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And if enough people do this to effectively lower the house edge, then the casino can just stop accepting zero confirmation deposits. The fact that a lot of casinos still accept zero confirmation deposits is evidence that very few people try to scam in this manner.
Which casinos accept zero confirmation deposits? I remember reading about a Russian scammer from several years ago that did a number of things to trick casinos into accepting his unconfirmed transaction, would make a single high probability bet, would see that his deposit transaction confirms if the bet wins, and double spends the deposit transaction if his bet loses. IIRC, at one point he used non-standard transactions that miners would not confirm by default but was able to get miners to confirm by his request, and at another point would use a chain of unconfirmed transactions, whose total fee was too low for miners to confirm under normal circumstances, but was able to get one to confirm his transactions upon his request.
I fail to see how the house edge get reduced, even if it was not the topic here.
Say, for example, a gambler deposits coin to a casino, places a bet that has a 95% chance of winning. If he wins, he receives 104.21% of his bet, allows his transaction to confirm, and withdraws his entire balance. He repeats this process an additional 18 times while placing the same bet amount each time. He has received a total of 79.99% of his bet amount from the casino, plus his original bet amount. On the 20th time the gambler does this procedure, the casino informs the gambler that he lost his bet, so the gambler double spends his deposit transaction. The casino has paid out ~80% of what the gambler bet on a bet that wins 95% of the time. The casino should have won the 20th bet but did not actually receive the coin from that bet. If the casino were to sum the 20 bets the player made, it expected to receive 20% of the player's bet amount, but instead paid out a total of 80% of the player's bet amount, while the player won the expected number of bets.
To put the above in more technical terms, when a casino sets the HE at, say 1%, it will set the odds and payout so that the EV of each bet a player makes is 1% of the bet amount. In order for each bet to have this EV value, each bet placed must involve value being transferred to the winning party according to the odds and payout multiplier.