MattUK
MattUK
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July 10th, 2020 at 6:32:15 AM permalink
Regulated online casinos show the "Theoretical Return To Player" on every game in percents, eg. 97.30% for a roulette. Some show the RTP along with the house edge, which is 100%-RTP. In that example, 97.30% RTP and 2.70% house edge. I suspect it's missing the cruicial information for a majority of players - how many bets it will take to be separated from one, assuming flat betting. It's unbelievably simple - 100/house edge. No online casino that I know publish it this way. Here's how this would look like:
















Game Loss of one unit per number of rounds RTP (%) house edge (%)
American Roulette 19 94.74 5.26
Sic Bo, even money bet 36 97.22 2.78
European Roulette 37 97.30 2.70
Sic Bo by Gamesys, any number bet 54 98.15 1.85
Roulette73 73 98.63 1.37
Money Back Roulette by Cayetano 74 98.65 1.35
Banker bet, 8-deck Baccarat 94.53 98.94 1.06
Banker bet, EZ Baccarat 98.20 98.98 1.02
Banker bet, 1-deck Baccarat 98.84 98.99 1.01
100 Bit Dice by 4ThePlayer (1% commission) 100 99 1
Street bet in European Roulette pays 11.21 100 99 1
Field bet pays 2.9 on 2&12 180 99.44 0.56
Craps by Playtech, best choice 220 (73.33 for house edge * 3) 99.55 0.45
Craps by Dragonfish, best choice 293.33 (73.33 for house edge * 4) 99.66 0.34
Craps by Gamesys (3-4-5x rule), best choice 366.67 (73.33 for house edge * 5) 99.73 0.27
Not So Ugly Deuces Video Poker 367.39 99.73 0.27
1.05 payout on European Roulette promotion 370 (house edge reduced 10 fold) 99.73 0.27
Microgaming Blackjack Classic Gold 1133 99.91 0.09
Craps with 20x Odds, best choice 1540 (73.33 for house edge * 21) 99.94 0.06
Craps with 100x Odds, Pass Line 4785 (70.71 for house edge * 67.67) 99.98 0.02
any fair bet, eg. "00" wins in American Roulette infinite 100 0


As you can see, with this metric more is better (as in miles per gallon, in contrast to the European liters per 100 km). I think this makes more sense by itself. However, some table games will show the exact natural number and the concept behind them may finally shine. For example, we all know that even money bet in French Roulette has a house edge of 1.35%, but this is approximation to the second digit. The true value is 1 loss per 74 rounds. At the same time, and I think this is the most important part, this gives the player a better sense how many rounds he can play, on average, before the "paying round".
Would you like to see it presented this way instead of RTP or per house edge?
Last edited by: MattUK on Jul 10, 2020
charliepatrick
charliepatrick
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July 10th, 2020 at 7:07:35 AM permalink
Personally I prefer HE or RTP, but there's also book value for sports racing (as usually it's a book for one race only).

I think there's a need to mention element of risk: for instance playing a flat Don't Pass bet has a HE of about 1.3636%, so on average that's about 73 bets. Playing with odds the initial bet will still last about 73 bets. (Pass is about 71, which is slightly worse bet.)

However it's different making a flat bet of $105 compared to $5 with $100 odds. btw you actually might need $120/$150/$200, so the measure is even more tainted.
MattUK
MattUK
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July 10th, 2020 at 7:30:25 AM permalink
Quote: charliepatrick

Personally I prefer HE or RTP, but there's also book value for sports racing (as usually it's a book for one race only).
I think there's a need to mention element of risk: for instance playing a flat Don't Pass bet has a HE of about 1.3636%, so on average that's about 73 bets. Playing with odds the initial bet will still last about 73 bets. (Pass is about 71, which is slightly worse bet.)
However it's different making a flat bet of $105 compared to $5 with $100 odds. btw you actually might need $120/$150/$200, so the measure is even more tainted.



Thanks for reply. Sports betting is a different animal with ALSO three ways to present it - decimal, fractional and the one I still don't understand - American. :-) Here we have RTP, house edge and whatever this may be called.
You're right about the difference between the house edge and the Element of Risk, but that's not confined to this measure. Almost all online casinos give 99.53 / 99.55% RTP for Craps anyway, adding something like "based on the best decision". On the contrary - for Don't Pass the house edge is 73.33 and the Element of Risk - 220, which beautifully shows WHY: you multiply it by 3. It's not immediately obvious when looking at 98.64% and 99.55% ratios. It's even easier for Craps by Dragonfish where you always quadruple your winning Come-Out stake. Hence you multiply 73.33 by 4 to get 293.33 average rounds. So this metric can be useful in explaining the Element of Risk. Just another advantage!
That more odds require bigger bankroll is also true and also not relevant here. It's about presenting (and explaining) the combined house edge.
Last edited by: MattUK on Jul 10, 2020
charliepatrick
charliepatrick
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July 10th, 2020 at 8:01:57 AM permalink
Quote: MattUK

...Almost all online casinos give 99.53 / 99.55% RTP for Craps anyway, adding something like "based on the best decision"...

I understand how they can try and add "based on the best decision". but I believe these figures are misleading and I assume these are not UK based.

The various Craps bets are outlined at https://www.ukcasinotablegames.info/dice.html . In land based casinos the House Edge would therefore have to be defined on the "Pass" bet rather than the combination of "Pass" and "[Taking] Odds" bets.

Also from an expected profit vs loss, once you have made your initial bet, there is no "optimal decision" as it doesn't matter whether you make the Odds bet or not. If you are measuring Element of Risk then you're better off taking maximum Odds.

What would be interesting is whether they count Odds betting towards the requirement when looking at having to recycle bets to gain bonuses. If so then 20x Craps would be a good place to use.


Track Odds
If you had three horses with odds of Evens, 2 to 1 and 3 to 1, the calculation would be as follows.
Horse A - 2.00, Evens (or 1/1), +100
Horse B - 3.00, 2/1, +200
Horse C - 4.00, 3/1, +300

The book value can be calculated either by looking at how much to win £100 or from first principles.
Horse A: £50, Horse B: £33.33, Horse C: £25 - total needed = £108.33. So book value = 108.33%
To win £12 you would need to bet A:£6, B:£4, C:£3 - total needed = £13. So the bookie makes £1 for every £13 bet = 7.69%

American odds against (+) are what you get back from a $100 bet (e.g. +150 = 6/4 pays $150) or odds on (-) what you have to bet to win $100 (e.g. -250 = 2/5 needs $250 wager).
MattUK
MattUK
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July 10th, 2020 at 8:19:38 AM permalink
Charlie, while it's kind from you to explain to me the American odds in sport, it was a joke and this is now off topic. I was able to show that this metric can easily explain the difference between the house edge and the Element of Risk - on the top of those described initially - and I thank you for your role in this discovery.
MattUK
MattUK
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July 10th, 2020 at 1:33:22 PM permalink
It's also more accurate with a very small house edge. For example, 0.27% house edge can be anything between 364 and 377 rounds. It doesn't even need a comma.
Mission146
Mission146
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July 11th, 2020 at 12:52:35 AM permalink
House Edge, as I think has been mentioned, is just:

1 - (RTP% expressed as a decimal) and then converted back to a percentage. Alternatively, 100% - RTP% = House Edge.

Personally, I think itís easiest for someone who doesnít gamble, or gambles very casually, to understand RTP. Itís easy to describe to them. 97% RTP and you can say, ďFor every $100 you bet, youíre expected to get $97 back, and in the extreme long-run, thatís how it will play out. Youíll lose $3 for every hundred in bets.Ē

When it comes to propositions over 100%, then the concept of House Edge either becomes Player Edge or Negative House Edge, which introduces a new term, in either case. With a 101% proposition, it would just be 101% RTP, so the terminology also never changes.
Vultures can't be choosers.
MattUK
MattUK
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Thanks for this post from:
Mission146
July 11th, 2020 at 2:16:35 AM permalink
Quote: Mission146

Personally, I think itís easiest for someone who doesnít gamble, or gambles very casually, to understand RTP. Itís easy to describe to them. 97% RTP and you can say, ďFor every $100 you bet, youíre expected to get $97 back, and in the extreme long-run, thatís how it will play out. Youíll lose $3 for every hundred in bets.Ē


Yes, RTP is useful, but so can be my metric (for other purposes). We can see already it beautifully explains how the Element of Risk works and differences between 5 roulette variants (5th being Atlantic with a score of 38 for even money and 19 for the rest). They both can be used interchangeably. I suspect it's TOO player-friendly for casinos!
Actually, here's the roulette comparison table!

Roulette comparison table



Variant Loss of one unit per number of rounds house edge (%)
American 19 5.26
Alphabetic 25 4
Card Roulette by OpenBet 27 3.70
European 37 2.70
Atlantic 38 for even money, 19 for other bets 2.63 / 5.26
Riverboat 38 for Blue and Orange bets, more for other 2.63 / scary
Roulette73 73 1.37
French - 1/2 is saved if 0 is spun 74 for even money, 37 for other bets 1.35 / 2.70
Money Back Roulette by Cayetano 74 1.35
European enhanced - Street pays 11.21 100 for Street, 37 for other bets 1 / 2.70
French enhanced - 2/3 is saved if 0 is spun 111 for even money, 37 for other bets 0.90 / 2.70
French enhanced - 3/4 is saved if 0 is spun 148 for even money, 37 for other bets 0.68 / 2.70
European enhanced - happy hour, Red pays 1.05 370 for Red, 37 for other bets 0.27 / 2.70
European enhanced - invitation only, 0 may tie infinite for selected bet, 37 for other bets 0 / 2.70
European enhanced - invitation only, 36 pays 36 infinite for 36, 37 for other bets 0 / 2.70

Please pay attention to my very own French enhanced variants. 5Dimes Bonus Casino enhances even money payouts to 1.04 which results in "ugly" score of 132.14. This is because they increase the payouts with the green zero still in place instead of nicely shredding the house edge. Here we have clean, easy and elegant score of 111 and even 148, which essentially separates smart guys from the other. In the "2/3" variant 30 returns 20 instead of 15, 150 returns 100 instead of 75 and so on. In the "3/4" the stake is halved again and the casino takes only a quarter.
Last edited by: MattUK on Jul 11, 2020
charliepatrick
charliepatrick
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July 11th, 2020 at 4:23:55 AM permalink
^ Not to be picky but historically UK, by law, used the same rules as "French". However according to https://www.ukcasinotablegames.info/roulette.html it would appear they can pay "even money, unless zero is spun whereby either half or all of the even chance bets will be lost, depending on the rules of the club.". There are a few casinos who do have double zero and outside bets lose on zero.
MattUK
MattUK
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July 11th, 2020 at 5:22:37 AM permalink
Every bet losing on 0 is called European and half-loss on even money is called French, eventually La Partage.

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