Suppose a number of players are given $100$ points each, and repeatedly engage in a gamble having positive expected value, with the goals of being the first player to reach $100000$ points. Solving for the optimal bet size per round to balance risk of ruin and speed of point accrual is a very difficult game theory problem, so the reasonable approach seems to be to impose a heuristic constraint on the risk of ruin, and optimize speed relative to that constraint. Let's say I decide I want no more than a $2$% probability of going bankrupt before reaching the $100000$ point goal. Now I can simulate the game a large number of times to find the bet size which reaches the goal in as few rounds as possible (probably the largest bet size) without exceeding the target risk of ruin.
However, suppose I am playing the game in practice, and have accrued a point total of $1000$. The remainder of the game is functionally equivalent to a new, identical game, except that in the new game, I start with $1000$ points instead of $100$ points. In other words, the game I've been describing has an optimal substructure. It seems to me that in the new game, my desired risk of ruin constraint should still be about the same, $2$% in the example; there seems to be no fundamental reason (apart from assessing my position relative to other players, which is beyond the scope of this question) to suppose I would have a different risk tolerance in the race from $1000$ to $100000$ than in the race from $100$ to $100000$. Allowing the risk of ruin to decline too much as the game progresses is an unnecessary speed concession.
The problem is that changing my strategy as the game progresses to retarget a $2$% risk of ruin means my original strategy actually had more than a $2$% risk of ruin. My present, $1000$ point self shouldn't care about this enough to dissuade me from retargeting (the past is in the past), but my past $100$ point self foreseeing this phenomenon cares a lot. It seems that what's needed is a function which maps every possible point total between $1$ and $99999$ to a bet size, where the risk of ruin at every input is more or less constant (maybe lower at the very end of the game due to the discreteness of the problem), but it is unclear that such a function is possible, because attaining points would always reduce risk of ruin no matter what function is chosen. Is is possible to construct such a function? If not, how can I rationally play this game when I know my underlying risk of ruin preferences won't change much as the game progresses, and I will not stick to any possible strategy I create?
EDIT regarding nature of gamble, as per request in comments: Suppose that each round consists of rolling fair dice, and the profit or loss a player attains for that round is computed based on the sum of the rolls (with a positive expected value). Profit or loss are always an integer multiple of the bet size. Each set of rolls is independent and identically distributed relative to their previous rolls and other players' rolls.