Optimum Bet Size Calculator

[Grind-It-Out]

We all know about Kelly for the long-term, but what about calculating bet size for a specified period of time and a specific target.

Example:

My bankroll is $100, I am betting on a -110 line and have a 55% chance of winning the game.

Kelly tells us to risk $5.50.

But, what if our goal is to reach a bankroll of $200 within 30 days (or, to make it more clearcut, within 30 bets, all one at a time)? What should we bet?

Would it be possible to create such a calculator?

My whole reason for asking this is that a lot of people deposit money with the mindset of "I'm going to try to double or triple my bankroll and then start playing conservatively."

[Pancho sanza]

You can't structure the bets over a period of time (esp over only 30 bets) so that you are guranteed a profit.

Your win rate is less than 100 % so there will always be risk of loss.

Best way to max bankroll growth is to just use kelly.

[Grind-It-Out]

I'm perfectly aware that I can't guarantee profit. Some players are willing to add extra risk in order to reach a short term goal, so I wanted to see if there was a mathematically-proven best strategy to go about it.

[Pancho sanza]

No, not without adding significant risk.

[Grind-It-Out]

No, not without adding significant risk.

Again, I KNOW there is risk involved. The whole reason I'm looking for this is for players who WANT a higher (or lower) risk/reward for a set period of time. Just because risk is involved doesn't mean there can't be a mathematical formula for such a situation.

[Flying Dutchman]

Yes, it can be done. Build a Monte Carlo simulation with added input of: the number of bets to be made over your betting period (you did not state this) and vary your Kelly fraction until you achieve the the double. Risk will rise with the greater fraction but so will your "win" average.

It's just like playing Russian roulette with more bullets.

[u21c3f6]

Given your scenario, here are some thoughts:

1. Kelly is optimal and unless you get a cluster of winners at the start, if you use a % greater than Kelly you will most likely have less money at the end of your series of wagers than if you simply used Kelly.
2. Increase your bankroll to $110 and make one wager (55% chance of success).
3. Make it a series of 40 wagers. You have a 5% edge. 40 wagers at $50 each (total $2,000 wagered) will result in a $100 profit (assuming you don't go bankrupt first). Of course, if you increase the number of wagers you can make to get to your target, you may get back to Kelly and/or at least decrease the chance of going bankrupt before you reach your goal.

Joe.

[Grind-It-Out]

Given your scenario, here are some thoughts:

1. Kelly is optimal and unless you get a cluster of winners at the start, if you use a % greater than Kelly you will most likely have less money at the end of your series of wagers than if you simply used Kelly.
2. Increase your bankroll to $110 and make one wager (55% chance of success).
3. Make it a series of 40 wagers. You have a 5% edge. 40 wagers at $50 each (total $2,000 wagered) will result in a $100 profit (assuming you don't go bankrupt first). Of course, if you increase the number of wagers you can make to get to your target, you may get back to Kelly and/or at least decrease the chance of going bankrupt before you reach your goal.

Joe.

Kelly is optimal for growth, but not for value. So, if you are seeking a set value, Kelly is probably not optimal.

For example. Say I have $100 and my goal is to have $200 after 1 bet. Let's say the bet is a +100 line and I have a 60% chance of winning.

Kelly tells me to bet $20. But, if I bet $20, I have ZERO chance of reaching my goal. My optimal solution is to bet $100. Will this lead to bankruptcy over time? Absolutely. But it also maximizes short term value.

What Flying Dutchman said makes sense, so I'll look into that. Thanks!

[Wrecktangle]

Kelly is optimal for growth given risk at whatever fraction you play. Most folks cannot employ it properly because they either don't really know their win % or don't realize that the win % can change over the season in any sport. Given this fact, it cannot be recommended as they will rapidly lose their bankroll.

[Cookie Monster]

The OP question has some application in real life. For example, in a betting tournament you have a fairly close estimation of the amount needed to qualify for the next stage. In such cases the objective is to maximize the possibilities of reaching your goal, which usually implies going bust if not.

In that cases the recommended strategy is starting conservative, (i.e. Kelly) for the most part of the tournament. That way you can have a better estimate of the goal. If you are lucky, you have also increased the bankroll (or have lost so much that no tournament strategy will help much). In the last few rounds you make a progression to reach your goal. Say, you have 900, goal is 1000, min bet is 1, payout 1:1. With 3 rounds to go, you bet 102 (goal 1002). If win, last 2 rounds, min bets. If lost, new amount 798, bet 203 (goal 1001). If lost, you have 595, you can go all in in your last bet, or just bet 405. That way your possibility of reaching your goal is 87.5%

Of course, tournament strategy is way more complex, there are different odds (moneylines are great in last rounds), the goal is not fixed, and you try to bet the contrary of the guys that you are chasing (or bet the same as the guys behind you).

[canon714]

Just go all in.... lol

[catalincoto]

Coeficients

Scenario

Bank = 100 => 1 um = 1%

I see many cappers recomended some coeficients, apply to this unit

Example

CIN Reds => ml 3*
CHI WHITE Sox => rl 2*
STL / PHIL => over 1*

My question is know anybody, a algorithm to do this or a calculator, spreadsheet, etc.

Thanks