I believe rich winning more is not only about budget. Budget may influence amount of money you are winning through gambling but it will not increase how many games you are winning. In my opinion rich has very relaxed and also wise take on money so they are open to different schemes with their money. Poor people mostly worry about money they lose so gambling can be very scary for them. Rich people know it lot better in summary. Rich mindset should definitely be understood.
It seems that what you mean is that the large amount of money that rich people have has absolutely no effect on winning in gambling, or it means that it does not have a big chance to get closer to luck. Hmm yes maybe that makes a little sense with the calm situation that the rich have it is possible to make them a wise gambler in their involvement because losing is not a big deal for people who already have a lot of money so maybe it creates a pretty good luck.
As we know that gambling always involves feelings and emotions that are within and when you experience bad things there and then you can't accept it then obviously things out of control are very likely for you to do because of the inability to accept reality which of course makes you do more trials and indirectly defeat increasingly dominate because luck will not always come according to what you want and that behavior is usually done by poor people who on average come to earn. I admit that calmness is quite influential, but in my opinion it is more of a precautionary measure and not necessarily an effect on increasing the chances of winning, doesn't it make sense? because obviously for the problem of winning no matter how calm your situation is, it all depends on how lucky you are at that time.
Acknowledging the fact that the rich may possess better decision skills than the poor is fine, but not all would be able to perform well in gambling. Pierre2 in this response may have meant that due to the money the rich possess they are more relaxed while gambling than the poor. Because the rich have less reason to worry about money like a low roller would in his gambling journey. These few instances or differences are enough to justify the fact that high rollers have some advantages over low rollers. But it does not apply to all rich gamblers. In the years of gambling and reading articles relating to gambling, we've also seen some rich people who made huge losses that were enough to affect their net worth. Gamblers sold properties, just to gamble. I think the higher the bankroll of a gambler, his choices increase as well, thereby exposing him to a greater risk than the low roller. So the effect of gambling still works on everybody regardless of their monetary status.
The emotions as you mentioned, Nara, as humans we all can't escape them, that's why some rich gamblers don't control themselves too and put in more amount of money to secure a bigger reward capable of covering all their losses. However, it's certain, that gamblers who are experienced and have good strategies differ in this gambling application. One wouldn't compare an experienced high roller's wins to that of an experienced low roller's reward. This is where the changes of reward may matter, as the stakes now count. A lot of experienced rich gamblers bank lots of profits in one win, although it may not cover all their losses, it's like a nitro to keep them moving and motivate the gambler to perform better. Therefore, the rich win more in cash than the low rollers. Both parties spend money, and that may not be accounted for in this comparison. No need to look at how much money the rich person has lost or the low roller. But, once in a while, the low roller could win a big amount of money that'll be big enough to compare to the high roller's profit.