge and standard deviation here. The house edge is listed in this table as a percentage. In the formula for EV you need to use it in the form 0.01 for 1% etc.
A few of the more common ones are:
Blackjack house edge approx 0.4%, standard deviation 1.07 EV for a £100 bonus and £3000 WR = 88
Roulette (single zero) 2.7%, s.d. 1.0 EV for above bonus and WR = 19
Video poker (All Aces) 0.8% s.d.8.08 EV = 76
Video poker (Jacks or Better) 0.46% s.d. 4.42 EV = 86.2
Baccarat 1.06 s.d. 0.93 EV = 68.2
Slots 3-6% s.d.varies (high) EV = -80 to 10
Keno 5-25% s.d varies (high) EV = -650 to -50
You will see from this that Jacks or Better video poker has almost the same house edge (and therefore EV) as blackjack, but a much higher variance, making blackjack the safer game to play for bonuses. It is perfectly obvious why bookies and casinos often restrict bonus play to slots and keno.
An example of calculating EV for a real bonus from the BetSeventyTwo forum.
coral reload bonus
by mikeymp » Thu Sep 24, 2009 7:41 pm
Is the BJ reload worth risking as it seems a hefty bonus turnover of x25?
by Darren » Fri Sep 25, 2009 7:54 am
I just look at the overall EV (expected value) and if it is a + then I will play, as long as we are not talking a very low figure for a huge amount of wagering, you do have to put a value on your personal time too (or use Casibot of course!).
I know what you mean on the face of it 55 x £25 (£1375) is a hell of a lot to unlock a £25 bonus but the maths do stack up in our favour for example assuming the house edge is 0.5% for BJ.
Approx Bonus Calculation (there is a more complex one to include standard deviation too)……
Bonus = £25
Wager = 55 x £25 = $1375
House edge 0.5% of $1375 = £6.87
Expected Value = £25 – £6.87 = £18.13
In fact you can play any flavour of BJ at Coral so Single Deck brings the house edge down to 0.14% !
Bonus = £25
Wager = 55 x £25 = $1375
House edge 0.14% of $1375 = £1.92
Expected Value = £25 – £6.87 = £23.08
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