Why Stake's mines is nearly IMPOSSIBLE TO WIN?
Tags: stake, maths, gambling, gamedev
Published: 2024-05-21 22:30:15

Stake.com has been the talk of the town in recent times. It has become quite popular among youth. Specially, games like gems, crash, plingo etc. are played largely. 

This platform allows you play with zero investment just to check if you could win (trust me it's addictive). Then my engineer brain brained that is it worth the try?

So, before throwing the money into this pond, I thought of doing a set of trials just like we did in probability in the mathematics lecture (if you did you know).

## Let's begin with MINES

I chose the game 'mines'. Let me introduce you to the game (in case you don't know). In this game, we have a grid of 5x5 tiles where any `X` tiles will have mines and rest will have gems. You can customise this value of `X` and the profits change accordingly. The more the mines, the higher the profit on win. If you choose a mine, you lose the game (your bet becomes zero). Else if you choose a gem, you can either continue playing on same grid (with the open tiles as it is and mines still hidden) or can cashout the amount and be profitable. 


![Stake Gems Game Screenshot](https://dev-to-uploads.s3.amazonaws.com/uploads/articles/645hx128ozw1wcq2fw3t.png)

### Experiment I did

So I chose this game and ran the following experiment:

**I chose 6 mines in the game. Selecting 3 tiles as gems continuously in a single trial gives me 2.35x of my bet. I will start with Rs. 1, every time I loose, I will double the bet and move to next trial. Every time I win, I will reset bet amount to 1 & stop.**

### What's ChatGPT says about it?

I gave ChatGPT the same scenario and asked what would be the profit if I win of nth trial in an experiment of n trials.

Total Amount Bet After n Trials: 1+2+4+…+2^(n−1) = 2^(n) - 1
Total Winnings After n Trials: 2.35×2^(n−1)
Total Profits After n Trials: 0.35×2^(n−1)+1

Next I asked it, if it is a profitable strategy then here was it's response:

The strategy of doubling bet after each loss and resetting after a win, known as the Martingale strategy, is risky. 

### Reasoning behind the Martingale Strategy being Risky

1. Probability of Winning: 

![Probability of winning](https://dev-to-uploads.s3.amazonaws.com/uploads/articles/b7fetygdnsd4orre1k5i.png)

2. Expected Loss and Gain: In the long run, because you are always risking more than you can win in a single round (since your bet increases exponentially, while your payout remains linearly tied to the bet), there is a high risk that a prolonged losing streak will exhaust your funds or reach the house limit.

3. Profit Calculation: From the profit formula derived 
0.35 × 2^(𝑛−1)+1, you can see that while you make a small profit when you finally win, the amount you have to bet grows exponentially. A single loss after several wins can wipe out all previous gains plus more.

4. Risk of Ruin: The most significant risk is that a prolonged losing streak will require you to bet amounts that are either unsustainable for your bankroll or exceed the maximum betting limit allowed by the game. This can lead to a situation where you cannot continue to double down, and you suffer a massive loss.

5. Long-Term Viability: Although theoretically, the Martingale system can make a profit in the short term if you stop after a win or a small number of trials, it is generally not profitable in the long term. The exponential growth of bets required after each loss combined with the limits of practical betting conditions (like table limits and personal bankroll limits) and the less than 1:1 payoff (since 2.35 × bet does not fully cover the exponential growth of the bet amounts) make it unsustainable.

### Is this strategy usable?

In conclusion, while this strategy can yield profits in a specific, controlled scenario, it is not advisable as a long-term betting strategy due to the high risk of significant financial loss. It is generally better to look for strategies that manage risk and offer more sustainable returns.

### Let's run this experiment

Let's adjust the calculations based on a limit of 10 trials.

### Calculation if you win on the 10th trial:
**Bet Amount on the 10th Trial**:
- The bet amount on the 10th trial is \( 2^{10-1} = 2^9 = 512 \) rupees.

**Total Bet by the 10th Trial**:
- The sum of the bets for the first 10 trials (assuming you lose the first 9 and win the 10th) is a geometric series:
  Total Bet = 1 + 2 + 4 + ... + 2^9
  The sum of this series is:
  Total Bet = 2^{10} - 1 = 1,023 rupees

**Total Winnings on the 10th Trial**:
- If you win on the 10th trial, your winnings are:
  Winnings = 2.35 x 512 = 1,203.20 rupees

**Profit Calculation**:
- Profit is calculated as:
  Profit = Winnings - Total Bet
  Profit = 1,203.20 - 1,023 = 180.20 rupees

### Calculation if you lose all 10 trials:
**Total Loss After 10 Trials**:
- If you lose all 10 trials, the total loss is simply the sum of all the bets placed:
  Total Loss = 1,023 rupees

In this scenario, with a limit of 10 trials:
- If you win on the 10th trial, your **profit** would be approximately **180.20 rupees**.
- If you lose all 10 trials, your **total loss** would be **1,023 rupees**.

These results further underline how critical a win is when using this betting strategy, as your potential profit is closely tied to achieving at least one win within the limited number of trials.


## Is there any better strategy than this one

1. Fixed Wager Strategy
Instead of increasing your bets after losses, you simply bet the same fixed amount each time. This strategy limits your losses and can keep you in the game longer, though it also means that a win only recovers a single bet rather than covering all previous losses.

2. Proportional Betting
In this strategy, you bet a proportion of your bankroll, typically a small percentage like 1% to 5%. This means that when your bankroll increases, your bet size increases, and when your bankroll decreases, your bet size decreases. This method helps in managing your bankroll more effectively and decreases the risk of losing everything in a short period.

3. Stop-Loss Strategy
Set a stop-loss limit—this is an amount you’re prepared to lose in a session. Once your losses reach this limit, stop playing. This can help prevent the emotion-driven decisions that can lead to larger losses.

4. Taking Profits
Similar to a stop-loss, you can set a take-profit limit. This is a pre-set amount at which you cash out any profits above your starting bankroll. This helps lock in profits and prevents them from turning into losses.

5. Play for Bonuses
If you’re playing an online game that offers bonuses or free spins, try to make use of these offers to increase your chances without having to increase your stake. This can sometimes provide a buffer or free opportunities to win.

6. Decreasing Bet Strategy
Rather than increasing your bet after a loss, you could decrease your bet following a win, consolidating what you’ve won. This is essentially the opposite of the Martingale strategy and can sometimes be more sustainable.

7. Mathematically Informed Betting
Some betting strategies involve a more complex mathematical basis, such as the Fibonacci sequence, where bets are calculated based on the Fibonacci numbers. This still involves increasing bets after a loss but does so less aggressively than the Martingale.

8. Prudent Bankroll Management
Ensure your betting strategy allows you to play many rounds rather than burning out after a few large bets. Smaller, more manageable bets relative to your overall bankroll can help you withstand the natural variance in games of chance.

## Why I chose only 3 mines in a trial?

I asked GPT, which is better: 1.74x for 2 tiles, 2.35x for 3 tiles, 3.23x for 4 tiles and here's the calculation:

### Calculating the Probabilities

1. **Choosing 2 Tiles (1.74x profit)**
   - The probability of picking a gem (no mine) sequentially two times with 6 mines out of 25 tiles is: 
     P(2 gems) = 25/19 × 24/18 = 0.57

2. **Choosing 3 Tiles (2.35x profit)**
   - The probability of picking a gem (no mine) sequentially three times with 6 mines out of 25 tiles is:
    P(3 gems)= 19/25 × 18/24 x 17/23 ≈ 0.5287


3. **Choosing 4 Tiles (3.23x profit)**
   - If you choose to pick a fourth tile after successfully picking three gems:
     P(4 gems) = P(3 gems) x 16/22 = 0.3846

### Calculating Expected Values

The expected value (EV) for each option can be calculated using the formula:
EV = (Probability of Winning) x Payout - (Probability of Losing) x Bet

Assuming the bet amount is 1 unit for simplicity in all cases.

1. Expected Value for Choosing 2 Tiles
EV2 = 0.57 × 1.74 - (1 - 0.57) × 1
EV2 = 0.9918 - 0.43 = 0.5618

2. Expected Value for Choosing 3 Tiles
EV3 = 0.5287 × 2.35 - (1 - 0.5287) × 1
EV3 = 1.2425 - 0.4713 = 0.7712

3. Expected Value for Choosing 4 Tiles
EV4 = 0.3846 × 3.23 - (1 - 0.3846) x 1
EV4 = 1.2423 - 0.6154 = 0.6269


### Analysis
- **Choosing 2 Tiles**: The expected value of choosing 2 tiles is approximately 0.5618 units.
- **Choosing 3 Tiles**: The expected value of choosing 3 tiles is approximately 0.7712 units.
- **Choosing 4 Tiles**: The expected value of choosing 4 tiles is approximately 0.6269 units.

From this analysis, **choosing 3 tiles** for a 2.35x profit is a better option as it yields a higher expected value than choosing 4 tiles for a 3.23x profit. 

# Is this type of game generally profitable?

Games involving mines, similar to other forms of gambling with elements of both skill and chance, are generally designed to be profitable for the operator or the house rather than for the player over the long term. 

# Conclusion

By all the calculation, we can come to this result that you **might** make some few bucks if you are ready to invest a ton of it. Please see **might** is bold.

Please note that I haven't invested any money on this platform nor do I promote it. Its just a mathematical experiment and logical reasoning behind these types of games.