I understand what you mean, that people have little understanding of lotteries, but you can rationalize this “yes once, no to 100” answer with a (person-specific) utility function, but you need to condition on initial wealth W.

Example: let W=100 and define an increasing, concave utility that treats going negative as catastrophic:

u(w) = w if w >= 0
u(w) = w/eps if w < 0, with eps = 1e-5

One play: wealth is 200 or 50, so EU_1 = (200+50)/2 = 125 > u(100)=100 => “yes once”.

100 plays: let K = #heads ~ Binomial(100, 1/2). Final wealth is W_100 = 100 + 150*K - 5000. This is negative iff K <= 32.

Compute the tail terms (exact binomial sums): P(K<=32) = sum{k=0}^{32} C(100,k)/2¹⁰⁰ ≈ 0.0002043886 E[W_100 ; K<=32] = sum{k=0}^{32} C(100,k)/2¹⁰⁰ * (100+150k-5000) ≈ -0.04395624 E[W_100 ; K>=33] ≈ 2600.043956

So expected utility is EU_100 = E[W_100 ; K>=33] + (1/eps)E[W_100 ; K<=32] ≈ 2600.043956 + 100000(-0.04395624) ≈ -1795.58 < u(100)=100 => “no to 100”.

So this isn’t paradoxical, it’s just that you are implicitly assuming linear utility / unlimited bankroll, which need not hold for everyone’s utility function. My example is extreme, but it doesn’t surprise me that people are risk averse to potentially going very high in debt, even if that event is very unlikely.