Simple Model
Before creating a real game where the house wins money, let's first create a simple version of the simulation game. The constraints of this game are: RTP = 100, and we only allow odds at 1, 2, 3, 4, and 5.
🌸Based on our set conditions:
• When betting at odds of 1: With RTP = Probability * Odds, Probability = 100%. That is, betting at odds of 1 will never be hurt, must be 100% pass, 0% explode.
• When betting at odds of 2: With RTP = Probability * Odds, Probability = 50%. Betting at odds of 2 must be 50% pass, 50% explode.
• When betting at odds of 3: With RTP = Probability * Odds, Probability = 33.33%. Betting at odds of 3 must be 33.33% pass, 66.67% explode.
And so on. Then distinguish the explosion point X:
• When 1 ≤ X < 2: Only players betting at odds of 1 win (get multiples).
• When 2 ≤ X < 3: Players betting at odds of 1 and 2 both win.
• When 3 ≤ X < 4: Players betting at odds of 1, 2, and 3 all win.
• When 4 ≤ X < 5: Players betting at odds of 1, 2, 3, and 4 all win.
• When X ≥ 5: Players betting at odds of 1, 2, 3, 4, and 5 all win.
Notice? Under the setting of **Random Number** from 0-1, the reciprocal of the random number ranges from 1 to infinity. That is to say, it is possible to design any multiplier limit for Crash, and even the interval division can be changed.
🌸Actual Model
The multipliers range from 1.01 → 1.02 → 1.03 ... → 5000. The probability is 1/1.01 → 1/1.02 → ... → 1/5000.
As per my habit, I like to place smaller values at the front, which depends on personal preference. When the random number is r:
• r<1/5000: All betting points win the multiplier
• r>1/1.01: All betting points do not win (explosion multiplier less than 1.01)
• Other explosion points are 1/r
For example, if r=0.45738291, then 1/r=2.18635. Any betting points less than 2.18 are considered successful. As for how to create a house advantage, I'll leave that to you all for a bit of brainstorming.
At this point, the curious Xiao Ming might ask another question: "Teacher, but not every player will necessarily Cash Out at the remaining fixed points, can I ensure that each player's final RTP is within our set value?"
We can look at this problem from another angle. If we can ensure that with a sufficient number of samples, the results converge to a specific value; then in fewer rounds, we will consider the data deviation as "fluctuation".
Why would players play a game that is bound to lose in the long run? I think the answer lies in "fluctuation". For an individual player, there may be wins and losses in the short term; but for the house, as long as enough people play, and the betting amounts are within an acceptable risk range, then through the law of large numbers, this game only needs time to accumulate, and it will steadily bring us profit.
🌸Conclusion
In terms of programming, generating a random number r (between 0 and 1), then 1/r is the explosion multiplier for that round:
• When r<1/maximum multiplier: triggers the upper limit, all betting points win (get the multiplier).
• When r>1/minimum multiplier (such as 1.01): immediate explosion, all betting points do not win.
• Other situations: explosion points are 1/r.
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