# Homework Help: A math problem related to betting

1. Oct 12, 2014

### the_man

I just want to say this is nothing illegal because Ive used the word "Betting". The thing is that I have a math problem and I need someone to help me find the best solution. I dont know if this is the right place to post it. If not, please dont delete it, just moved it. Thanks.

1. The problem statement, all variables and given/known data

So for those who are not familiar with betting here is an example:

STAKE x ODDS = PAYOUT ---- 10*3 = 30
PROFIT = PAYOUT - STAKE ---- PROFIT = 30-10 -> +20

But the problem is that my bookmaker takes 7% commission on PROFIT. What I want is to adjust my numbers so that my winnings/profits/stats are like they would be if there is no commision? In the previous example my profit was +20, when bookie takes 7%, Im left with +18,6. But I dont want that, I want my profit to be +20, so thats why I made little formula to adjust my STAKE, so that my profit is +20 after the 7% commission. You find the formula on the picture bottom-right corner or under "Relevant equations".

Example 1
But lets forget about my STAKE Adjusting Formula for a second and let me show you an example.
If I bet: 10 * 3 = +20 and I LOSE, my Overall Balance is -10
and I bet again 10 * 3 = +20 and I WIN, bookie takes 7% and I have a profit of +18,6 which I add to my Overall Balance and I get +8,6.

Example 2
Now lets do the same thing but with my Adjusted Stake which instead of 10 is now 10,75. That number allows me to win an original profit of in our example +20 after commision instead of +18,6 when stake is =10. So lets do this:
If I bet 10,75 * 3 = +21,5 and I LOSE, my Overall Balance is -10,75
and I bet again 10,75 * 3 = +21,5, and I WIN, bookie takes 7% and I have a profit of +20, which I add to my Overall Balance and I get +9,25.

Example 3
Now you see the problem. The right thing if there is no commission would look like this and this is what I want to accomplish.
If I bet: 10 * 3 = +20 and I LOSE, my Overall Balance is -10
and I bet again 10 * 3 = +20 and I WIN, there is no commission because its a perfect world we live in, and I have a profit of +20which I add to my Overall Balance and I get +10.

Now is there any way that I can accomplish the same numbers as shown in Example 3 with commission included. The thing to remember is that bookie only takes 7% on winning bets when I make profit. I am calculating my profit and do my stast at the end of the month. I have around 180 bets a month with the winning rate of 38%-45%. Maybe I can somehow return it on a long term.

2. Relevant equations

A) STAKE = PROFIT / (1 - 7/100) * (ODDS -1)

3. Picture attached

HERE

2. Oct 12, 2014

### RUber

It looks like you are asking if it is possible to risk $10 at 3:1 odds and receive a net$20 in winnings after the bookie gets his share.
To that, I would say no.
If you are asking if there is a way for WIN + LOSS = $10, then probably. WIN + LOSS =$10
WIN = (BET*3)(1-.07)-BET
LOSS = BET
WIN = (3 LOSS)(.93)-LOSS
WIN = 1.79 LOSS
Plug this back into the original WIN + LOSS = 10 and there you have it.