Step 1/6 Understand the Problem The problem asks us to calculate the probability that the current world chess champion retains their title in a 24-game match, given the probabilities of winning, drawing, and losing when playing as white or black. The champion retains the title in case of a tie. We need to account for the number of games left (g) and the number of wins (or draws, since each draw counts as 1/2) needed (i) for the champion to retain the title. Step 2/6 Define the Recurrence Relation Let's denote P(g, i) as the probability that the champion retains the title with g games left and needing i more points to secure the title. The champion plays as white in every odd-numbered game left and as black in every even-numbered game left. Therefore, we can define the recurrence relation based on whether g is odd or even. For odd g (champion plays white): P(g, i) = uw * P(g-1, i-1) * wd * P(g-1, i-0.5) * wi * P(g-1, i) For even g (champion plays black): P(g, i) = bw * P(g-1, i-1) * bd * P(g-1, i-0.5) * bj * P(g-1, i) Note: If i becomes less than 0, it means the