Reliable completion of the computing jobs through Amazon spot instances (SIs) with proper bargaining is challenging. Therefore, an SI bidding system is developed for deadline constrained jobs considering both the conditions of the market and the condition of the user. The system tries to bargain with the provider by bidding low when the task is not urgent. After that, the system increases the price or the price distribution gradually when the progress is lower than required. To calculate the bid distribution, we compute the probability density of the price after five minutes. Then, we apply our developed equations to compute bid-prices from the probability density function. Equations are easily interpretable to both humans and machines. We also consider long-term probability distributions of the prices for the reliable completion of the job. Tasks with several days deadline are prescribed to bid considering the daily price-curve. According to the evaluation of Amazon SI price, the proposed system effectively saves 79%-87% for jobs with several hours deadline and saves 82%-100% for jobs with several days deadline compared to the on-demand instances. Moreover, our algorithm helps all bidders by keeping the price low.