That sounds tough-- if the betting is their favorite part, you'll probably have a hard time separating them from it. Some possibilities:
1. Bet tokens that aren't money
If you bet poker chips instead of cash, the gambling element is still there but doesn't cost anyone any money. The tokens can still have some kind of value (being worth a chore, or control of the TV channel, or something else). They could even be redeemable for cash (i.e., they're good for chores but can also be traded at a face value of $1 or something).
They might not like this, as betting behaviors can be very different when the stakes are for money versus something else. But if the tokens have mutually appreciated value to you and your siblings it could be a great alternative.
2. Bet, but don't really collect
You can still bet on games, and win and lose those bets, without having any money actually change hands. If you instead keep a family ledger of outstanding "debts", it can still be clear who is winning and losing over time but the tab never needs to be closed out. Over the long run I would expect the debts to mostly cancel out, though even if that's not the case as long as the tab is not called it wouldn't really matter.
3. Make book!
This is my favorite approach. If you have studied (or are willing to study a bit of) statistics, you can organize bets and side bets between your siblings. This is more complicated than just saying "I'll bet $5 I win this game", but also allows for more interesting bets (with varied odds, conditions, etc.). Correctly assigning odds to attract bets in workable proportions means that you generally won't lose any money. If you take a margin on payouts you can even make money (though I personally would not do so in a case like this).
This would allow betting to occur to your siblings' preferences, inherently removes you from betting, and (depending on what you find interesting) may add something of interest to you in the betting process.