Casino refunds are the matched betting of the casino world. You can receive some or all of your stake back if you lose. My current favourite is SportingBet who give 50% back on your casino losses every Thursday up to £10. It might be tempting to play it safe and play £1 bets on red/black on the roulette wheel for a couple bets, or even skip this offer altogether. They are however a goldmine and I will endeavour to show you why in this article.
You Should Always Play the Minimum Number of Bets Needed
In all casino games the house has an edge which means that over time your bankroll will be depleted. Typical values for the house edge are 0.5, 2.7, and 5% for blackjack, roulette and slots respectively. In essence this means that for every £100 you wager, on average you will lose £0.5, £2.70 and £5 for each game. For this reason it doesn’t make sense to wager in small amount and hope that we win since we have a substantially greater chance that we’ll lose. This massively reduces the potential reward and hence the expected value of the offer. Here is an example:
Suppose the we get a 100% refund up to £10 if we lose on roulette. If we play the £10 on red, given that the probability of winning is 48.6% the EV is:
EV = 0.486*£10 – 0.514*£0 = £4.86
If however we play £5 at a time on red until we either reach a profit of £10 or we lose £10 then:
WW = 0.486*0.486 = 0.236 (Chance of two wins)
WLWW, LWWW = 0.486*0.514*0.486*0.486 = 0.059
WLWLWW, LWLWWW, WLLWWW, LWWLWW = 0.0147
LWLWLWWW, WLWLWLWW, WLLWWLWW, LWWLWLWW, LWWLLWWW, LWLWWLWW, WLWLLWWW, WLLWLWWW = 0.003675
Hence the chance is 1*0.236 + 2*0.059 + 4*0.0147 + 8*0.003675 + … = 0.236 + 0.118 + 0.059 + 0.0147 + … = 0.236*(1+1/2+1/4+1/8 …) = 0.236*2 = 0.472
=> EV = 0.472*£10 – 0.528*£0 = £4.72
You can see that the EV is lower simply due to the fact that we will be wagering more often if we choose £5 stakes compared to £10. The trend of lowering EV continues the more we reduce our stake, not to mention the time it’ll take to reach the target profit!
Be sure to check the T&Cs for each offer (as usual) however as sometimes e.g. with Ladbrokes they state that you cannot stake more than 30% of the refund amount at any time.
The Odds of Your Bet is Important Too
If we take the same refund offer but put the £10 on a single number, then the EV is:
EV = 0.027*£350 – 0.973*£0 = £9.45
In other words the EV is nearly twice that of simply attempting to doubling our money. This is because the house edge stays the same, however we will receive more refunds which is where the value lies. Below is a chart that plots the EV of a £10 stake vs the number of roulette numbers covered for a 100%, 50%, and 15% refund:
One needs to take into consideration however that the standard deviation (a measure of variance) for a single number bet is 6 times greater than an even money bet. I have discussed this in greater depth before in the final half of Cassava Bingo Part 2 so I will not discuss it again here. For a 50% or 100% refund, as we lose very little to no money with this offer I would recommend covering 8 numbers or fewer in order to retain most of the value. The variance should not be too hard to stomach. On the other hand, any less than a 50% refund then it makes more sense to do an even money bet. Refund offers below 50% tend to allow greater stakes up to a £100, so in reality you would not want to risk such an amount on a small probability unless your bankroll allows it.
Refunds for Other Games
Sometimes the refunds and bonuses are for a specific casino game, usually blackjack or slots. These are just as profitable as roulette, however in the case of slots you will need to be prepared to have long streaks of not winning anything. Often with slots you will receive your stake amount back or a fraction of it when playing. If this happens place the remaining winnings on another spin until you either get lucky and obtain a substantial profit or you reach your loss limit for the refund. Slots are very high variance so even if your £10 spin returns £2, there is still a chance that your next £2 spin could win you several hundred.
What if the Refund is in the Form of a Bonus?
Due to the large wagering requirements of most bonuses these require what’s known as two-tier betting in order to be profitable. This is where you try and multiply up your bonus before you begin griding away at the wagering requirements with small stakes. Because most of the time you will lose your bonus straight away you will then be completing less wagering on average which means less profit taken by the house edge. My next casino article will detail more about the practicalities and profitability of this technique.
As a final note here are some bookies that often have these types of casino refunds:
Ladbrokes – If they still consider you a casino ‘mug’ they will often send you a casino refund offer every week, normally for about £10 on net losses. After withdrawing my entire balance they once gave me a £25 offer!
William Hill – Offer a risk free £20 to new vegas players
SportingBet – As mentioned in the opening paragraph they typically have 50% refunds three times a week!
Paddy Power – Mostly have 15% cashback on net losses however they sometimes have bigger amounts.