Card1:5x reward of bet amount
Card2:5x reward of bet amount
Card3:5x reward of bet amount
Card4:5x reward of bet amount
Card5:10x reward of bet amount
Card6:18x reward of bet amount
Card7:28x reward of bet amount
Card8:38x reward of bet amount on winning card 
I want to split my bet amount  on 8 cards and I want always profit ,bet amount should be multiples of 10, only one card will win and I always wants profit for any amount below 10000, pay out from any winning card should be equal or greater than bet amount 

To ensure that you always make a profit regardless of which card wins, we need to distribute your total bet strategically across the 8 cards, considering their respective reward multipliers. The key is to structure your bets so that the payout from any winning card will at least cover the total bet placed and guarantee profit.

### Step-by-step Approach:
1. **Identify the total bet amount**: Let's denote your total bet amount as \( B \), which should be split across 8 cards.
   
2. **Set variables for each bet**: Denote the amount bet on each card as follows:
   \[
   x_1, x_2, x_3, x_4, x_5, x_6, x_7, x_8
   \]
   where each \( x_i \) corresponds to the bet on card \( i \).

3. **Condition for payout and profit**: For each card, we want the payout (reward multiplier times the bet on the winning card) to be at least greater than the total bet:
   \[
   r_i \times x_i \geq B + p
   \]
   where \( r_i \) is the reward multiplier for card \( i \), and \( p \) is the minimum profit. We can also assume \( p > 0 \) since you want a guaranteed profit.

   For simplicity, let's consider \( p = 0 \), which means the payout equals the total bet, ensuring no loss. Later, we can adjust to add profit.

4. **Reward Multiplier Values**:
   - Card 1–4: \( 5x \)
   - Card 5: \( 10x \)
   - Card 6: \( 18x \)
   - Card 7: \( 28x \)
   - Card 8: \( 38x \)

5. **Create the system of equations**: For each card, set the condition that ensures the payout covers the total bet. For example, for card 1:
   \[
   5x_1 = B
   \]
   Similarly, for card 8:
   \[
   38x_8 = B
   \]
   Thus, we can solve for each \( x_i \) and distribute the total bet.

### Solution Outline:
We'll start with a simple strategy: minimize the total bet on cards with high multipliers (since they need less investment) and increase it on cards with lower multipliers.

1. **Example Solution**: 
   Let's choose \( B = 1000 \) and distribute it across the cards.

   - Cards 1–4 (5x reward):
     \[
     x_1 = x_2 = x_3 = x_4 = \frac{1000}{5} = 200
     \]
   - Card 5 (10x reward):
     \[
     x_5 = \frac{1000}{10} = 100
     \]
   - Card 6 (18x reward):
     \[
     x_6 = \frac{1000}{18} \approx 56
     \]
   - Card 7 (28x reward):
     \[
     x_7 = \frac{1000}{28} \approx 36
     \]
   - Card 8 (38x reward):
     \[
     x_8 = \frac{1000}{38} \approx 26
     \]

   ### Final Bets:
   \[
   (x_1, x_2, x_3, x_4) = 200, \quad x_5 = 100, \quad x_6 = 56, \quad x_7 = 36, \quad x_8 = 26
   \]

   - Total bet: \( 200 \times 4 + 100 + 56 + 36 + 26 = 1000 \)
   - Guaranteed profit since any payout will be at least equal to 1000.

### Do you have any questions or want further details on how this solution works? Here are some follow-up questions:

1. What happens if I increase the total bet above 1000? How does it affect profit?
2. Can we add a fixed amount of profit into the solution?
3. What if I want to optimize for maximum profit on specific cards?
4. How do these reward structures compare to traditional betting strategies?
5. How can the bet distribution change with different total amounts?

**Tip**: Always consider adjusting your betting strategy based on how much risk you're willing to take, especially for cards with lower reward multipliers.

Card1: 5x reward of bet amount
Card2: 5x reward of bet amount
Card3: 5x reward of bet amount
Card4: 5x reward of bet amount
Card5: 10x reward of bet amount
Card6: 18x reward of bet amount
Card7: 28x reward of bet amount
Card8: 38x reward of bet amount on winning card
I want to split my bet amount on 8 cards and I want always profit, bet amount should be multiples of 10, only one card will win and I always want profit for any amount below 10000, payout from any winning card should be equal or greater than bet amount.

Discover how to distribute bets across 8 cards with different reward multipliers to guarantee profit, even with a bet amount below 10,000. Learn the mathematical approach to solving this optimization problem using algebra and inequalities.

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