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Dice (Encrypted Version)
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Introduction
This section discusses the popular game known as 'dice', typically found in online casinos that utilize it cryptocurrency for wagering and transactions. This game is distinct from traditional six-sided dice; instead, outcomes depend on a random integer between 0 and 10,000. It's also important not to confuse it with other games simply labeled 'dice'.
Rules
- Unlike what the name suggests, the outcomes in this game are determined by a randomly selected integer that falls within the range of 0 to 10,000.
- Players have the option to choose either a target number for winning or specify the odds (for instance, 2 to 1).
- The objective to win could involve rolling a number that exceeds a certain specified limit or falls below another.
- Should a player modify one aspect of their bet (be it the target for winning or the odds), the game will adjust the opposite accordingly to maintain a winning odds ratio that is inversely related to the winning probability, guaranteeing consistent house odds across all betting scenarios.
Example
Imagine a scenario where a game guarantees a 99% return. If the player sets their odds to 2 to 1, then their winning chance gets adjusted to 0.99 divided by 2, resulting in approximately 49.5%. Possible targets to achieve this include:
- Over 5050
- Under 4950
Players can switch between these winning targets at their discretion.
If a player alters their odds to 3 to 1, the game recalibrates their winning chance to approximately 0.99 divided by 3, equal to 33%. The goals that would fulfill this winning condition include:
- Over 6700
- Under 3300
I'm uncertain how ties are resolved when the winning number is an integer. The house advantage is reduced by 0.01% if ties are considered pushes as opposed to losses.
The table below outlines various winning goals correlated to the return to player (RTP) for bets that yield a 2 to 1 payout. For instance, if the winning goal is set below 4975, the RTP would be 99.5%.
Return to Player Guide
| Return to Player |
Probability Winning |
Under | Over |
|---|---|---|---|
| 99.5% | 49.75% | 4,975 | 5,025 |
| 99.4% | 49.70% | 4,970 | 5,030 |
| 99.3% | 49.65% | 4,965 | 5,035 |
| 99.2% | 49.60% | 4,960 | 5,040 |
| 99.1% | 49.55% | 4,955 | 5,045 |
| 99.0% | 49.50% | 4,950 | 5,050 |
| 98.9% | 49.45% | 4,945 | 5,055 |
| 98.8% | 49.40% | 4,940 | 5,060 |
| 98.7% | 49.35% | 4,935 | 5,065 |
| 98.6% | 49.30% | 4,930 | 5,070 |
| 98.5% | 49.25% | 4,925 | 5,075 |
In the image above, bets awarded a 2 to 1 payout range between below 49,600 and above 53,999. The statistics presented indicate that this translates to a 99.2% RTP, which can easily be calculated as 2 multiplied by (49,600/100,000) equals 99.2%.
Provably Fair
Consider that Amy and Bob want to play rock-paper-scissors online without relying on mutual trust. How can they achieve this?
This can easily be accomplished through the use of encrypted moves. Numerous encryption tools are available online, such as one at miniwebtool.com . For example, if Amy opts to play scissors, she can encrypt the word 'scissors' and receive an encrypted message known as a hash.
17f174ce4953e98e7418d22b29f7569505e4bcc39859e7825500d43a5ec1b87d d521d508d6ece5397021013c0c561bcd9ba947f1f40ac1a2f3a670b485b0aff6
She could send this hash to Bob before he makes his choice, serving as evidence that her move was predetermined. If Bob declares paper as his choice, Amy can assert her win by having Bob encrypt 'scissors' and demonstrating it results in the same hash she initially provided.
However, Bob, aware that there are only three outcomes, could hash 'scissors' himself to recognize its respective hash and subsequently choose rock. To mitigate this issue, Amy should incorporate additional random text to make her hash indecipherable. For instance, she might encrypt 'b980Cql98lbaj -- scissors' and receive a different hash.
5e4c68f7b35503c79b1aa31df87c6043bd30a1cff28b8431394cbbb829c90d4d51dec1b25ac5be44873572dbabd735c41006c83aff59ce06d3efe86513a57108
It's noteworthy that a hash comprises only 16 possible characters, which include numbers 0 to 9 and letters a to f. Essentially, the complete hash represents a numeral written not in base-10, but in base-16, known as hexadecimal .
The principle translates similarly in gaming environments described as 'probably fair'. However, an extra security measure is included by allowing players to have some influence over the betting outcome. Otherwise, casinos might exploit this feature. For example, a casino could notice that a player predominantly bets 'over' in Dice and then assigns them a low result as the game outcome, even after encryption.
In simple terms, here’s how the system functions:
- The casino generates a random string of characters, referred to as a Seed, encrypts it into a Hash, and then presents this hash to the player to demonstrate that the casino's contribution to the final outcome was predetermined.
- The player chooses his own seed.
- Players makes a bet.
- These two strings are combined (in any order).
- The resulting string from the previous step is then encrypted into a hash.
- A portion of the hash is converted from base 16 to base 10.
- Certain parts of the outcome from the previous step, potentially the last six digits, are mapped to a range from 0 to 999,999. This will determine the result of the game.
- Upon completion of the bet, the casino will disclose its own Seed, allowing the player to verify that it hashes to the Hash they received prior to placing the bet. This confirms that the outcome was predefined once the player chose their own Seed.
Nonetheless, the casino still has the capacity to manipulate outcomes. One strategy could involve utilizing a default player Seed. If players access the Fair Gaming screen, they will notice a default player Seed displayed. While players can opt for different seeds or enter a custom one, I suspect very few take the time to do this. A deceitful casino might meticulously select the default player Seed alongside their casino Seed to amalgamate them into a losing result.
Another method for casino deception could entail simply choosing a casino seed that results in a losing outcome, even if it doesn't match the hash provided to the player before the bet. This is what occurred during my experience at Wixiplay . If you encounter a situation where the casino's seed and hash do not align, what options do you have? If you accuse them of dishonest practices, they may either deny the charges without explanation or ignore your claim entirely. My experience with Wixiplay was that they initially disregarded me. Later, when I escalated the issue to the Curacao Gaming Control Board , I didn't even receive a response.
Provably Fair Casinos
Gaming Outcome Program
It can be quite tedious to navigate all of the steps mentioned above to ascertain if a game outcome is fair. To streamline the process, I developed a PHP program designed to easily establish the game outcome, provided both player and casino seeds are known. This program will function correctly only if the game outcome is determined as follows:
- First, combine the server and client seeds, starting with the server seed.
- Then, generate a SHA-512 hash of the string from the first step.
- Convert the initial five characters of the hash from hexadecimal to decimal.
- If the result obtained in the previous step exceeds 999,999, move five positions forward in the hash and repeat step 3. Otherwise, proceed to step 5.
- Extract the last five digits from the preceding step. This will determine the game result.
This script is applicable for the Dice game at Crypto.Games. Other casinos might have different methods for determining the random six-digit number or may utilize a hashing function other than SHA-512.
To use my program, go to this PHP Sandbox , adhere to the instructions provided in the comments at the start regarding when to input information and press 'Execute code.' The resulting game outcome along with confirmation of a legitimate Server Seed will appear in the Result box beneath the code.
As a contingency, the button below will disclose my code.
// Dice game conversion for Crypto.Games
// To utilize, enter the Client Seed on line 5, Server Seed on line 6, and the Hash of the next Server Seed on line 7.
$client_seed = \"f0g9s8f7g097sdfg098sd7f0g87s0fg897\";
$server_seed = \"SxG74IkdDRmWh0jT015TCA01fUoCA0lI2N3KxS8L\";
$next_hash = \"1c42ef7fcbb94c2841d4ee88467c13813c30f5f774260f1a308b960884a7fd8b\";
$server_seed_hash = hash(\"sha256\",\"$server_seed\");
$combined_seed = $server_seed.$client_seed;
echo \"Combined seed = $combined_seed\
\";
$combined_hash = hash(\"sha512\", $combined_seed);
echo \"Hash of combined seed = $combined_hash\
\";
$position=0;
$first_five=substr($combined_hash,$position,5);
// echo \"First five characters, starting with position $position = $first_five\
\";
do
{
$hex_to_dec=hexdec($first_five);
$position+=5;
}
while ($hex_to_dec > 999999);
// echo \"Converted to decimal = $hex_to_dec\
\";
$mod5=$hex_to_dec%100000;
echo \"\
Game outcome = $mod5\
\";
if ($server_seed_hash == $next_hash)
{ echo \"Server seed match.\
\"; }
else
{
echo \"SERVER SEED MISMATCH!\
\";
echo \"Server seed =\\t$server_seed\
\";
echo \"Server seed Hash=\\t$server_seed_hash\
\";
echo \"Alleged next Hash=\\t$next_hash\
\";
}
// Procedure
// 1. Join server and client seeds, with the server seed first.
// 2. Generate a SHA-512 hash of the combined string from step 1.
// 3. Convert the first five characters of the hash from hexadecimal to decimal.
// 4. If the outcome from step 3 is over 999,999, advance five characters in the hash and repeat step 3. If not, proceed to step 5.
Encrypted Dice Version - Wizard of Odds
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This section discusses a game commonly referred to as 'dice,' which is frequently found in online casinos that utilize casino blacklist .