Slot Expected Value, Finding the Best Betting Strategy
The St. Petersburg quince theory is a very profound quince theory philosophy in slot machine design. Calculate the expected value of the slot machine to find the best slot machine betting strategy based on the influence of the RTP value. The current RTP value usually exceeds 100. Although the extreme slot machine design attracts players, it is also holy. According to Peter Bo’s calculations, for every slot machine designer, the probability is the main lesson forever. In every design, it is necessary to bring out the fun, but the winning probability dominates the length of the game time.
St. Petersburg Quince Theory
St. Petersburg quince theory Daniel Bernoulli (1738) was quite fond of this mathematical theory, this theory is also used in the expected effect argument, in 1730 brought the mathematician Daniel Bernoulli’s cousin Nicholas I’Bernoulli wrote a letter to the French mathematician Pierre ‘Haimon’ de Montmartre, in which he asked about flipping a coin, assuming that the first toss is heads, you can earn 1 yuan, if If the tail is thrown, it must be thrown again. If the second throw is heads, you can get 2 yuan. If the second throw is tails, you must throw it a third time.
There may be endless results following such a game, but how much money is willing to spend to participate in such a game during such a game, the expected value of this St. Petersburg quince theory is: E=1/2X1+4 points 1. However, it starts to form an infinite cycle power of N, and the expectation value in the game will gradually increase infinitely. The money paid for the game to obtain the experience is of course infinite growth. In the game, you can choose to earn 1 yuan or 2 yuan , Unlimited amounts ranging from 4 yuan, these multiple calculation methods have been answered in the 1738 paper.
In Bolun’s principle, the expected value is determined to determine the strategy standard:
1. The principle of diminishing marginal utility: a person makes the most effective use of his own wealth, and the possible influence derivative of each order in the function becomes zero, then in the process of increasing wealth, the satisfaction conditions will also change step by step And down, the amount originally set will continue to increase.
2. The principle of maximizing benefits: Under the conditions of risks and unknowable results, every behavioral criterion in decision-making can maximize one’s own benefits, but the expected value of benefits does not represent the absolute expected amount.
Calculating slot machine expected value method
Suppose we want to play a slot machine game, and the cost of participating in this game is 100,000 yuan. Usually, such regulations will lose many customers, because the amount is set too high to achieve the degree of freedom of choice, then if we use St. Petersburg quince In terms of the expected value of the slot machine, assuming that the slot machine needs to spend 100,000 yuan for each rotation, and the probability of each rotation is 50% winning and 50% not winning, then 1/2 of the game will win 1 yuan. When there is no win in the round, the double betting amount paid in the next round is also 50% winning and 50% not winning. Such calculation results will reach 1/2 to the K power.
Well, in the professional terminology of gaming games, what players like is to pursue small gains and enjoy the feeling of winning money. Therefore, free games and bonus games that can be triggered in slot machines are the slot games with good RTP value that the public pursues. , in the absence of detailed data, the player’s expected value of winning is always greater than the expected value of the slot machine.
For the gambling games produced by too high Volatitity, the St. Petersburg quince theory has become an extreme betting strategy. In the absence of infinite RTP value, the casino can make a stable profit of 0.1 yuan as long as the RTP value is set at 99.9. Therefore, the best betting strategy is to leave today’s slot machine game if you win more than 1% of the principal. Otherwise, when the banker wins 0.1% of the income, the slot machine players will eventually be swallowed by the banker bit by bit.
Slot machine important basic terms and data
1.Base Game :
Also known as the Main Game, the main game is the wheel game when the player spends money and presses the Spin button every time
2. Feature Game :
It can be roughly divided into two categories: Free Game and Bonus Game. Free games usually refer to the gameplay based on the Base Game plus one or several features. another wheel game
3. Jackpot :
Bonuses are divided into two categories: stand-alone accumulation and online accumulation, which can be subdivided into a variety of different accumulation methods and payout mechanisms
4.RTP (Return To Player) :
How many points can a player win for every 100 points invested on average
Real money games will have different regulations in different regions to limit the RTP range. Generally speaking, the RTP of the entire game will fall between 85 and 98
Virtual currency is usually not restricted by regulations, and it can exceed 100. The following is the generally recommended RTP range
Base Game RTP : 45~75
Feature Game RTP : 20~50
Jackpot RTP: 1~10
In the payout table, prizes are usually awarded for more than 3 lines, and there are also some games where 2 lines or even 1 line alone will give points
6. Lines :
Players can bet on the maximum number of lines, usually between 9 and 50 lines, some will be designed to freely adjust the number of bet lines, and some will be designed to be a fixed number of bet lines
7.Feature Frequency :
How many rounds the player plays can trigger a free game, generally between 65 and 130
8.Feature Average Pay :
How many times the total bet points of a single game can be obtained on average by playing a free game
9. Hit Rate :
The proportion of games scored by the player in each game played by the player. This data cannot be directly obtained from the Excel calculation. It can only be counted by the simulator. The order of the rollers, the number of bets and the paytable Data has the most direct impact
10. Volatility :
Game wins and losses fluctuate, there is no standard mathematical formula to calculate, and the standards used by various manufacturers to evaluate this data are not consistent
Slot Machine Design Process – Game Designer
1. At the beginning, determine the platform and market for this game, and determine the game theme, features and fluctuations in winning and losing according to the platform and market
2. Preliminary calculation and planning for Game Rules, RTP, PayTable, Lines, Feature Frequency & Average Pay
3. After calculating the Excel Parsheet and writing the simulator, interactively verify the correctness and obtain Hit Rate and many other statistical data
4. Repeatedly play and adjust mathematics to increase the game experience and make the game meet the original goal
For example: (The numbers in the following steps are random examples)
1. The goal is to make a Social Slot Game on the mobile platform, the Asian market, sports themes, and fluctuate greatly in winning and losing
2. Do basic calculation and planning for some important data, must meet the goal of step 1
Game Rules : 1 Free Game with Sticky Wild
RTP : 95, Base 55 + Feature 40
PayTable: 3 or more lines give prizes, the highest odds symbol 5 lines 10000 points
Feature Frequency & Average Pay : 120 & 48X Total Bet
3. Calculate the Parsheet and write the slot machine simulator for interactive verification, and get the Hit Rate and other statistical data
4. Adjust various mathematics according to the data and trial play until you are satisfied
In these steps
The platform and market of step 1 are usually already decided, and the theme, features and fluctuations of winning and losing may be determined by the producer
Step 2 is a test of the experience of the game designer, the more experienced the more experienced in this step can make the preliminary plan closer to the final product
Step 3 is the basic work of game designers. Unless it is a particularly difficult feature that requires a game designer who is good at calculation, this step should be the easiest and the least subjective
Step 4 is an extension of 2. It is also to adjust the balance of mathematics according to the needs of step 1. Step 2 has a good preliminary plan, and step 4 can proceed more smoothly