The reason you wouldn't bet 1 yen, is to discourage others from throwing their money into the pool too. The moment all 3 bet on A, and fourth bet 1 yen on B, the first person would then say "actually, in addition to my bet on A, I also bet 0.3 yen on b to double-dip!" (1.3 / 3 = 0.3... when you round ).Gambling can be terrifying, but it doesn't normally work much like in the story. Normally, a gambler doesn't offer some fixed payment against just whatever an opposing party subsequently chooses to bet. If someone offered a bet of $1000 against any counter-bet, then I'd just bet 1¢ unless I thought that my opponent had selected a genuine sure thing. Instead, most gambles involve stated odds, something such as $100 at five-to-one odds, or such as $10 against ten doughnuts. Ordinarily, even when odds aren't precisely known, they are constrained.
If three people jointly offered ¥1600 against ¥10000, they'd have jointly accepted eight-to-fifty odds, and the normal payoff for each would be at those odds. So, if they won, the fellow who'd offered ¥800 would normally get that back plus ¥5000 (for a total of ¥5800), the fellow who'd offered ¥500 would get that back plus ¥3125, and the fellow who'd offered ¥300 would get the remainder.
Again, I was writing about how gambling is normally done. Alternatives, with odds-caps and so forth are possible, but the discussion should state any deviations from the norm.The reason you wouldn't bet 1 yen, is to discourage others from throwing their money into the pool too. The moment all 3 bet on A, and fourth bet 1 yen on B, the first person would then say "actually, in addition to my bet on A, I also bet 0.3 yen on b to double-dip!" (1.3 / 3 = 0.3... when you round ).
If he is absolutely certain that B will win (aka matchfixing), then the large bet is a way to near-guarantee noone bets with him forcing him to share the prize (a third of a large bet, is still a bet large enough he will lose money if A - his letter of choice - wins), while also inviting newcomers to join the coalition of A-betters raising the prize-pool.
In addition to that, there is the fact that often you can't earn more than you bet to begin with (can only double your money), regardless of odds. Simple way to let the bookie earn tons. Also/or a way to get the suckers to continue betting by letting them regain some money even at a loss.